5+ Crystal Lattice Examples: Types and Facts around It

800px Snowflake Detail 300x200 1

In this article the topic of “Crystal lattice examples” will be summarize. The term pattern of crystal lattice is created by the points. Crystal lattice is use to personate the place of repeating structural substance.

5+ Crystal Lattice Examples are listed below,

Sodium chloride:-

The sodium chloride is actually an ionic mixture. For make the compound of sodium chloride the chloride and sodium is mix together in 1:1 ratio. The common name of the sodium chloride is common salt or halite, table salt.

Chemical formula for the sodium chloride is NaCl.

Properties of the Sodium Chloride:-

  1. Sodium Chloride can be easily soluble in the water. In some other liquids the sodium chloride can be insoluble or partially soluble.
  2. Sodium Chloride is white crystal.
  3. Sodium Chloride is very good quality conductor because of the movements of the free ions.
  4. Molar mass of the Sodium Chloride is 58.443 gram per mol.
  5. Density of the Sodium Chloride is 2.17 gram per cubic centimetre.
  6. Boiling point of the Sodium Chloride is 1465 degree centigrade.
  7. Melting point of the Sodium Chloride is 800.7 degree centigrade.
  8. Heat capacity of the Sodium Chloride is 50.7 joule per Kelvin mol.
  9. Solubility in water of the Sodium Chloride is 360 gram per 1000 gram pure water at the temperature of 25 degree centigrade.
  10. Solubility in ammonia of the Sodium Chloride is 21.5 gram per litre.
crystal lattice examples
Image – Crystal structure with sodium in purple and chloride in green;
Image Credit – Wikipedia

Preparation of the Sodium Chloride:-

When chloride and sodium is comes together in the ratio of 1:1 at that time the solid matter is made which is known as Sodium Chloride.

2Na(s) + Cl2(g) → 2NaCl(s)

Snowflakes:-

Snowflake is single ice crystal.  The snowflakes have sufficient size to amalgamate to each other.

800px Snowflake Detail
Image – Naturally formed snowflakes differ from one another through happenstance of formation. The characteristic six branches is related with the crystal structure of ice; Image Credit – Wikipedia

Types of the snowflakes:-

Snowflakes can be divided in eight broader groups,

  1. Plane crystal
  2. Column crystal
  3. Germs of ice crystal
  4. Combination of plane and column crystal
  5. Rimed crystal
  6. Irregular crystal
  7. Aggregation of snow crystal
  8. Other solid precipitation crystal

Sucrose:-

Another term for the sucrose is table sugar or sugar. The sucrose molecules have 11 oxygen atoms, 22 hydrogen atoms and 12 carbon atoms. 

Sucrose from xtal 3D bs 17
Image – Structure of the sucrose;
Image Credit – Wikipedia

Properties of the Sucrose:-

  1. Sucrose can be easily soluble in the water. In some other liquids the sucrose can be insoluble or partially soluble.
  2. Sucrose is white crystal.
  3. Sucrose is odour less.
  4. The taste of the sucrose is sweet.
  5. Molar mass of the sucrose is 342.30 gram per mol.
  6. Density of the sucrose is 1.587 gram per cubic centimetre.
  7. Melting point of the sucrose is 186 degree centigrade.

Diamond:-

Diamond is a rare, naturally occurring mineral composed of carbon. Each carbon atom in a diamond is surrounded by four other carbon atoms and connected to them by strong covalent bonds – the strongest type of chemical bond. This simple, uniform, tightly-bonded arrangement yields one of the most durable and versatile substances known.

It is also chemically resistant and has the highest thermal conductivity of any natural material. Diamond is the hardest known natural substance.

Rough diamond
Image – The slightly misshapen octahedral shape of this rough diamond crystal in matrix is typical of the mineral. Its lustrous faces also indicate that this crystal is from a primary deposit;
Image Credit – Wikipedia

Properties of the Diamond:-

  1. Density of the diamond is 3.5 to 3.53 gram per cubic centimetre.
  2. Melting point of the diamond is depending on the pressure.
  3. Specific gravity of the diamond is 3.52±0.01.
  4. An optical property of the diamond is isentropic.
  5. Formula mass of the diamond is 12.01 gram per mol.
  6. Colour of the diamond will be brown, gray, and yellow to colourless.

Quartz:-

In the Earth’s crust Quartz is one of the most common minerals. As a mineral name, quartz refers to a specific chemical compound having a specific crystalline form. t is found in all forms of rock: igneous, metamorphic and sedimentary. Quartz is physically and chemically resistant to weathering. When quartz-bearing rocks become weathered and eroded, the grains of resistant quartz are concentrated in the soil, in rivers, and on beaches. The white sands typically found in river beds and on beaches are usually composed mainly of quartz, with some white or pink feldspar as well.

598px Quartz Tibet
Image – Quartz;
Image Credit – Wikipedia

Properties of the Quartz:-

  1. Formula mass of the quartz is 60.083 gram per mol.
  2. Melting point of the quartz is1670 degree centigrade to 1713 degree centigrade.
  3. Quartz is brittle type.

Crystal lattice types:

The crystal lattice is classified in sever sections they are listed below,

The classification types of the crystal lattice is describe below,

Triclinic system:-

In the triclinic system the three axes are dangling at each other. In the system of the triclinic the length of the axes remains same. On the base of three dangling angles various types of crystal can make paired faces.

Examples:-

Examples of the triclinic system are listed below,

  1. Amazonite
  2. Labradorite
  3. Kyanite
  4. Rhodonote
  5. Turquoise
  6. Aventurine Feldspar

Tetragonal system:-

The tetragonal system is containing three axes. The main axis of the tetragonal system can be differing in length. The length of the axis can be longer or shorter. Other two axis of the tetragonal system stays in the same plane and the are will be at same length. Depend on the structure of the rectangular inner the shape of the tetragonal system crystal will be four sided prism, double and eight edgy pyramids, pyrite and trapezohedrons.

Monoclinic system:-

The monoclinic system is containing three axes. The two axes of the monoclinic system stay at right angle to each one and the third one axis is dangling. The three axes of the monoclinic system have different length.

The inner structure of the monoclinic system contain prism and basal pinacoids with the inclined end faces.

Examples:-

Examples of the monoclinic system are listed below,

  1. Gypsum
  2. Diopside
  3. Howlite
  4. Hiddenite
  5. Vivianite
  6. Petalite

Hexagonal system:-

The hexagonal system is containing three axes. Among the four axes the three axes are stays in the similar plane and the fourth one is stays in plane. The axes of the hexagonal system are intersecting to each other at the angle of sixty degree. In the hexagonal system the crystal shape will be based on the inner structure such as four sided pyramid, double sided pyramid, double pyramid,

Examples:-

Examples of the hexagonal system are listed below,

  1. Apatite
  2. Cancrinite
  3. Beryl
  4. Sugilite

Orthorhombic system:-

The systems of the orthorhombic have three axes. The axes of the orthorhombic system intersect at the right angles to every with other. The length of the axe will be different to each other. In the orthorhombic system the crystal shape will be based on the rhombic structure such as double pyramid, pyramid, pinacoids, and rhombic pyramid.

Examples:-

Examples of the orthorhombic system are listed below,

  • Lolite
  • Tanzanite
  • Topaz
  • Zoisite

Trigonal system:-

In the system of the trigonal the axis and angels are similar to hexagonal system. In the system of the trigonal have three sides and in the system of the hexagonal have six sides. In the trigonal system the crystal shape will be based on the inner structure such as rhombohedra, scalenohedral and three sided pyramid.

Examples:-

Examples of the trigonal system are listed below,

  • Calcite
  • Agate
  • Ruby
  • Tiger’s eyes
  • Jasper
  • Quartz

Cubic system:-

In the system of the cubic the three angles are intersect with the right angles. The are will be in same length. In the cubic system the crystal shape will be based on the inner structure such as cube, octahedron, hexaciscoherdron.

Examples:-

Examples of the cubic system are listed below,

  1. Gold
  2. Silver
  3. Diamond
  4. Garnet

Laminar Flow in Pipe: What, How, Conditions, Different Factors, Different Types

Laminar flow 300x87 1

In this article the term “Laminar flow in pipe” and laminar flow in pipe related several facts will be discussed. Streamline flow is another term for the laminar flow.

Laminar flow in pipe or stream line in pipe can be describe as in this way, when a fluid is flow inside a tube or pipe in a motion that time there is no breakdown is present between the layers. In the low velocity the fluid can flow very smoothly without any transverse mixing.

What is laminar flow in pipe?

Laminar flow in pipe can be characterized by highly ordered motion and smooth streamline. The laminar flow in pipe fluid is flow uniformly in both direction and velocity.

The laminar flow in a pipe can be deriving as,

  1. If the range of the Reynolds number is 2000 and less than 2000 then this flow of fluid is known as laminar flow.
  2. Mathematical analysis of the laminar flow is not complicated.
  3. Velocity of the laminar flow is very low for this reason the flow of the fluid is fluid very smoothly without any transverse mixing.
  4. Regular movement can be observe in the fluids which in laminar flow and flow in a motion.
  5. Laminar flow in generally rare type of flow of fluid.
  6. Average motion can observe in which side the fluid is flowing.
  7. In the laminar flow the velocity profile is very less in the center section of the tube.
  8. In the laminar flow the velocity profile is high in the wall of the tube.
laminar flow in pipe
Image – In the case of a moving plate in a liquid, it is found that there is a layer (lamina) that moves with the plate, and a layer of stationary liquid next to any stationary plate;
Image Credit – Wikipedia

Laminar flow in pipe formula:

With the help of Poiseuille’s equation we can understand the pressure drop of a flowing fluid is happened for the viscosity. The equation of Hegen Poiseuille’s is applicable for Newtonian fluid and incompressible fluid.

The equation of Hegen Poiseuille’s is not applicable for close entrance of the pipe. The equation of laminar flow is,

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Where,

Δp = The amount of difference of pressure which is occur in the two end points of the pipe

μ = The dynamic viscosity of the flowing fluid in the pipe

 L = Length of the pipe

Q = Volumetric flow rate

R = Radius of the pipe

A = Cross sectional area of the pipe

The above equation is not appropriate for very short or very long pipe and also for low viscosity fluid. In very short or very long pipe and also for low viscosity fluid turbulent flow is causes, for that that time the equation of Hegen Poiseuille’s is not applicable. In that case we applied more useful equation for calculation such as Darcy – Weisbach equation.

The ratio between from length to radius of a tube is more than the one forty eighth of Reynolds number which is valid for the law of Hegen Poiseuille’s. When the tube is very short that time the law of Hegen Poiseuille’s can be result as high flow rate unphysical.

The flow of the fluid is restricted by the principle of Bernoulli’s under excepting restrictive condition just because of pressure is not can be less than zero in an flow of incompressible.

Δ p = 1/2ρ v-2

Δ p = 1/2ρ(Qmax/π R2}2)

gif

Laminar flow in pipe derivation:

The equation of laminar flow is,

gif

Where in,

The Pressure Gradient (\Delta P):-

The pressure differential between the two ends of the tube, defined by the fact that every fluid will always flow from the high pressure to the low-pressure area.

The flow rate is calculated by the 

Δ P = P1 – P2

The radius of the narrow tube:-

The flow of liquid direct changes with the radius to the power four.

Viscosity (η):-

The flow rate of the fluid is inversely proportional to the viscosity of the fluid.

Length of the arrow tube (L):-

The flow rate of the fluid is inversely proportional to the length of the narrow tube.

Resistance(R):-

The resistance is calculated by 8Ln/πr4 and hence the Poiseuille’s law is

Q = (Δ P) R

Heat transfer in pipe flow:

The equation of thermal energy convection-diffusion is given below,

The left-hand side equation is consider convective heat transfer, which transferred by the fluid’s motion. The radial velocity is zero, so the first term equation of the left-hand side can be avoided.

The right-hand side of the equation is representing the thermal diffusion. Since the flow is laminar, we can assume that the dimensionless Eckert number, which represents the ratio between a flow’s kinetic energy and its heat transfer driving force, is small enough to disregard viscous dissipation.

Therefore, the thermal energy equation can be supplemented with the velocity profile defined in the previous section.

A constant heat flux value condition implies that the temperature difference between the wall and the fluid is equal. However we already know that the temperature of the fluid is of non-constant value within the pipe. Therefore, we shall introduce a bulk mean temperature denoted by:

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Assuming that the local temperature gradient and the bulk mean temperature gradient in the streamwise direction are equal and of constant value, integration of the aforementioned thermal energy transport equation results in the following formula for radial temperature distribution:

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Where, a = k/ρc is the thermal diffusivity coefficient . The mean temperature gradient can be obtained by applying the desired volumetric flow rate Q and heat flux q to the heat conservation equation:

Qρc dTm/dz = πDq

To satisfy the constant wall flux condition, the value of the wall temperature has been coupled with the bulk mean temperature gradient.

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Laminar flow in pipe boundary conditions:

Laminar boundary layers are appear when a moving viscous fluid is comes in the touch with a surface which is state in solid and the boundary layer, a layers of rotational fluid forms in response to the action of no slip boundary and viscosity condition of the surface.

Reynolds number for laminar flow in pipe:

The values for the laminar flow for the particular determination of Reynolds number is depend on the pattern of the flow of the fluid through a pipe and geometry of the system through which fluid is flow.

The expression for the Reynolds number for laminar flow in pipe is given below,

Re = ρuDH/μ = u DH/ν = QDH/νA

Where,

Re = Reynolds number

ρ = Fluid density of the pipe and unit is kilogram per cubic meter

u = The mean speed of the flowing fluid in the pipe and unit is meter per second

μ = The dynamic viscosity of the flowing fluid in the pipe and unit is kilogram per meter second

A = Cross sectional area of the pipe and unit is meter square

Q = Volumetric flow rate and unit is cubic meter per second

DH = Hydraulic diameter of the pipe through which fluid is flowing and unit is meter

ν = The kinematic viscosity of the flowing fluid in the pipe and unit is meter square per second

The expression of ν is,

ν = μ/ρ

Laminar flow in pipe
Image – A sphere in Stokes flow, at very low Reynolds number. An object moving through a fluid experiences a drag force in the direction opposite to its motion;
Image Credit – Wikipedia

Nusselt number for laminar flow in pipe:

When internal laminar flow is fully developed in that case, Nusselt number for laminar flow in pipe can be express as,

Nu = hDh/kf

Where,

Nu = Nusselt number

h = Convective heat transfer coefficient

Dh = Hydraulic diameter of the pipe through which fluid is flowing

kf = Thermal conductivity for flowing fluid in the pipe

Friction factor for laminar flow in pipe:

Friction factor for the laminar flow can be express as,

fD = 64/Re

Where,

fD = Friction factor

Re = Reynolds number

gif

Where,

ν = The kinematic viscosity of the flowing fluid in the pipe and unit is meter square per second

μ = The dynamic viscosity of the flowing fluid in the pipe and unit is kilogram per meter second

ρ= Fluid density of the pipe and unit is kilogram per cubic meter

v = Mean flow velocity and unit is meters per second

D = Diameter of the pipe through which fluid is flowing and unit is meter

ν = μ/ρ

Fully developed laminar flow in pipe:

Fully developed flow is appearing when the viscous effects are happened for the shear stress by the fluid particles and tube wall create a fully developed velocity profile. 

For this to appear the fluid must go through a length of a straight tube. The velocity of the fluid for a fully developed flow will be at its fastest at the centre line of the tube (equation 1 laminar flow).

The velocity of the fluid at the walls of the pipe will theoretically be zero.

The fluid velocity can be expressed as an average velocity.

vc = 2Q/πR2……eqn (1)

The viscous effects are caused by the shear stress between the fluid and the pipe wall. In addition, shear stress will always be present regardless of how smooth the pipe wall is. Also, the shear stress between the fluid particles is a product of the wall shear stress and the distance the molecules is from the wall. To calculate shear stress use equation 2.

gif

Due to the shear stress on the fluid particles, a pressure drop will occur.  To calculate the pressure drop use equation 3.

P2 = P1 – Δ P…… eqn (3)

Finally, the viscous effects, pressure drop, and pipe length will affect the flow rate. To calculate the average flow rate, we need to use equation 4. 

This equation can only applies to laminar flow.

Q = πD4ΔP/128μ L…… eqn (4)

Laminar flow in circular pipe:

In a circular pipe from where fluid is flow in laminar the diameter is express as D_c, for that case the friction factor of the flow is inversely proportional to the Reynolds number by which we can easily published or measured physical parameter.

Taking the help of Darcy – Weisbach equation laminar flow in circular pipe can be express as,

Δp/L = 128/π = μQ/D4c

Where,

Δp = The amount of difference of pressure which is occur in the two end points of the pipe

L = Length of the pipe through which fluid is flow

μ = The dynamic viscosity of the flowing fluid in the pipe

Q = Volumetric flow rate of the flowing fluid in the pipe

Instead of mean velocity the flowing fluid in the pipe volumetric flow rate can be used and its expression is given below,

gif

Dc = Diameter of the pipe through which fluid is flowing

Laminar flow in a cylindrical pipe:

The cylindrical pipe which one contain flowing full, uniform diameter express as D, the loss of pressure for the viscous effects express as \Delta p is directly proportional to the length.

Laminar flow in a cylindrical pipe can be taking the help of Darcy – Weisbach equation is given below,

Where,

Δp = The amount of difference of pressure which is occur in the two end points of the pipe

L = Length of the pipe through which fluid is flow

fD = Darcy friction factor

ρ = Fluid density of the pipe

<v> = Mean flow velocity

DH = Hydraulic diameter of the pipe through which fluid is flowing

Laminar flow in a pipe velocity profile:

Laminar flow is appearing at very low velocities, under a threshold at that point the flow of the fluid is became turbulent.

The pipe velocity profile for laminar flow can be determined using the Reynolds number. The pipe velocity profile for laminar flow is also depending on the density and viscosity of the flowing fluid and dimensions of the channel.

gif

Where,

Re = Reynolds number

ρ = Fluid density of the pipe and unit is kilogram per cubic meter

u = The mean speed of the flowing fluid in the pipe and unit is meter per second

μ = The dynamic viscosity of the flowing fluid in the pipe and unit is kilogram per meter second

A = Cross sectional area of the pipe and unit is meter square

Q = Volumetric flow rate and unit is cubic meter per second

DH = Hydraulic diameter of the pipe through which fluid is flowing and unit is meter

ν = The kinematic viscosity of the flowing fluid in the pipe and unit is meter square per second

The expression of ν is,

ν = μ/ρ

Laminar flow in vertical pipe:

Flowing of fluid in laminar in vertical pipe is given below,

Laminar flow profile 1
Image – The velocity profile associated with laminar flow resembles a deck of cards. This flow profile of a fluid in a pipe shows that the fluid acts in layers that slide over one another;
Image Credit – Wikipedia

Laminar flow in rough pipe:

The pressure drop in a fully developed laminar flow through pipe is proportional to mean velocity or average velocity in pipe. In laminar flow, the friction factor is independent of roughness because boundary layer covers the roughness.

9+ Boiling Characteristics: Detailed facts

boiling characteristics 0

The term “Boiling characteristics” and boiling characteristics related conditions will be prate in this article. Boiling is a very quick vaporization condition for any liquid substance when it reaches to boiling point.

10+ Boiling Characteristics in a mini channel is listed below,

Specific heat:-

Specific heat can be deriving as; the amount of heat is needed to raise the temperature of one gram of a matter by one Celsius degree. The units of the specific heat are such as calories or joules per gram per Celsius degree.

Specific heat is also known as massic heat capacity. As an example, the specific heat of water is 1 calorie (or 4.186 joules) per gram per Celsius degree.

Formula:-

The formula for the specific heat is,

gif

Where,

Q = Heat energy is absorbed by a substance

m = Mass of a substance

c = Specific heat capacity of a matter which is depend upon the material of the matter

ΔT= Change in temperature

boiling characteristics
Image – Graph of temperature of phases of water heated from −100 °C to 200 °C – the dashed line example shows that melting and heating 1 kg of ice at −50 °C to water at 40 °C needs 600 kJ;
Image Credit – Wikipedia

Cross sectional area:-

The term cross sectional area in geometry is defined as; the shape is carry by the intersection of the surface of a solid substance. The cross sectional area is present in three dimensional shape is a two dimensional shape of the geometry. In other way cross sectional area is that, the shape is can get through cutting rigid parallel to the foundation.

Types of cross sectional area:-

The cross sectional area can be classified in two sections,

Vertical cross sectional area

Horizontal cross sectional area

Grafico 3d x2xyy2
Image – A graph of z = x2 + xy + y2. For the partial derivative at (1, 1, 3) that leaves y constant, the corresponding tangent line is parallel to the xz-plane;
Image Credit – Wikipedia

Temperature:-

For a material temperature represent a physical quantity which helps to understand the state of the matter. Temperature can measure with the help of thermometer. In body temperature and heat both are not same physical parameter.

The physical parameters which are affect temperature such as, thermal conductivity, strength, corrosion, solubility, density vapour pressure and many more.

When the temperature is increases that time the boiling of a matter is also increases and if the temperature is decreases that time the boiling of a matter is also a decrease.

Thermally Agitated Molecule
Image – Thermal vibration of a segment of protein alpha helix, with its amplitude  increases with temperature;
Image Credit – Wikipedia

Volumetric flow rate:-

In the field of engineering and physics volumetric flow rate is widely used. Another form of the volumetric flow rate is fluid flow rate or volume flow rate.

Inside of a pipe or a channel, the volume of the liquid substance is moving through a cross sectional area of the pipe or channel in a particular fixed time period at some standard condition where the temperature and pressure is remains unchanged.

In another word we could express that, the volumetric flow rate is the ratio between the changes of volume with the change in time.

Formula:-

The formula of the volumetric flow rate in piping system is,

Volumetric flow rate = (Flow velocity of the liquid substance) *(Cross sectional area of a pipe or a channel)

The mathematically form of the volumetric flow rate of the piping system is,

Q = vA

Where,

Q = Volumetric flow rate of a liquid substance

V = Velocity of a liquid substance

A = Cross sectional area through which fluid is flow by a open system

FlowRate gv52
Image – Volumetric flow rate; Image Credit – Wikimedia Commons

Mass flow rate:-

Mass flow rate can be defined as the molecules present in the liquid substance are flow through in a given cross sectional area in a fixed time period at standard condition.

Formula:-

The formula of mass flow rate is,

Mass flow rate = (Density of the fluid)* (Velocity of the liquid)* (Cross sectional area)

The mathematical form of the mass flow rate is, ṁ = dm/dt

Where,

ṁ= Rate of the mass flow for the fluid substance

dm = Change in mass

dt = Change in time

Thermal conductivity:-

Thermal conductivity states that the rate at which heat is transferred through a given material is proportional to the negative value of the temperature gradient. And it is also proportional to the area through which the heat flows, but inversely proportional to the distance between the two isothermal planes.

The formula for the thermal conductivity is,

K = Qd/AΔT

Where,

K = Thermal conductivity of a matter and unit is Watt m-1K-1

Q = The net quantity of heat transfer by a material and unit is Watts or Joules/second

d = Distance by the two planes which are isothermal

A = Area of the surface and unit is square meters

ΔT= Temperature difference and unit is Kelvin

Simple definition of thermal conductivity 1
Image – Thermal conductivity can be defined in terms of the heat flow q across a temperature difference;
Image Credit – Wikipedia

Heat transfer coefficient:-

Heat transfer coefficient can be deriving as, the amount of heat can be passes through in a system per unit area in a fixed time period. For this reason the space in added in the equation of heat transfer coefficient which is express the space over which the total amount of heat transfer of heat included.

The overall rate of the heat transfer for mixed modes can be express as in the form of an overall heat transfer coefficient or overall conductance. In this case the rate heat transfer can be express as below expression,

= hA(T2-T1)

Where,

= Heat transfer rate

h = Heat transfer coefficient and unit is watt per square meter Kelvin

A = Area of the surface through which heat transfer is happened and unit is square meter

T2= Surrounding fluid temperature and unit is Kelvin

T1= Solid surface temperature and unit is Kelvin

Formula:-

The general equation for the heat transfer coefficient is given below,

h = q/ ΔT

Where,

h = Heat transfer coefficient and unit is watt per square meter Kelvin

q = Heat flux and unit is Watt per square meter

Thermal power through unit area express as, q = dQ̇/dA

ΔT= The temperature difference by the surrounding area of the fluid and surface of the solid and unit is Kelvin

Heat flux:-

The term heat flux has both magnitude and direction for this reason heat flux is a scale of vector. The S.I. unit of the heat flux is watts per square metre.

The heat flux or thermal flux can be derive as, the amount of heat flow density, rate of heat flow intensity or heat flux density is a expression of flow of energy of a particular space in a fixed time.

Law of Fourier’s in one dimension:-

The total heat flux can be determined from Fourier’s law. Most of the matter which is stays in solid heat is transfer from one space to another space by convection method.

Formula:-

Mathematical form of law of Fourier’s in one dimension is given below,

φq = -K (dT(x)/dx)

Where,

k = Thermal conductivity

In the equation the negative sign represent that flow of the heat direction is from lower side to higher side.

Heat Flux from Temperature Differential Across Thermal Insulation 1
Image – Diagram depicting heat flux through a thermal insulation material with thermal conductivity, k, and thickness, x. Heat flux can be determined using two surface temperature measurements on either side of the material using temperature sensors if k and x of the material are also known;
Image Credit – Wikipedia

Density:-

The density of a matter can be derive as, the mass contain of the matter per unit volume. The symbol is used to express the density for a matter is \\rho.

Formula:-

The formula of the density of the fluid is below,

ρ = m/v

Where,

ρ= Density of a fluid

m = Mass of a fluid

v = Volume of a fluid

From the law of conversion of mass we get a clear concept about the density of fluid. The conversion of mass flow rates states that, the amount of the mass of a particular object cannot not be created or destroyed. The mass of a body is measured by lever balance.

Artsy density column 1
Image – A graduated cylinder  containing various non- miscible colored liquids with different densities;
Image Credit – Wikipedia

Pressure drop:-

The term pressure drop can be explain as, the dissimilation in net pressure between two points which are carried by a fluid as network. The pressure drop is appear when the frictional force is appear for the reason of resistance to flow, which is act as a fluid that it flow in a motion inside a pipe.

The pressure drop and flow rate of the fluid is dependent to each other. The pressure drop and flow rate of the fluid is directly proportional to each other means when the amount of flow rate of a fluid is increases that time the amount of pressure drop is also increases and the amount of flow rate of a fluid is decreases that time the amount of pressure drop is also decreases.

Forced Convection Heat Transfer

forced convection heat transfer 0

In this article “Forced convection heat transfer” term and forced convection heat transfer related facts will be prate in a brief manner. Forced convection heat transfer uses in pump, ceiling fan, suction device.

Forced convection heat transfer is a term that is a classification of transport or forced convection heat transfer is a mechanism which helps to produce motion of a flowing fluid by applying force from externally. Almost in everywhere forced convection heat transfer is used such as steam turbine, central heating and many more.

What is forced convection heat transfer?

Alongside thermal conduction, natural convection and thermal convection is are the classification of transferring the heat and also allow to sufficient quantity of heat energy should be transform without any hassle.

Forced convection heat transfer is actually a very special classification of heat transfer. By the help of forced convection heat transfer a fluid is impression to move from one are to another area by applying force from outer side. In this case the amount of heat transfer is an increase for this it’s another term is Heat Rises.

Forced convection heat transfer equation:

When potentially mixed convection is analyze in that case the physical parameter known as Archimedes Number.

In the Archimedes Number two conditions are involves forced convection and free of relative strength. Forced convection heat transfer equation is given below,

Ar = Gr/Re2

Where,

Ar = Archimedes Number

Gr = Grashof Number

Re = Reynolds Number

By the help of Grashof number buoyancy force is express and by the help of Reynolds number inertia force is express. So, from the forced convection heat transfer equation it is clear that Archimedes Number also means ration of Grashof number and square of Reynolds number.

When the value of Ar < < 1 then its represent forced convection heat transfer equation.

The another physical parameter to express forced convection heat transfer is Peclet number. Peclet number is ratio of movement by current means advection and movement from higher to lower concentration means diffusion.

Pe = UL/α

When the value of Pe > > 1 means advection dominates diffusion.

When the value of Pe < < 1 means diffusion dominates advection.

forced convection heat transfer
Image – Forced convection by a fan in a snow machine;
Image Credit – Wikipedia

Forced convection heat transfer coefficient:

The equation of the forced convection heat transfer coefficient is discuss below,

Forced convection heat transfer coefficient in internal flow and laminar flow:-

Tate and Sieder give a concept of correlation to account for laminar flor in entrance effect.

A forced convection heat transfer coefficient in internal flow and laminar flow can be express as,

NuD = 1.86 (Re . Pr)1/3 (D/L)1/3bw})0.14

Where,

D = Internal diameter

μb = Fluid viscosity of bulk mean temperature

μw= Fluid viscosity at the wall temperature of the pipe

NuD= Nusselt number

Re =  Reynolds Number

Pr = Prandtl number

L = Length of the tube

When laminar flow is fully developed in that case Nusselt number stays at constant and value of the Nusselt number will be 3.66. In that case the forced convection heat transfer coefficient in internal flow and laminar flow can be express as,

Nu_D = 3.66 + (0.065 x Re x Pr x D/L)/(1 + 0.04 x (Re x Pr x D/L)2/3

Forced convection heat transfer coefficient in internal flow and turbulent flow:-

When in a circular tube fluid is flowing in that case Reynolds number stays at the range between 10,000 to 12,000 and Prandtl number stays at the range between 0.7 to 120. Forced convection heat transfer coefficient in internal flow and turbulent flow can be written as,

hd/k = (0.023 jd/μ)0.8 (μ cp/k)n

Where,

d = Hydraulic diameter

μ = Fluid viscosity

k = Thermal conductivity for the bulk fluid

cp = Isobaric heat capacity for the fluid substance

j = Mass flux

n = 0.4 for hotter wall than the bulk fluid and 0.33 for cooler wall than the bulk fluid

How forced convection does affect heat transfer?

The most advantage of the forced convection heat transfer than the free convection heat transfer is to able increasing more amount of heat transfer.

By the help of forced convection heat transfer the amount of heat transfer can be increases by the help of force exerted by outer side. The relations between the forced convection heat transfer and heat transfers is directly proportional. Increasing the forced convection the heat transfer of the system source also increases.

What affects Convective heat transfer coefficient?

The convective heat transfer coefficient is depending on some factors. They are listed below,

Fluid velocity:-

Fluid velocity or flow velocity is a vector field. By the help of fluid velocity motion of a flowing fluid can be determine in the mathematical form. The total amount of length of the fluid velocity is determined as fluid speed. Flow velocity in fluids is the vector field that provides the velocity of fluids at a certain time and position.

The formula of the fluid velocity is given below,

Q = vA

Where,

Q = Volumetric flow rate of the liquid substance

V = Velocity of the liquid substance

A = Cross sectional area of the open system

Density of the fluid:-

From the law of conversion of mass we get a clear concept about the density of fluid. The conversion of mass flow rates states that, the amount of the mass of a particular object cannot not be created or destroyed. The mass of a body is measured by lever balance.

Density of fluid can be defined as the, an object which is containing mass is constant at standard temperature and pressure.

The formula of the density of the fluid is given below,

ρ = m/v

Where,

ρ = Density of the fluid

m = Mass of the fluid

v = Volume of the fluid

The S.I. unit of the density of the fluid is kilogram per cubic meter

Artsy density column
Image – A graduated cylinder containing various non – miscible various  colored liquids with different densities;
Image Credit – Wikipedia

Thermal conductivity:-

Thermal conductivity states that the rate at which heat is transferred through a given material is proportional to the negative value of the temperature gradient. And it is also proportional to the area through which the heat flows, but inversely proportional to the distance between the two isothermal planes.

The formula of the thermal conductivity is given below,

K = Qd/AΔT

Where,

K = Thermal conductivity and unit is

Q = The quantity of heat transfer unit is Joules/second or Watts

d = Distance by the two planes of the isothermal unit is  

A = Area of the surface unit is square meters

ΔT = Temperature difference unit is Kelvin

Simple definition of thermal conductivity
Image – Thermal conductivity can be defined in terms of the heat flow q across a temperature difference;
Image Credit – Wikipedia

Dynamic viscosity of the fluid:-

Dynamic viscosity of the fluid can be deriving as the ration between the shear stress to the shear strain. The unit of the dynamic viscosity of the fluid is Pascal. By the help of dynamic we can easily understand which product how much thick and how can the fluid can flow in a motion means by the help of viscosity we can recognize the behaviour of the fluid.

The formula of the dynamic viscosity of the fluid is given below,

η = T/γ

Where,

η = Dynamic viscosity of the fluid

T = Shearing stress

γ= Shear rate

Viscosities 1
Image – A simulation of liquids with different viscosities. The liquid on the left has lower viscosity than the liquid on the right;
Image Credit – Wikipedia

Specific heat:-

Specific heat can be deriving as; the amount of heat is needed to raise the temperature of one gram of a matter by one Celsius degree. The units of the specific heat are such as calories or joules per gram per Celsius degree.

Specific heat is also known as massic heat capacity. As an example, the specific heat of water is 1 calorie (or 4.186 joules) per gram per Celsius degree.

The formula of the specific heat of the fluid is given below,

Q = mcΔ T

Where,

Q = Heat energy

m = Mass of the fluid

c = Specific heat capacity

ΔT= Change in temperature

Water temperature vs heat added.svg
Image – Graph of temperature of phases of water heated from −100 °C to 200 °C – the dashed line example shows that melting and heating 1 kg of ice at −50 °C to water at 40 °C needs 600 kJ;
Image Credit – Wikipedia

How to find convective heat transfer coefficient for air?

Common units which are used to measure the Convective heat transfer coefficient for air is listed below,

  1. 1 W/(m2K) = 0.85984 kcal/(h m20 C) = 0.1761 Btu/(ft2 h 0 F)
  2. 1 kcal/(h m20 C) = 1.163 W/(m2K) = 0.205 Btu/(ft2 h 0 F)
  3. Btu/hr – ft2 -0 F = 5.678 W/(m2K) = 4.882 kcal/(h m20 C)

Forced convection heat transfer through a pipe:

When in a circular tube fluid is flowing in that case Reynolds number stays at the range between 10,000 to 12,000 and Prandtl number stays at the range between 0.7 to 120.

Forced convection heat transfer coefficient in internal flow and turbulent flow can be written as,

hd/k = 0.023 (jd/μ)0.8 (μ cp/k)n

Where,

d = Hydraulic diameter

μ= Fluid viscosity

k = Thermal conductivity for the bulk fluid

cp = Isobaric heat capacity for the fluid substance

j = Mass flux

n = 0.4 for hotter wall than the bulk fluid and 0.33 for cooler wall than the bulk fluid

The properties of the flowing fluid are need for the application in the method of the equation and can be calculated at bulk temperature for this reason iteration can be avoided.

Application of forced convection heat transfer:

The Application of forced convection heat transfer is listed below,

  1. Heat removal
  2. Heat sink simulation
  3. Thermal optimization
  4. Heat sensitivity studies
  5. Electric fan simulation
  6. Computer case cooling
  7. Cooling system design
  8. Heating system design
  9. Fan cooled central possessing unit
  10. Water cooled central possessing unit
  11. Printed circuit board simulation

Forced convection heat transfer examples:

Examples of the forced convection heat transfer is listed below,

  1. Air conditioning system
  2. Convection oven
  3. Pump
  4. Suction device
  5. Ceiling fan
  6. Hot air balloon
  7. Refrigerator
  8. Car radiators

Difference between free and forced convection heat transfer:

The major difference points between free and forced convection heat transfer is given below,

ParameterFree convection heat transferForced convection heat transfer
DefinitionFree convection heat transfer is appearing for density difference between the higher temperature fluid and lower temperature fluid.By the help of forced convection heat transfer a fluid is impression to move from one are to another area by applying force from outer side
Application1. Heat exchanger
2. Gas turbine blades
3. Solar water heater
4. Nuclear reactor design
5. Aircraft cabin insulation
1. Air conditioning system
2. Pump
3. Suction device
4. Ceiling fan  
Heat transfer rateHeat transfer rate for free convection heat transfer lowHeat transfer rate for forced convection heat transfer high
External equipmentNot neededNeeded
Motion of particlesSlowMove faster
Equipment sizeThe size of equipment used in the free convection heat transfer is larger.The size of equipment used in the forced convection heat transfer is smaller.
Flow of moleculesNot controlledControlled
Heat transfer coefficientLessHigh
Movement of the moleculesFor the reason of temperature and density difference free convection heat transfer work.For the reason of exerted force apply forced convection heat transfer work.

How does forced convection heat transfer work?

Forced convection heat transfer work when the area of the gaseous substance or liquid substance is facing higher temperature or lower temperature comparative to greater than their neighbouring temperature and causes a difference between the system temperature and neighbouring temperature.

The temperature gap causes the spaces to move as the higher temperature less dense space rise, and the lower temperature more dense space sink.

Heat Exchanger Efficiency: What, Formula, How to Calculate Different Heat Exchanger Efficiency, FAQs

450px Shell and Tube Heat Exchanger of Chiller 225x300 1

The concept of “Heat exchanger efficiency” with heat exchanger efficiency related several facts will be summarize. Depending on the performance of the ideal system heat exchanger efficiency will be determined.

The term of  Heat exchanger efficiency can be explain as the relationship between the amount of heat which is transfer in the physical heat exchanger to the  amount of heat which is transfer in the ideal heat exchanger. With the help of heat exchanger efficiency we can analysis and design of the heat exchanger.

What is heat exchanger efficiency?

The process of heat exchanger is happened between two fluids which are containing different temperature and the fluids can be classified by any solid wall or the fluids can be touched position to each other.

The term of heat exchanger efficiency explain as, the proportion between the quantity of heat transfer through heat exchanger that is the actual one which one works as a input of the system and the quantity of heat transfer through heat exchanger that is the practical one which one works as a out of the system.

The term heat exchanger efficiency can be written as,

η = Qact/Qideal

Where,

η = Heat exchanger efficiency

Qact = The amount of heat which is transfer in the physical heat exchanger

Qideal = The amount of heat which is transfer in the ideal heat exchanger

Heat exchanger efficiency formula:

The formula of the heat exchanger efficiency is given below,

Q̇ = UA ΔT

Where,

Q̇= The amount of heat flow through the heat exchangers and its unit is Watt

U = Heat transfer coefficient and its unit is Watt per meter square degree centigrade

A = The area from where heat is floe and its unit is square meter

ΔT= Temperature difference and its unit is Kelvin.

heat exchanger efficiency
Image – Partial view into inlet plenum of shell and tube heat exchanger of a refrigerant based chiller for providing air-conditioning to a building;
Image Credit – Wikipedia

How to calculate heat exchanger efficiency?

For the system of heat exchanger the efficiency can be calculating by comparing the factors of actual performance with practical performance.

Heat exchanger efficiency = Actual output / Output of the practical system ….eqn (1)

But where the practical heat exchanger is not available for that case eqn (1) is not applicable. In that case we can use the product of heat transfer coefficient and the surface area from where the heat is flowing which is express as UA to express the best rate of the heat transfer that can be easily can get by the given process condition ΔT. So, the equation we are used in that case is given below,

Q = UA(FΔTLM) ….eqn (2)

Where,

Q = The amount of heat flow through the heat exchangers and its unit is Watt

U = Heat transfer coefficient and its unit is Watt per meter square degree centigrade

A = The area from where heat is floe and its unit is square meter

FΔTLM = Log mean temperature difference and its unit is Kelvin

The LMTD approach is applied when input and output temperature is given but the size of the heat exchanger is not selected. The alternative approach for the LMTD the thermal effectiveness method is applied which is calculating the practical world heat transfer amount and the inside of a heat exchanger heat transfer amount. The expression is given below,

E = Q/Qmax ...eqn (3)

Typical heat exchanger efficiency:

The term typical heat exchanger efficiency explain as, the relationship between the amount of heat which is transfer in the physical heat exchanger to the  amount of heat which is transfer in the ideal heat exchanger is gives the flow rate near about 90 percentage.

Typical heat exchanger efficiency value is more than the shell and tube, spiral, kettle and tubular heat exchanger.

How to improve heat exchanger efficiency?

Improving the efficiency of heat exchanger is given below,

  1. Online cleaning
  2. Offline
  3. Periodic cleaning
  4. Maintaining heat exchanger
  5. Cleaning of the PHE manually

Online cleaning:-

Online cleaning helps to prevent the scaling and fouling without interrupting the operation of the heat exchanger or without stopping the operation of the heat exchanger. Online cleaning including the basket, brush and ball type system. Online cleaning treat a chemical conjunction arrangement and standalone approach.

Offline:-

The offline cleaning another name is pigging. Offline cleaning is very useful to improve the efficiency of heat exchanger. In this process a equipment which is use looks like a bullet which is placed in every tube of the heat exchanger and pushed down with air high pressure. Chemical cleaning, hydro lancing and hydro blasting are common methods to use offline cleaning.

Periodic cleaning:-

The most useful methods to clean the dirt and debris from the heat exchanger are periodic cleaning. After a certain time lots of unwanted dirt will gather into the system which decreases the working efficiency thus after a time periodic cleaning is very essential.

Maintaining heat exchanger:-

To boost the efficiency of the heat exchanger regular maintenance is very important. The maintaining of heat exchanger helps to prevent blockage, leakage and fouling of the system.

Cleaning of the PHE manually:-

Manual cleaning is important to follow the instruction of the manufacturer’s. When PHE is installed when prefer to clean the plates of the system without isolate them from the frame of the system.

How to calculate plate heat exchanger efficiency?

For the system of heat exchanger the efficiency can be calculating by comparing the factors of actual performance with practical performance.

Heat exchanger efficiency = Actual output / Output of the practical system ….eqn (1)

But where the practical heat exchanger is not available for that case eqn (1) is not applicable. In that case we can use the product of heat transfer coefficient and the surface area from where the heat is flowing which is express as UA to express the best rate of the heat transfer that can be easily can get by the given process condition ΔT. So, the equation we are used in that case is given below,

Q = UA(FΔTLM) ….eqn (2)

Where,

Q = The amount of heat flow through the heat exchangers and its unit is Watt

U = Heat transfer coefficient and its unit is Watt per meter square degree centigrade

A = The area from where heat is floe and its unit is square meter

FΔTLM = Log mean temperature difference and its unit is Kelvin

The LMTD approach is applied when input and output temperature is given but the size of the heat exchanger is not selected. The alternative approach for the LMTD the thermal effectiveness method is applied which is calculating the practical world heat transfer amount and the inside of a heat exchanger heat transfer amount. The expression is given below,

E = Q/Qmax …eqn (3)

How to improve efficiency of plate heat exchanger?

The way the improve efficiency of plate heat exchanger is listed below,

  1. Reduce the thickness of the plate
  2. Plate should be choose
  3. Decreasing the thermal resistance

Reduce the thickness of the plate:-

The design of the plate thickness is not depend on the corrosion resistance. The plate design thickness is depending on the pressure bearing capacity. The plate thickness the heat exchanger can be increases by the pressure bearing capacity.

Plate should be choosing:-

Choosing the plate for the heat exchanger plays a very role. The materials which have thermal conductivity such as copper alloy, stainless steel, titanium steel are selected. The thermal conductivity for the stainless steel is about 14.4 watt per meter Kelvin.

Decreasing the thermal resistance:-

The thermal resistance is of heat exchanger of fouling layer is reduce just because of to avoid scaling from the plate. The fouling thickness is when about 1 mm that time the amount of heat transfer coefficient is reduces about 10 percentages. For this reason it is important to control the quantity of water on the both portions of the heat exchanger.

800px PHE Trieste 013
Image – An interchangeable plate heat exchanger directly applied to the system of a swimming pool;
Image Credit – Wikipedia

How to calculate shell and tube heat exchanger efficiency?

For the system of heat exchanger the efficiency can be calculating by comparing the factors of actual performance with practical performance.

Heat exchanger efficiency = Actual output / Output of the practical system ….eqn (1)

But where the practical heat exchanger is not available for that case eqn (1) is not applicable.

So, the equation we are used in that case is given below,

Q = UA(FΔTLM) ….eqn (2)

Where,

Q = The amount of heat flow through the heat exchangers and its unit is Watt

U = Heat transfer coefficient and its unit is Watt per meter square degree centigrade

A = The area from where heat is floe and its unit is square meter

FΔTLM = Log mean temperature difference and its unit is Kelvin

The LMTD approach is applied when input and output temperature is given but the size of the heat exchanger is not selected. The alternative approach for the LMTD the thermal effectiveness method is applied which is calculating the practical world heat transfer amount and the inside of a heat exchanger heat transfer amount. The expression is given below,

E = Q/Qmax …eqn (3)

How to increase efficiency of shell and tube heat exchanger?

The process of the increases efficiency of shell and tube heat exchanger is listed below,

  1. Online cleaning
  2. Offline
  3. Periodic cleaning
  4. Reduce the thickness of the plate
  5. Plate should be choose
  6. Decreasing the thermal resistance
  7. Maintaining heat exchanger
  8. Cleaning of the PHE manually

Heat exchanger efficiency vs. effectiveness:

The major difference between heat exchanger efficiency and effectiveness is discuss below,

ParameterHeat exchanger efficiencyHeat exchanger effectiveness
DefinitionHeat exchanger efficiency is the quality or state of being suitable in performance.Heat exchanger effectiveness is a degree which defines the success story of something which creates desired result.
FocusHeat exchanger efficiency focuses on the resources and process.Heat exchanger effectiveness focuses on Goal of the result.
ThinkingHeat exchanger efficiency is only applied for present state.Heat exchanger effectiveness applied in long term.
Belief’sTo do things correct in process.To do correct things in process.

Heat exchanger efficiency vs. flow rate:

The major difference between heat exchanger efficiency and flow rate is discuss below,

ParameterHeat exchanger efficiencyFlow rate
DefinitionThe relationship between the amount of heat which is transfer in the physical heat exchanger to the  amount of heat which is transfer in the ideal heat exchangerA fluid is flow in a particular time volume of per rate time.
FormulaQ̇= UAΔTQ = vA

Advantages of Fireplace heat exchanger efficiency:

Advantages of Fireplace heat exchanger efficiency is listed below,

  • Smoke is not produced
  • Efficient energy
  • Economical
  • Maintenance is low
  • Long lifespan
  • Availability

Water to water heat exchanger efficiency:

Water to water heat exchanger efficiency can be explain as, the type of heat exchanger device which carry liquid cooling and which is appropriate process for reduce heat from many classifications of industrial methods.

Air to air heat exchanger efficiency:

In the unit of air to air heat exchanger air runs for long time is greater the device of heat exchanger. The amount of recovery heat is about 80 percentages. The units of air to air heat exchanger are long, rectangular and shallow.

What affects heat exchanger efficiency?

The effect of the heat exchanger efficiency is with the increasing of capacity ratio for the counter flow heat exchanger is also an increase and with the increasing of capacity ratio for the flow heat exchanger is also a decrease.

What is the maximum efficiency for parallel flow heat exchanger?

No matter how large the exchanger is or how high be the flow of overflow at transfer coefficient, the maximum efficiency for parallel flow heat exchanger is 5%.

Total Reflux: What, How to Find, Several Facts

800px Synchrotron radiation energy flux 300x128 1

The term “Total reflux” will be briefly discussed in this article. Reflux is a part of distillation process which is related to vapours condensation and also back to condensate to the source of the system.

Total flux can be explain as, the condition of a method where the two state of a matter liquid and vapor can pass through in the column although product will be not decreases. The law of mass conservation is state that the total reflux is not possible to happen.

Only for the continuous operation total reflux is accepted by the beginning up.

Total reflux ratio:

Reflux is used widely for apparatus setup in the laboratory distillation, continuous distillation columns in industries.

Total reflux ratio can be describe in this way,

Total flux ratio can be explain as, returning all the excess amount of product is again back to the column as the form of flux and the liquid of the system is again back to the reboiler for vaporisation and fed to the column.

So the total flux is,

F = 0, W = 0, D = 0

VN+1 = Ln

In the reflux ratio the total reflux ratio is represent as limiting value.

The method of total reflux is essential to determine the number of plates is needed in the minimum number.

Product withdrawal rate will be zero in the total reflux ratio.

Total flux formula:

Total flux can be derive as, the net amount of electric field lines which are passes through a certain area in a fixed time.

The total flux formula is derive below,

From where the electric field lines are passes the plane is normal then the total flux can be express as,

gif

Now in the case if the plane is lifted with an angle of θ then the projected area will be A cos θ in that case the total flux foe the plane will be express as,

φ= EA cosθ

Where,

E = Magnitude for the electric field

A = Area by which the amount of electric flied will be determine

θ= The angle which is created by the surface of the plane and the direction of the electric field by which the electric field is flow parallel to the axis.

total reflux
Image – Laboratory apparatus using reflux to supply energy to chemical reactions. An Erlenmeyer flask is used as a receiving flask. Here the distillation head and fractionating column are combined in one piece;
Image Credit – Wikipedia

How to calculate total flux?

The relationship between the total flux and the net number of lines of electric field is directly proportional to each other by which the surface area the total flux is flow.

Total flux can be calculated in three ways, they are listed below,

Total flux through a small surface area:-

If the field from where the total flux flow is uniform then total flux through a small surface area can be written as,

E = E.dS

Where, The Electric field which is express as E is multiplied by area component which is perpendicular to the given field.

Total flux through a surface:-

The total flux through a surface is S, for this reason surface integral can be express as,

Total flux through a closed surface:-

The dimensional formula for the total flux through a closed surface is L3MT-3I-1 and S.I unit of the through a closed surface is kg.m3.s-3.A-1

Total flux through a closed surface is discuss below,

Where,

E = Electric field

S = Any type of closed surface

Q = The total amount of electric charge inside the surface of S

ε0= Electric constant which is also known as Permittivity and value is

m

Total flux through a closed surface is also identified as, Gauss Law for the electric field in a surface area. The equation stays in integral form and the equation is form of the Maxwell’s equation.

Total reflux condition is possible?

No, total reflux condition is not possible.

The total reflux in general an operating situation in the column where the two states of a matter such as vapor and liquid are passes by each other and in this situation no product is reduced.

Where,

R = L/V = ∞ and D = 0

The slope value in the operating line is, L/V = 1.0

The slope value in the operating line is represent the mass balance for the each plate of y = x.

Total reflux in distillation:

Total reflux is used in a large of industrial fields such as distillation columns, fractionators like chemical plants, petroleum refiners, and natural gas and also in petrochemical processing industries. 

Total reflux in distillation is the type of condensed vapor from which distillation method is done and after completing the process the vapor again back to the process. The liquid used in this that is recycled back to column’s top portion which is known as reflux.

Continuous Binary Fractional Distillation
Image – The reflux system in a typical industrial distillation column;
Image Credit – Wikipedia

What is total luminous flux?

The term total luminous flux, luminous power or photometry derives as the measurement of the light of perceived power. The radiant flux and total luminous flux is not the same factors. The S.I. unit of the total luminous flux is Lumen.

Luminosity
Image – Photopic (black line) and scotopic (green line) luminosity functions. The photopic includes the CIE 1931 standard (solid), the Judd-Vos 1978 modified data (dashed),and the Sharpe, Stockman, Jagla & Jägle 2005 data (dotted).The horizontal axis is wavelength in nm; Image Credit – Wikipedia

What is total heat flux?

Total heat flux has both magnitude and direction for this reason total heat flux is a scale of vector. The S.I. unit of the total heat flux is watts per square metre.

The total heat flux or thermal flux can be derive as, the amount of heat flow density, rate of heat flow intensity or heat flux density is a expression of flow of energy of a particular space in a fixed time.

Heat Flux from Temperature Differential Across Thermal Insulation
Image – Diagram depicting heat flux through a thermal insulation material with thermal conductivity, k, and thickness, x. Heat flux can be determined using two surface temperature measurements on either side of the material using temperature sensors if k and x of the material are also known; Image Credit – Wikipedia

Law of Fourier’s in one dimension:-

The total heat flux can be determined from Fourier’s law. Most of the matter which is stays in solid heat is transfer from one space to another space by convection method.

Mathematical form of law of Fourier’s in one dimension is given below,

gif

Where,

k = Thermal conductivity

In the equation the negative sign represent that flow of the heat direction is from lower side to higher side.

What is total ion flux density?

Total ion flux density can be deriving as; the total amount of ion flux is passes by a particular fixed area to the perpendicular direction of the ion flux. The total ion flux density S.I. unit is Teslas or Webers per square meter.

Mathematically the total ion flux density can be written as,

B = μH

Where,

B = Flux density

μ = Ion flux density

H = Ion field

What is total radiation flux?

Total radiation flux can be any classification of radiation such as sound, particles radioactive, electromagnetic.

Total radiation flux is a measurement of physical parameter by which receiving of particle radiation can be determine through a matter from a particular given source.

800px Synchrotron radiation energy flux
Image – Synchrotron radiation energy flux;
Image Credit – Wikimedia Commons

The mathematical form of total radiation flux is given below,

gif

Where,

L = Total radiation flux

r = The distance from the source of radiation

The units of the total radiation flux is watt per metre squared (W.m-2) and kilograms cubic metres (kg.s-3).

Total flux through a closed surface:

The dimensional formula for the total flux through a closed surface is L3MT-3I-1 and S.I unit of the through a closed surface is kg.m3.s-3.A-1

Total flux through a closed surface is discuss below,

Where,

E = Electric field

S = Any type of closed surface

Q = The total amount of electric charge inside the surface of S

ε0 = Electric constant which is also known as Permittivity and value is

m

Total flux through a closed surface is also identified as, Gauss Law for the electric field in a surface area. The equation stays in integral form and the equation is form of the Maxwell’s equation.

Frequent Asked Questions:-

Question: – Explain and classified distillation depends on the applications and techniques.

Solution: – Depend on the applications and techniques the distillation can be classified generally in four sections they are,

Simple distillation:-

In the method of simple distillation the matter which is already evaporated is passes by the tube which is made with plastic. This condition is happened when liquid mixture contains higher temperature means stays in heated situation. The process of condensation is completed that time end portion of the plastic tube is by cool chill water to outer wall of the plastic tube. After that the gas in condensed in the wall of the plastic tube and passes the heat to the chill cool water. Taking the heat the chill cool water became hotter and chemical matter is condensed in the end portion of the plastic tube.

Steam distillation:-

Steam distillation is a processby which we can separate heat-sensitive components from a mixture. For this reason steam distillation is used as a purification method for mixture having impurities. The components in the mixture should be volatile in order to do this separation. The principle behind steam distillation process is to separate the components by vaporisation precess them at temperatures below their actual boiling point. Unless otherwise, some compounds may decompose at their boiling points and the separation cannot be done accurately.

Vacuum distillation:-

In the process of the vacuum distillation the heat is not essential. In the method of vacuum distillation pressure stays at the above of the mixture of liquids. The value is decreases than the normal value of vapor pressure and evaporation took place of the most volatile particles.

Fractional distillation:-

Fractional distillation is the process used to separate hydrocarbon components in crude oil. The fractional distillation method includes the separation of important components according to the difference between their boiling points. In other words, it uses distillation for the fractionation of crude oil.

Question: – Explain about magnetic flux.

Solution: – Magnetic flux can be deriving as, the net amount of magnetic field lines which are passes through a certain area in a fixed time.

512px Surface integral illustration.svg
Image – The magnetic flux through a surface—when the magnetic field is variable—relies on splitting the surface into small surface elements, over which the magnetic field can be considered to be locally constant. The total flux is then a formal summation of these surface elements;
Image Credit – Wikipedia

Formula:-

The formula for the magnetic flux is,

φ B = B. A = BA cos θ

Where,

φB = Magnetic flux

B = Magnetic field

A = Area

Theta = The angle which is created by the surface of the plane and the direction of the magnetic field by which the magnetic field is flow parallel to the axis.

7+ Heat Exchanger Function: Detailed Facts

Evaporator 265x300 1

Heat exchangers are a pivotal part of many devices and systems that we use daily. They are found in home heating systems, car engines, and industrial processes. But what exactly is a heat exchanger, and how does it work? Let’s delve into the fascinating world of heat exchangers.

Definition of Heat Exchanger

A heat exchanger is a device designed to efficiently transfer (or exchange) heat from one medium to another. These mediums are usually separated by a solid wall to prevent mixing or contamination. The mediums can be gas, liquid, or even solid, and can be the same (e.g., air to air) or different (e.g., air to water).

Main Purpose of Heat Exchanger

The primary purpose of a heat exchanger is to transfer heat between two or more fluids, achieving desired temperatures without letting the substances mix with each other. For instance, in a car engine, a heat exchanger uses air to cool down the hot engine coolant. Similarly, in a home heating system, a heat exchanger transfers heat from the furnace‘s hot air to the cooler air circulating in the building.

Importance of Heat Exchanger

Heat exchangers play a crucial role in many applications. They are vital for thermal efficiency, heat recovery, and temperature control in various systems. Here are some reasons why heat exchangers are so important:

  1. Energy Efficiency: Heat exchangers can recover waste heat from industrial processes, improving overall energy efficiency. This heat recovery process can significantly reduce energy costs and environmental impact.
  2. Temperature Regulation: In systems like car engines or industrial machinery, heat exchangers help maintain optimal operating temperatures, preventing overheating and potential damage.
  3. Comfort and Safety: In buildings, heat exchangers ensure a comfortable indoor temperature and provide hot water. They also play a role in systems like refrigerators and air conditioners.
  4. Industrial Processes: Many industrial processes require precise temperature control. Heat exchangers provide this control, ensuring product quality and safety.

Heat Exchanger Design and Operation

The design of a heat exchanger depends on its intended application. Key factors include the types of fluids involved, the desired temperature change, and the available space. Heat exchanger design also considers the heat transfer coefficient, heat capacity rate, and potential for fouling (build-up of unwanted material on the heat exchanger surfaces).

The operation of a heat exchanger involves fluid flow through tubes or channels. The heat transfer process occurs as one fluid heats up the exchanger’s walls (the “hot” fluid), and another fluid cools it down (the “cold” fluid). The efficiency of this process depends on the materials used, the flow rates, and the temperature difference between the fluids.

Heat Exchanger Maintenance and Repair

Evaporator
Wikimedia Commons

Regular inspection and cleaning are essential for maintaining heat exchanger performance. Over time, fouling can reduce the heat transfer efficiency and cause a pressure drop. In severe cases, it can lead to system failure or even a dangerous situation like a crack in the exchanger.

Maintenance tasks include cleaning the heat exchanger tubes and checking for signs of wear or damage. If necessary, repair or replacement of components may be required. Proper heat exchanger maintenance can extend the device’s lifespan, improve its efficiency, and prevent costly breakdowns.

Heat Exchanger Applications

Heat exchangers have a wide range of applications. They are used in heating, ventilation, and air conditioning (HVAC) systems, power generation, waste heat recovery, and many industrial processes. Some specific examples include:

  • Home Heating Systems: A heat exchanger transfers heat from the furnace to the air circulated throughout the home.
  • Car Engines: Heat exchangers (or radiators) cool the engine coolant, preventing the engine from overheating.
  • Power Plants: Heat exchangers transfer heat from the combustion process to produce steam, which drives the turbines.
  • Refrigeration Systems: Heat exchangers remove heat from the refrigerant, allowing it to cool the inside of the refrigerator or air conditioner.

Understanding the Function of Heat Exchangers

Heat exchangers are crucial components in a wide range of applications, from air conditioning systems in buildings to engines in vehicles. They function by transferring heat from one fluid to another, without the two fluids coming into direct contact. This heat transfer process is fundamental to the operation of many systems and is governed by the heat transfer coefficient.

Heat Transfer Coefficient

The heat transfer coefficient (h) is a measure of the heat transfer rate between the surface of the heat exchanger and the fluid flowing through it. It is influenced by several factors, including the type of fluid, its velocity, and the surface area of the heat exchanger. The higher the heat transfer coefficient, the more efficient the heat exchanger is at transferring heat.

For instance, in a heat exchanger where water is used to cool a system, a higher heat transfer coefficient would mean that the water can absorb more heat from the system, thus cooling it more effectively.

Heat Transfer Functions

Heat transfer in a heat exchanger can occur through three main mechanisms: conduction, convection, and radiation.

  • Conduction is the process of heat transfer through a solid material. In a heat exchanger, this occurs when heat is transferred from the hot fluid to the heat exchanger material (usually metal), and then to the cold fluid.
  • Convection is the process of heat transfer through a fluid (liquid or gas) caused by the fluid’s movement. In a heat exchanger, this occurs when the hot and cold fluids flow over the heat exchanger’s surfaces.
  • Radiation is the process of heat transfer through electromagnetic waves. It plays a minor role in most heat exchangers, but can be significant in high-temperature applications, such as furnaces.

How Heat Exchangers Function

The operation of a heat exchanger is based on the principle of heat transfer. In a typical heat exchanger, two fluids of different temperatures flow through separate channels. The hot fluid loses heat to the heat exchanger material, which then transfers the heat to the cold fluid. This process continues until the temperatures of the two fluids equalize or until the heat exchanger is shut off.

For example, in a car engine, a heat exchanger (or radiator) uses air to cool the engine coolant. The hot coolant flows through tubes in the radiator, transferring heat to the radiator’s metal fins. Air flowing over the fins then absorbs the heat, cooling the coolant.

Heat Transfer Function of Time

The rate of heat transfer in a heat exchanger can change over time due to several factors, including changes in the temperatures and flow rates of the fluids, fouling of the heat exchanger surfaces, and degradation of the heat exchanger materials.

For instance, the buildup of scale or other deposits on the heat exchanger surfaces (a process known as fouling) can reduce the heat transfer coefficient, leading to a decrease in the heat exchanger’s performance over time. Regular cleaning and maintenance of the heat exchanger can help to mitigate this issue.

Types of Heat Exchangers

800px 2008 07 11 Air conditioners at UNC CH 2
Wikipedia

Heat exchangers are devices that facilitate the transfer of heat from one medium to another. They are widely used in various industries, including HVAC, automotive, and power generation. The heat transfer process in these devices is crucial for their thermal efficiency. Now, let’s delve into the different types of heat exchangers.

Double Pipe Heat Exchanger

The double pipe heat exchanger, also known as a pipe-in-pipe system, is the simplest type of heat exchanger. It consists of one pipe inside another larger pipe. One fluid flows through the inner tube while the other flows through the annular space between the two tubes. The heat transfer occurs through the wall of the inner tube.

The design of this type of heat exchanger is straightforward and easy to install. However, its heat transfer coefficient is relatively low, which means it’s not as efficient as other types. Despite this, it’s commonly used in industries due to its simplicity and low cost. Regular inspection and cleaning are essential for maintaining its performance and preventing fouling.

Baffle Heat Exchanger

The baffle heat exchanger is a type of shell and tube heat exchanger. It features a series of baffles or metal plates that direct the fluid flow across the tube bundle. This design increases the turbulence of the fluid, enhancing the heat transfer process and improving the exchanger’s thermal efficiency.

However, the increased turbulence also results in a higher pressure drop, which can affect the overall efficiency of the system. The baffle design also makes the exchanger more prone to fouling, requiring regular maintenance and cleaning. Despite these challenges, baffle heat exchangers are widely used due to their high heat transfer rates and robustness.

Plate Heat Exchanger

The plate heat exchanger consists of a series of thin, corrugated metal plates stacked together. The plates create channels for the fluids to flow between them. The corrugated design increases the turbulence of the fluids, enhancing the heat transfer process.

Plate heat exchangers are known for their high thermal efficiency, compact size, and low fouling tendency. However, they can be challenging to clean and maintain, and they may not be suitable for high-pressure applications. They are commonly used in HVAC systems, power plants, and food processing industries.

Tube Heat Exchanger

Tube heat exchangers, also known as shell and tube exchangers, are the most common type of heat exchanger. They consist of a shell (a large pressure vessel) with a bundle of tubes inside it. One fluid flows through the tubes, and the other flows outside the tubes but inside the shell.

Tube heat exchangers are known for their robust design, high heat transfer rates, and ability to handle high pressures and temperatures. However, they are relatively large and require more space compared to other types of exchangers. They also require regular inspection and cleaning to prevent fouling and maintain their performance.

Specific Applications of Heat Exchangers

Heat exchangers are integral components in a variety of systems and industries, from home heating to large-scale industrial processes. They function by transferring heat from one fluid to another, without the two fluids directly interacting. This heat transfer process is central to their operation and efficiency. Let’s delve into the specifics of how heat exchangers function in various applications.

Heat Exchanger Function in Furnace

In a furnace, the heat exchanger plays a crucial role. It separates the combustion process from the breathable air in your home, ensuring safety and efficiency. The furnace burns fuel (like gas or oil) to produce heat. This heat warms up the metal walls of the heat exchanger. As cool air from your home flows over the warm exchanger, it absorbs the heat and is then redistributed back into your home.

This process is a prime example of a heat exchanger’s ability to transfer heat from one medium (the hot furnace gases) to another (the cool air in your home) without the two ever coming into direct contact. This is crucial not only for thermal efficiency but also for safety, as it prevents harmful combustion gases from entering your home’s air supply.

Heat Exchanger Function in Chilled Water System

In a chilled water system, a heat exchanger is used to cool down water that will be circulated throughout a building for air conditioning purposes. The heat exchanger uses refrigerant to absorb heat from the water, thus cooling it down before it is sent through the building’s air handling units.

The heat absorbed by the refrigerant is then expelled outside the building, ensuring that the interior remains cool. This is a prime example of a heat exchanger’s application in heat recovery and its role in maintaining a building’s thermal comfort.

Heat Exchanger Function in Oil and Gas Industry

In the oil and gas industry, heat exchangers are used in a variety of ways. For instance, they are used in the process of refining crude oil. The crude oil is heated in a furnace, and then it flows into a heat exchanger where it is cooled by water or air.

Heat exchangers are also used in natural gas processing plants to cool and condense the gas. This is a critical step in the process, as it allows for the removal of impurities and the collection of valuable byproducts.

In these applications, heat exchangers must be made from materials that can withstand high temperatures and pressures, such as certain types of metal. Regular inspection and maintenance are also crucial to ensure their performance and longevity.

Heat Exchanger Function in Chiller

In a chiller system, a heat exchanger is used to transfer heat from the liquid being cooled (usually water) to the refrigerant. The refrigerant absorbs the heat from the water, causing it to evaporate. The now cool water is then circulated throughout the building for cooling purposes.

The refrigerant, now in a gaseous state and carrying the absorbed heat, is then compressed and sent to another heat exchanger. Here, it releases the heat it absorbed earlier, condenses back into a liquid, and the cycle begins anew.

Car Heat Exchanger Function

In a car, a heat exchanger, often referred to as a radiator, is used to cool the engine. As the engine runs, it generates a lot of heat. If this heat is not properly managed, it could lead to engine overheating and potential damage.

The car’s heat exchanger uses coolant to absorb heat from the engine. The hot coolant then flows through the radiator where it is cooled by air flow. The cooled coolant is then recirculated back into the engine, and the process repeats.

Components of Heat Exchangers

Heat exchangers are devices designed to transfer heat from one medium to another. They are critical in many industrial processes, including power generation, chemical processing, and HVAC systems. The main components of a heat exchanger include the shell, tubes, tube sheets, baffles, and tie rods. Now, let’s delve into the details of these components and their roles in the heat transfer process.

Shell

The shell is the outer casing of a heat exchanger. It is typically made from a durable material like metal to withstand the pressure and temperature of the heat transfer process. The shell houses the tubes and other internal components, and it also directs the flow of the shell-side fluid.

Tubes

The tubes are the primary heat transfer surface in a heat exchanger. They are usually made from materials with high thermal conductivity, such as copper or stainless steel, to facilitate efficient heat transfer. The fluid flowing inside the tubes is known as the tube-side fluid. The design of the tubes, including their diameter, length, and arrangement, significantly affects the heat exchanger’s performance.

Tube Sheets

Tube sheets are the plates that hold the tubes in place. They are typically made from the same material as the tubes to prevent differential thermal expansion, which could lead to cracking or other damage. The tube sheets also prevent the tube-side and shell-side fluids from mixing.

Baffles

Baffles are components installed inside the shell to direct the flow of the shell-side fluid across the tubes. This increases the fluid’s velocity, enhancing the heat transfer coefficient and improving the heat exchanger’s thermal efficiency. However, baffles also cause a pressure drop, which must be considered in the heat exchanger design.

Tie Rods

Tie rods are used to hold the baffles in place and maintain the structural integrity of the heat exchanger. They are usually made from strong, heat-resistant materials.

Heat Exchanger Types

There are several types of heat exchangers, including shell and tube, plate, and regenerative heat exchangers. Each type has its unique design features, advantages, and applications.

Shell and Tube Heat Exchangers

Shell and tube heat exchangers are the most common type. They consist of a shell housing a bundle of tubes. One fluid flows inside the tubes, while the other flows outside the tubes but inside the shell. This design is versatile and can handle a wide range of temperatures and pressures.

Plate Heat Exchangers

Plate heat exchangers consist of a series of thin, corrugated plates stacked together. The fluids flow in alternate channels between the plates, allowing for efficient heat transfer. Plate heat exchangers are compact and efficient, but they are not suitable for high pressure or temperature applications.

Regenerative Heat Exchangers

Regenerative heat exchangers, also known as heat recovery units, use the same fluid for heating and cooling. The fluid is alternately heated and cooled in a cyclic process, making these units highly efficient.

Heat Exchanger Applications

Heat exchangers are used in a wide range of applications, from heating homes to cooling industrial processes. Here are a few examples:

  1. HVAC Systems: Heat exchangers are used in HVAC systems to transfer heat between the air inside a building and the outside air, or between the air and a coolant fluid.
  2. Power Generation: In power plants, heat exchangers are used to convert the heat energy from burning fuel into electrical energy.
  3. Chemical Processing: Heat exchangers are used in chemical plants to control the temperature of chemical reactions, which can affect the reaction rate and product yield.
  4. Automotive: In cars, heat exchangers are used to cool the engine and the passenger compartment.

Heat Exchanger Maintenance and Operation

Proper maintenance and operation are crucial for the performance and longevity of a heat exchanger. This includes regular cleaning to prevent fouling, inspection for damage or wear, and repair or replacement of worn-out components. The fluid flow rates, temperatures, and pressures should also be monitored and controlled to ensure optimal heat transfer and prevent damage to the heat exchanger.

Heat Exchangers in Different Systems

Heat exchangers are integral components of many systems, facilitating the heat transfer process from one medium to another. They are designed to optimize thermal efficiency, and their applications are diverse, ranging from heating homes to cooling large industrial processes.

Refrigeration System

In a refrigeration system, heat exchangers are used to cool a substance or space. The refrigerant, often a fluid, absorbs heat from the substance or space that needs to be cooled and then flows through the heat exchanger. Here, the refrigerant releases the absorbed heat, thereby cooling down before it is recycled back into the system.

The heat exchanger design in a refrigeration system is crucial for its efficiency. The heat exchanger tubes must be made of a material with high thermal conductivity, such as copper or aluminum, to facilitate the heat transfer process. Moreover, the tubes should be kept clean to prevent heat exchanger fouling, which can reduce thermal efficiency and increase the heat exchanger pressure drop.

Chillers

Room cooler
Wikimedia Commons

Chillers are another application of heat exchangers. They use a refrigeration cycle to cool water, which can then be used in air conditioning systems or industrial processes. The chiller’s evaporator acts as a heat exchanger, absorbing heat from the water and transferring it to the refrigerant.

The heat exchanger heat capacity rate, which is the product of the mass flow rate of the fluid and its specific heat capacity, is a key factor in the performance of the chiller. A higher heat capacity rate means that the heat exchanger can absorb more heat, leading to a cooler output water temperature.

Air Conditioning System

In an air conditioning system, heat exchangers are used to cool and dehumidify the air. The system’s evaporator coil acts as a heat exchanger, absorbing heat from the indoor air and transferring it to the refrigerant. This cools the air, which is then circulated back into the building.

The heat exchanger operation in an air conditioning system is influenced by several factors, including the heat exchanger heat transfer coefficient, the heat exchanger heat load, and the fluid flow rate. Regular heat exchanger maintenance, such as cleaning and inspection, is necessary to ensure optimal performance and prevent issues such as heat exchanger fouling or heat exchanger repair needs.

Crude Oil Cooling

Heat exchangers are also used in the petroleum industry for crude oil cooling. The hot crude oil flows through the heat exchanger tubes, transferring its heat to a cooling medium, usually water or air. This cools the crude oil, making it easier to transport and process.

The heat exchanger materials used in this application must be resistant to corrosion and able to withstand high temperatures and pressures. Moreover, the heat exchanger design must ensure a high heat transfer rate to cool the crude oil efficiently.

Frequently Asked Questions about Heat Exchangers

Heat exchangers are integral components in a variety of systems, from home heating systems to industrial processes. They facilitate the transfer of heat from one fluid to another, enhancing thermal efficiency. Let’s delve into some frequently asked questions about heat exchangers.

Heat Exchanger Transfer Function

What is the function of a heat exchanger?

A heat exchanger’s primary function is to transfer heat between two or more fluids without them mixing. This heat transfer process can involve gases or liquids and can be used for both heating and cooling purposes. The fluids can be the same or different; for example, air to air, water to water, or air to water.

How does a heat exchanger work?

A heat exchanger works by allowing a hot fluid to flow past a cold fluid, separated by a solid wall (usually metal) to prevent mixing. The heat from the hot fluid is transferred through the wall and into the cold fluid, which becomes warmer. This process is governed by the heat transfer coefficient, which depends on the materials used, the fluid flow rates, and the surface area available for heat transfer.

What is heat exchanger efficiency?

Heat exchanger efficiency is a measure of how effectively the exchanger transfers heat from the hot fluid to the cold fluid. It is calculated by comparing the actual heat transfer to the maximum possible heat transfer. Factors that can affect efficiency include the heat exchanger design, the materials used, and the presence of any fouling (deposits that can build up on the heat exchanger surfaces and impede heat transfer).

Location of Heat Exchanger in a Furnace

Where is the heat exchanger located in a furnace?

In a furnace, the heat exchanger is typically located between the combustion chamber and the blower. The combustion gases heat up the exchanger, and then the blower pushes air across its surface. The air absorbs the heat and is then distributed throughout the building.

What happens if the heat exchanger in a furnace cracks?

If a heat exchanger cracks, it can allow combustion gases, including carbon monoxide, to leak into the building’s air. This situation is potentially dangerous and requires immediate attention. Regular heat exchanger inspection and maintenance can help prevent such issues.

Applications of Heat Exchanger

Chiller in a large commercial building Brisbane
Wikimedia Commons

What are some applications of heat exchangers?

Heat exchangers are used in a wide range of applications. In homes, they are used in heating systems to transfer heat from a furnace or boiler to the air or water used for heating. In cars, they are used in the radiator to remove heat from the engine coolant. In industrial settings, they can be used for process cooling, heat recovery, and many other applications.

What is a regenerator in the context of heat exchangers?

A regenerator is a type of heat exchanger that temporarily stores heat from a hot fluid and then releases it to a cold fluid. This process is used in some industrial processes and power generation systems to improve thermal efficiency.

What materials are used in heat exchangers?

Heat exchangers can be made from a variety of materials, including metals like steel, copper, and aluminum, which have high thermal conductivity. The choice of material depends on the heat exchanger design, the fluids being used, and the operating conditions.

Frequently Asked Questions

1. What is the importance of a heat exchanger in thermal efficiency?

A heat exchanger plays a crucial role in enhancing thermal efficiency. It allows heat transfer from one medium to another without direct contact, minimizing energy loss and maximizing efficiency. It is used in various industries, including HVAC, oil and gas, and power generation, to improve energy conservation and process efficiency.

2. How does a heat exchanger function in the heat transfer process?

A heat exchanger functions by allowing heat to flow from a hot fluid to a cooler fluid without the two fluids coming into direct contact or mixing. This heat transfer process is facilitated by the exchanger’s material, which is typically metal due to its high thermal conductivity.

3. What is the main purpose of a heat exchanger in a chiller system?

In a chiller system, the heat exchanger’s main purpose is to transfer heat from the liquid being cooled to the refrigerant. This process cools the liquid, which can then be circulated through a system to absorb heat and cool equipment or conditioned spaces.

4. What types of materials are commonly used in a heat exchanger?

Heat exchanger materials must be thermally conductive to facilitate heat transfer. Common materials include various metals such as copper, aluminum, stainless steel, and titanium. The choice of material depends on factors like the type of fluids being used, the expected heat transfer rate, and the operating conditions.

5. How does a baffle heat exchanger function?

A baffle heat exchanger uses baffles, or obstructions, to direct the flow of fluid and increase the turbulence. This increased turbulence enhances the rate of heat transfer and improves the exchanger’s overall performance.

6. What are the key components of a heat exchanger?

The key components of a heat exchanger include the shell (outer casing), tubes (where one fluid flows), tube sheets, baffles, and headers. These components work together to facilitate efficient heat transfer.

7. How does a heat exchanger work in an oil and gas industry application?

In the oil and gas industry, heat exchangers are used to control process temperatures. They can heat crude oil to reduce its viscosity for easier transport, or cool down gases and liquids to safe temperatures before storage and transport.

8. Where is the heat exchanger located on a furnace?

In a furnace, the heat exchanger is typically located between the combustion chamber and the blower. It absorbs heat from the combustion gases and transfers it to the air that is blown through the HVAC system.

9. What is the role of a heat exchanger in a chilled water system?

In a chilled water system, the heat exchanger transfers heat from the chilled water to the refrigerant. This process cools the water, which can then be used to cool buildings or industrial processes.

10. How does the heat transfer function of a plate heat exchanger work?

A plate heat exchanger uses a series of thin, corrugated plates to transfer heat between two fluids. The plates are arranged to create a network of parallel flow channels. One fluid flows through the odd-numbered channels, and the other fluid flows through the even-numbered channels. The corrugations in the plates induce turbulence, which enhances heat transfer and efficiency.

13+ Application of Heat Exchanger: Detailed Facts

Hand Gesture Hand Shake

In this article “Application of heat exchanger” and application of heat exchanger related facts that will be talk. Heat exchanger is a device which one exchanges the heat between two different temperature fluids.

13+ Application of Heat Exchanger is listed below,

Warm the muscles of the back with the heating pad:-

From the definition of heat exchanger we can understand that two matters when they are stays in different temperature start to exchanging temperature until they reach to the same temperature. The matters can be separated by a wall which will be stays in solid state to stave off amalgamation or the matters can be stay in direct contact to each other. For the case of warm the muscles of the back with the heating pad the matters are divided by solid state .

When warm heating pad is applied in the back of the patient that time heating pad contain high temperature and back of the patient stays at low temperature but when two different temperature is comes closer they start to heat exchanging between to each other and as a result the temperature starts to come in equilibrium condition. The patient easily can take the temperature from heating pad and gets comfort from his back muscle pain.

Mixing hot food item with a spoon:-

For the case of mixing hot food item with the help of spoon the matters are not divided by solid state they stay at direct contact to each other. When warm food item is comes to connect with cold spoon that time hot food item contain high temperature and spoon stays at low temperature but when two different temperature is comes closer they start to heat exchanging between to each other and as a result the temperature became starts to come in equilibrium condition. So, mixing hot food item with a spoon is another example of application of heat exchanger.

Mixing cold food item with a spoon:-

For the case of mixing cold food item with the help of spoon the matters are not divided by solid state they stay at direct contact to each other. When cold food item is comes to connect with comparative hot spoon that time hot food item contain low temperature and spoon stays at high temperature but when two different temperature is comes closer they start to heat exchanging between to each other and as a result the temperature became starts to come in equilibrium condition. So, mixing cold food item with a spoon is another example of application of heat exchanger.

Making of tea:-

For the case of making of tea the matters are not divided by solid state they stay at direct contact to each other. When warm water is mixing with the cold milk that time hot water contain high temperature and cold milk stays at low temperature but when two different temperature is comes closer they start to heat exchanging between to each other and as a result the temperature became starts to come in equilibrium condition. So, making of tea is another example of application of heat exchanger.

Shaking hands:-

Shaking hand between two different people is another example of application of heat exchanger. When two hands are shaking that time the body temperature of two people definitely stay at different temperature but when the hands get closer that time heat exchanging started and as a result the temperature comes in an equilibrium condition.

Hand Gesture Hand Shake
Image – Shaking hands;
Image Credit – Wikimedia Commons

Touch overheated oven:-

Touch into the overheated oven the matters are separated by a wall which will be stays in solid state. For the case when warm heated pan is touched by hand that time heated oven contain high temperature and hand stays at low temperature but when two different temperature is comes closer they start to heat exchanging between to each other and starts to come in equilibrium condition for this reason when overheated oven is touched injury can be appear.

Touch ice cube:-

Touching an ice cube is another example of application of heat exchanger. For the case when in a cool ice cube is touched by hand that time ice cube contain low temperature and hand stays at high temperature but when two different temperature is comes closer they start to heat exchanging between to each other and starts to come in equilibrium condition for this reason when cooled ice cube is touched we feel cold.

Refrigeration system:-

From the term of refrigeration we can get that cooling an area, system or matter to decreases or maintain the temperature below the surrounding one the rejection of heat at a higher temperature. Refrigeration a human made artificial cooling system. Energy that is present in state of heat is rejected from a reservoir which stays in low temperature to a reservoir which stays in high temperature. The application of refrigeration is in wide range such as cryogenics, household refrigerators, air conditioning and industrial freezers.

800px Kuehlregal USA
Image – Commercial refrigeration; Image Credit – Wikipedia

Humans:-

The nasal passage of the human being is works as a heat exchanger. By the help of nasal passage cold air is enter and hot air is exist. The effectiveness of the nasal passage easily can be examined putting the hand in front of exhaling and face, firstly by the nose and in next step by the mouth.

Air conditioning:-

With the air conditioning system in certain place or maintain the temperature, air purity and relative humidity below the surrounding one the rejection of heat at a higher temperature. The air conditioning system is applied for personal comfort. It industries air conditioning system widely used to ensure appropriate operation of parts or machinery.

Application of heat exchanger
Image – Air conditioning condenser units outside a building;
Image Credit Wikipedia

Advantages of air conditioning system:-

  1. The quality of the air can be improved.
  2. House can be protected from insects.
  3. Keep from the heat exhaustion
  4. Work efficiency can be improve
  5. Getting helps to good sleep
  6. Furniture of the protected from humidity
  7. Cool down electrical appliances

Disadvantages of air conditioning system:-

  • A sudden temperature changing is not good at all
  • Skin became dry
  • Noise
  • Not Eco friendly
  • Not economical

Fish, birds, marine mammals:-

Countercurrent heat exchangers naturally appear in the circulation system of birds, fish and marine mammals. Arteries into the skin bearing warm blood are intertwined along from the skin bearing cold blood, causing the warm blood of the arterial to transfer heat with cold blood venous.

512px Countercurrent conservator.svg
Image – Counter-current exchange conservation circuit;
Image Credit – Wikipedia

Petroleum refineries:-

Petroleum refineries or oil refineries is a engineering industrial field where the petroleum is transfer and after that the petroleum is refined into some useful products like kerosene, petroleum naphtha, heating oil, gasoline, fuel oils, diesel fuel and many more.

Sewage arrangement:-

Sewage arrangement is a waste treatment process by which contaminates are removed from sewage to created an effluent which is perfect for exit to the environment.

Moscow Kuryanovo wastewater plant asv2018 08
Image – Sewage arrangement plant; Image Credit – Wikipedia

Advantages of sewage arrangement:-

  1. Time efficient
  2. Eco friendly
  3. Design is simple
  4. Easy installation
  5. Experts not needed
  6. Maintenance cost low
  7. Occupies meager space

Disadvantages of sewage arrangement:-

  1. Power supply needed
  2. Maintenance needed

Frequent Asked Questions:-

Question: – Describe the classifications of heat exchanger.

Solution: – The classifications of heat exchanger is listed below,

  1. Plate heat exchanger
  2. Shell and tube heat exchanger
  3. Pillow plate heat exchanger
  4. Plate and shell heat exchanger
  5. Finned tube heat exchanger
  6. Waste heat recovery units heat exchanger
  7. Plate fin heat exchanger
  8. Adiabatic wheel heat exchanger
  9. Phase change
  10. Dynamic scraped surface
  11. Microchannel heat exchanger
  12. Direct contact heat exchanger
Shell and tube heat exchanger
Image – Shell and tube heat exchanger;
Image Credit – Wikipedia

Question: – Write some applications of Shell and tube type heat exchanger.

Solution: – Some applications of Shell and tube type heat exchanger is listed below,

  1. HVAC
  2. Refrigeration
  3. Power generation
  4. Mining
  5. Cooling of engines
  6. Metals extraction
  7. On ships heating and cooling for both
  8. Air process
  9. Paper industry
  10. Pulp industry

Question: – Write some applications of Plate type heat exchanger.

Solution: – Some applications of Plate type heat exchanger is listed below,

  1. HVAC
  2. Refrigeration
  3. Metallurgical industry
  4. Power industry
  5. Machinery industry
  6. Textile industry
  7. Paper industry
  8. Chemical industry
  9. Beverage and Food industry

Crankshaft Types: Bike, Engine, Marine Engine and Facts

800px IPH Kurbelwelle 225x300 1

In this article “Crankshaft types” and how crankshaft types are related with others facts that will be discuss. In the system of power transmission crankshaft plays a very important role.

The crankshaft is a shaft which is rotate in a motion and transfer piston’s reciprocating motion to rotation motion. The types of crankshaft is listed below,

Detail explanation of Crankshaft types:-

Welded crankshaft:-

The parts of the welded crankshafts such are journals, crank web, crank pin, crank arms are separately manufactured and after that welded with each other. Among the all types of the crankshafts welded crankshaft is stronger and stable. For manufactured the welded crankshaft became very for costly and maintenance is also quite high for this reason in general application the welded crankshaft is not preferred.

Fully built crankshaft:-

In the fully built up crankshaft by its name it define that all components of the fully built crankshaft is manufactured and fabricated separately with taking helping of the pieces of the matter which are multiple separate. The parts which are machined separately they are crankpins, journals and crank webs. The parts are heated and finally artificially shrink fitted together.

When the parts are cooled loosing the excess amount heat the size of the parts are shrink and make a tight grip to each other. The end portion of the connecting rod of the fully built crankshaft is made with a single solid piece of the material.

The making of the fully built crankshaft is easy because small size parts are assembly to make bigger size equipment. The weight of the fully built crankshaft is heavier.

Semi built crankshaft:-

By the name of semi built crankshaft we easily can recognize that the every parts of the crankshaft is not arrange together some of the parts are only constructed and forged together to make a whole crankshaft design. The parts which are shaped, forged, built together in the semi built crankshaft are bearings, crank web. In diesel engine semi built crankshaft is used.

Billet crankshaft:-

With the help o the 4340 alloy steel the billet crankshaft is manufactured. The 4340 alloy made with chromium, nickel, molybdenum and aluminium. The billet crankshaft transfer maximum amount of power to the load. Minimal balancing is required to the billet crankshaft and also it have lowest amount of machining time for this reason in  the system of power transmission this type of crankshaft widely used.

Forged crankshaft:-

By the name of forged crankshaft we easily can recognize that with the help of forging process the forged crankshaft is make. A block of metal or with a single piece of metal the forged and finally crankshaft shaped is given to it. For arranging the all parts of the forged process welding is not required. The engines where need medium speed like generator there only forged crankshaft can be used.

The engines which are bulky and heavy like two stroke engines there forged crankshaft is not suitable al all. Improving the strength of the forged engine induction hardening process is used. It is robust and moderate economical to use.

crankshaft types
Image – Forged Crankshaft;
Image Credit – Wikipedia

Solid single crankshaft:-

From the term of the solid single crankshaft we can recognize that this type of crankshaft is made with solid one single piece of material.  The solid single crankshaft can work in bothlow speed and high speed for this particular reason in multi cylinder engine solid single crankshaft widely used. The end portion of the connecting rod with two pieces of material solid single crankshaft is made. This structure passes through cyclic tension and load during firing.

The solid single crankshaft is stressed for the reasons of axial vibration torsional vibration, misalignment of the main bearing.

Cast crankshaft:-

Cast crankshaft is made with casting malleable iron. In the engines of diesel and petrol cast crankshaft is used in a wide range. The manufacturing cost is very less comparative to the other types of crankshaft and its maintenance cost is also not too high. For improving tensile strength to the cast crankshaft heat preparation is done and for this reason rate of tear and wear is decreases. The lifetime of this crankshaft is also high.

Engine crankshaft types:

The types of the engine crankshaft are listed below,

  1. Billet crankshaft
  2. Forged crankshaft
  3. Cast crankshaft

The crankshaft of the diesel engine is made with alloy steel. For making the crankshaft of the engine at first alloy steel is heated at very high temperature and after that moulded in shape taking the help of forging die. The engine of the diesel have longer stroke comparative to bore diameter, for this particular reason the crankshaft use in the diesel engine larger than the other parts.  Billet crankshaft is use in diesel engine for improving the performance than the other classifications of the crankshaft.

Bike crank set types:

The types of the bike crank set are listed below,

  • Welded crankshaft
  • Fully built crankshaft
  • Semi built crankshaft
  • Billet crankshaft
  • Forged crankshaft

Diesel engine crankshaft types:

The types of diesel engine crankshaft are listed below,

  1. Fully built crankshaft
  2. Semi built crankshaft
  3. Welded crankshaft
  4. Solid single piece crankshaft

Types of crankshaft in marine engine:

The types of crankshafts in marine engine are listed below,

  1. Fully built crankshaft
  2. Semi built crankshaft
  3. Welded crankshaft
  4. Forged crankshaft
Marine Crankshafts 8b03602r
Image – Continental engine marine crankshafts,
Image Credit – Wikipedia

Frequent Asked Questions:-

Question: – Explain the causes behind the unbalancing of crankshafts.

Solution: – The causes behind the unbalancing of crankshafts is listed below,

  1. Explosion or crankcase fire
  2. For the reason of torsion and twist is evolved in the crankshaft.
  3. For the reason of power stroke. After completing the power stroke inside the engine the piston of the engine exerted a jerk force inside the crankshaft thus the crankshaft can make rotation.
  4. The motion of the reciprocating of the piston of the engine inside the chamber of the combustion.
Cshaft 2
Image – Flat-plane crankshaft (red), pistons (gray) in their cylinders (blue), and flywheel (black);
Image Credit – Wikipedia

Question: – Mention the symptoms by which we can recognize the bad conditions of the crankshaft.

Solution: – The symptom by which we can recognize the bad condition of the crankshaft are listed below,

crankshaft types
Image – Schematic of operation of a crank mechanism;
Image Credit – Wikipedia

Noise:-

When the excessive unwanted noise is produce inside the engine that time we can recognize the bad condition of the crankshaft.

Knocking:-

When inside the crankshaft main journal and connecting rod bearing extreme wear is produce that time knocking is appear in the engine of the machine. Knocking is the symptom by which we can recognize the bad condition of the crankshaft.

Difficulty in starting:-

When the system crate problem in starting that time we can recognize the bad condition of the crankshaft.

Excessive vibration of the engine:-

The CKP sensor easily can detect and bounds the generated vibration of the engine of the vehicle to produce stable power input. If unwanted excessive amount of vibration is produce in the engine that helps us to recognize bad condition of the crankshaft.

Stalling and Backfiring:-

When the default position sensor failure of crankshaft is happened that time backfiring and stalling is occur. The CKP sensor failure causes the engine of the system shut down abruptly and after that starting the engine of the system without any reason. The symptom by which we can recognize the bad condition of the crankshaft among them stalling and backing one of them.

Question: – Write the reasons failure behind the diesel engine.

Solution: – The reasons failure behind the diesel engine is listed below,

  1. Misaligned crankshaft
  2. Develop of the cracks on the fillets.
  3. Excessive amount of vibration is appearing for the reason of torsion that can created cracks in the main journals and crankpin.
  4. Excessive speeding of the engine on load.
  5. Stray current or eddy current is passes from the faulty alternator.
  6. Cylinder of the engine is over pressurized for the reason of hydraulic lock for the reason of water leakage in the system’s engine.

Question: – Write the advantages of crankshaft.

Solution: – The advantages of crankshaft is listed below,

  1. Increases the power of the engine
  2. Provides better torque
  3. Greater efficiency
  4. Smooth running

Question: – Write the disadvantages of crankshaft.

Solution: – The disadvantages of crankshaft is listed below,

  1. Failure of bearing
  2. Manufacturing cost is high
  3. Maintenance cost is high
  4. Friction appear more

Darcy Friction Factor: What, How to Find, Chart, Different Entities

667px Darcy Friction factor for Re between 10E3 and 10E8 for values of relative roughness.svg 300x180 1

In this article the topic named “Darcy friction factor” and Darcy friction factor related facts will be discuss. In fluid mechanics the Darcy friction factor equation is play a very important role.

The Darcy friction factor is a physical parameter which is related to head loss or loss of pressure for the reason of friction along the certain amount of length of a coil or pipe to the average velocity of the incompressible fluid. The Darcy friction factor is a dimensionless physical quantity.

What is Darcy friction factor?

The Darcy friction factor is a physical parameter which is use to describe the loss for a coil or pipe due to friction. The Darcy friction factor is applicable for both open channel flow and close channel flow.

667px Darcy Friction factor for Re between 10E3 and 10E8 for values of relative roughness.svg
Image – Darcy Friction Factor;
Image Credit – Wikimedia Commons

The Darcy friction factor is a physical parameter which is describe as it is a physical quantity which is use for calculate the frictional energy loss. The Darcy friction factor is cased for resistance due to friction and velocity of the incompressible fluid inside a coil or pipe.

The Darcy friction factor widely used in turbulent flow for calculating the amount of head loss during the friction in the pipe.

Darcy friction factor formula:

The equation for Darcy friction factor is given below,

Hf = 4fLv2/2gD

Where,

Hf = Pressure loss or head loss

f = Coefficient of friction factor or Coefficient of friction factor

L = Length of the coil or pipe

v = Velocity of the incompressible fluid

g = Acceleration due to gravity (value of g is 9.8 meter per square second)

D = Diameter of the coil or pipe

Pressure loss equation:-

In a cylindrical coil or pipe where incompressible fluid is flow in a motion, the cylindrical coil or pipe which have a uniform diameter D, the pressure loss is appear during the viscous effect which is express as Δp is directly proportional to the length of the cylindrical coil or pipe can be express as with the help of Darcy – Weisbach equation,

gif

Where,

Δp/L= The amount of pressure loss of per unit length is, which express as Pacals per meter

fD = Coefficient of friction factor or Coefficient of friction factor

v = Velocity of the incompressible fluid which is express as meter per second

DH= Hydraulic diameter which express as meter

ρ = The density of the fluid which is express as kg per cubic meter

Head loss form:-

The term of head loss which is express as Δh is the pressure loss appears for reason of friction in term of same length of a column of the incompressible fluid.

The mathematical form of the head loss is,

Δp =ρgΔh

Δh= The head loss appears for reason of friction in term of same length of a coil or pipe and unit is meter.

g = Acceleration due to gravity (value of g is 9.8 meter per square second)

It is beneficial the head loss appears for reason of friction in term of same length of a coil or pipe is,

gif

Where,

L = Length of the coil or pipe and unit is meter

Darcy – Weisbach equation can be writing for head loss,

gif

In form of volumetric flow:-

The relation between volumetric flow rate and mean flow velocity is,

Q = A * <v>

Where,

Q = Volumetric flow rate unit is cubic meter per second

A = Cross sectional area of the coil or pipe and unit is square meter

v = Velocity of the incompressible fluid which is express as meter per second

In a coil or pipe the fluid is flow with pipe diameter D_c,

gif

Darcy – Weisbach equation can be written as,

gif

Shear stress form:-

Darcy – Weisbach equation can be in form of shear stress,

gif

How to calculate Darcy friction factor?

The process of calculating friction factor for turbulent flow is given below,

  1. At first we need to determine the value of Reynolds number for the turbulent flow using this formula,
  2. ρ x V x D x μ
  3. In the next step relative roughness should be calculated using \\frac{k}{D} formula which value to under 0.01
  4. In the final step use the Moody formula for the roughness with the help of Reynolds number,
  5. f = 0.0055 x [1 + (2 x 10^4 x k/D +106/Re)1/3

Darcy friction factor for laminar flow:

Darcy friction factor for laminar flow can be written as,

Darcy friction factor for laminar flow in Circular pipes:-

fD = 64/Re

Where,

Re = Reynolds number

gif

Where,

μ= Viscosity of the incompressible fluid

v = μ/ρ

Darcy friction factor for laminar flow in Non Circular pipes:-

f = K/Re

Range of the Darcy friction factor for laminar flow in Non Circular pipes is,

gif

Laminar flow:-

  1. When the value of Reynolds number is less than 2000 this type of flow called laminar flow.
  2. Mathematical analysis of the turbulent flow is easy.
  3. Velocity of the turbulent flow is too low.
  4. Regular movement is appearing in fluids which are flow in a motion in laminar flow.
  5. Laminar flow in general very rare type of flow.
  6. The velocities profile of the flow laminar the wall of the pipe or rod maximum.
  7. The velocity profile of the flow laminar in the center section of the rod or pipe is minimum.
  8. Average motion is appearing in which side fluid is flowing.
800px Closeup of Horseshoe Falls
Image – A closeup view of water pouring down;
Image Credit – Wikipedia

Darcy friction factor for turbulent flow:

Maximum system of the fluid in the nuclear facilities is work with the flow type of turbulent flow. The resistance of this flow obey the equation of Darcy – Weisbach.

The friction of the turbulent flow is measurement of the shear stress which is applied in the wall of a rod or pipe during the flow of turbulent. The flow of turbulent is obeying the equation of Darcy – Weisbach which is directly proportional to square of mean velocity of the flowing fluid in a certain area.

Turbulent flow:-

  1. Reynolds number is more than 3500 .
  2. Velocity is too high.
  3. Irregular movement is appearing
  4. Average motion is appearing in which side fluid is flowing.
  5. The velocity profile of the flow turbulent in a certain area is quickly drops when it comes to the wall of the pipe or rod.
  6. The velocity profile of the flow turbulent in a certain area is clearly flat when it comes to the center section of the rod or pipe

Friction factor for turbulent flow formula:

The Colebrook–White equation is define as f for the Darcy friction factor, the function of for Reynolds number as Re, pipe relative roughness express as, ε / Dh for both smooth pipes and rough pipes.

The friction factor for turbulent flow formula is,

gif.latex?%5Cfrac%7B1%7D%7B%5Csqrt%7Bf%7D%7D%20%3D%20 %202%20log%20%28%5Cfrac%7B%5Cvarepsilon%20%7D%7B3.7%20D h%7D%20+%20%5Cfrac%7B2

or,

gif.latex?%5Cfrac%7B1%7D%7B%5Csqrt%7Bf%7D%7D%20%3D%20 %202%20log%20%28%5Cfrac%7B%5Cvarepsilon%20%7D%7B14.8%20R h%7D%20+%20%5Cfrac%7B2

Where,

Dh (m , ft) = Hydraulic diameter for filling the fluid in circular conduits

Dh = D= Inside diameter of the area from where flow of turbulent is flowing

Rh (m , ft) = Hydraulic radius for filling the fluid in circular conduits

Rh = D/4= Inside diameter of the area from where flow of turbulent is flowing/4

The equation of Colebrook is solved by numerically for its implicit nature. Now a day Lambert W function is also use to obtain outspoken reformulation the equation of Colebrook.

gif

a = 2.51/Re

gif

or,

10-1/2 = ax +b

p = 10-1/2

We will get,

px = ax + b

Expanded forms:-

Additional mathematical form of the equation of Colebrook is,

Where,

1.7384…. = 2 log (2 * 3.7) = 2 log (7.4)

18.574 = 2.51 * 3.7 * 2

And,

gif.latex?%5Cfrac%7B1%7D%7B%5Csqrt%7Bf%7D%7D%20%3D%201.1364%20.....%20 %202%20log%20%28%5Cfrac%7BD h%7D%7B%5Cvarepsilon%20%7D%29%20 %202%20log%20%281+%20%5Cfrac%7B9

Or,

gif.latex?%5Cfrac%7B1%7D%7B%5Csqrt%7Bf%7D%7D%20%3D%201.1364%20.....%20 %202%20log%20%28%5Cfrac%7B%5Cvarepsilon%20%7D%7BD h%7D%20+%20%5Cfrac%7B9

Where,

1.1364…. = 1.7384… = – 2 log (2) = 2 log

(7.4) – 2 log (2) = 2 log (3.7)

9.287 = 18.574/2 = 2.51 * 3.7

Darcy friction factor chart:

Darcy friction factor chart is combination of four physical parameters such as, pressure loss coefficient, Reynolds number, and relative roughness of the coil or pipe and diameter ratio of the coil or pipe.

Darcy friction factor chart is dimensionless physical factor with the help of Darcy – Weisbach equation can be written as,

gif

Pressure drop can be calculate as,

gif

Or,

gif
Darcy friction factor
Image – Darcy Friction Factor Chart; Image Credit – Wikipedia

The expression for Darcy friction factor for laminar flow is,

gif

In the flow of turbulent the relation between Reynolds number represent as Re, friction factor represent as fD, and relative roughness represent as ∈/D is complicated.

The expression for Darcy friction factor for turbulent flow is,

D%20%7D%7B3.7%7D%20+%20%5Cfrac%7B2

Darcy friction factor for different materials:

The Darcy friction factor for different material is given below,

Pipe materialAbsolute roughness
FeetMicrons
Copper or drawn brass0.0000051.5
Commercial steel0.00015045
Concrete0.001 – .01300 – 3000
Wood stave0.0006 – 0.003200 – 900
Wrought iron0.00015045
Riveted steel0.003 – 0.03900 – 9000

Darcy friction factor for pipe:

The moody chart or friction factor for pipe is plotted the relative roughness of a coil or pipe which is express as ∈/D and Reynolds number.

Darcy friction factor for water:

The moody chart or friction factor is for water derives as the pressure loss of water n a coil or pipe for the reason of friction between the pipe and the water flow inside of it.