# Mass Flow Rate And Heat Transfer:Effect, Relation ,Problem Examples

The mass flow rate and heat transfer analysis used in many heat transfer problems.

The mass flow rate or volume flow rate vary the heat transfer with direct relation. In convection heat transfer, the mass flow rate plays a vital role.

The enhancement of convective heat transfer is convenient by raising the mass flow rate or volume flow rate of the system. The mass flow rate is function of the density, velocity and cross-sectional area the fluid is passing.

m° = ρ A v

Where,

• ρ = Density of the fluid in kg/m3
• A = cross-sectional area in m2
• v = Velocity of the fluid in m/s

The relation of mass flow rate and the heat transfer rate is expressed as below,

ΔQ = m° Cp ΔT

where,

• ΔQ = Rate of heat transfer (kW)
• m° = Mass flow rate (kg/s or LPM)
• ΔT = Temperature difference in Kelvin

## How does mass flow rate affect heat transfer?

The heat transfer depends on many factors like temperature difference, velocity etc.

The heat transfer rate ΔQ is proportional to the mass flow rate m° in direct relation. It means heat transfer increases with an raising the mass flow rate

The mass flow rate m° or volume flow rate V° is the actual mass (m) or volume (v) circulating through the system per unit of time. It is given in Kg/s or LPM (liter per min).

The equation of heat transfer in relationship with mass flow rate is,

ΔQ = m° Cp ΔT

where,

• ΔQ = Rate of heat transfer (kW)
• m° = Mass flow rate (kg/s or LPM)
• ΔT = Temperature difference in Kelvin
• Cp = Specific heat at constant pressure (kJ/kg K)

This equation is elementary in thermodynamics to calculate heat transfer.

The heat transfer can be enhanced by increasing the mass flow rate of the system.

For example :

Suppose refrigerant is circulating through evaporator and condenser at specific mass flow rate X.

Now, the requirement for cooling is increased. If we put the refrigerator at max, The mass flow rate of the refrigerant will get increase. The change in mass flow rate m° can enhance the heat transfer performance of the system.

In any heat exchanger, the heat transfer can be enhanced by increasing the mass flow rate of the coolant or working fluid.

## How to calculate mass flow from the heat?

The mass flow rate is calculated from the heat transfer equation

The mass flow rate can be calculated by heat transfer equation ΔQ = m° Cp ΔT. It is also measured by using a flow measuring instrument.

If we have values of the heat transfer rate (kW), specific heat at constant pressure (kJ/kg K) and the temperature difference in K.

The mass flow rate is generally measured rather than a calculation from heat. It is measured with flow measuring instruments like rotameter, Coriolis meter, orifice meter, venturimeter etc.

The mass flow rate has linear relation with velocity. If we change the velocity of the working fluid, the mass flow rate will get change.

The variation of mass flow rate is needed when we cannot change the other parameter like temperature difference or specific heat. Water is used as the standard working fluid in most heat transfer systems.

m° = ΔQ /Cp ΔT

The mass flow rate of the system is measured or calculated as the system start work with steady flow.

## Mass flow rate and heat transfer coefficient

The heat transfer coefficient (h) is function of the convective heat.

The heat transfer coefficient is increased with the increasing velocity of the working fluid. The mass flow rate has direct relation with velocity.

As per Newton’s law of cooling, The convective heat transfer ΔQ is proportional to the heat transfer coefficient in direct relation.

ΔQ = h A ΔT

Where,

• h = heat transfer coefficient in W/m2 K
• A = cross-sectional area in m2
• ΔT = Temperature difference between the hot side and cold side in K (Kelvin)
• ΔQ = Rate of convective heat transfer in kW

The Nusselt number is expressed as the heat transfer with convection divide by heat transfer with conduction

Nu = h l/k

Where

• h = heat transfer coefficient W/m2 K
• l = Effective length for heat transfer in m
• k = Thermal conductivity (W/mK)

The convective heat transfer is generally given with the Nusselt number. The Nusselt number is also equated in function of Reynolds number Re and the Prandtl number Pr.

The Reynold number is the function of velocity. The mass flow rate of system is function of the velocity of fluid.

So, there is a linear variation m° and the heat transfer coefficient (h).

## Overall heat transfer coefficient and mass flow rate

The different layers of the heat transfer system possess thermal resistance.

The overall heat transfer is dependent on the geometry of the system and the different thermal resistance.

The overall heat transfer coefficient’s notation is U- factor. The heat transfer rate ΔQ is proportional to the overall heat transfer coefficient in direct relation.

ΔQ = U A ΔT

This is unsteady-state heat transfer. The overall heat transfer coefficient can be worded as how better heat is exchanged through the thermal resistance. There are three (3) modes as below.

• Conduction
• convection

The heat transfer through the wall is conduction. The heat exchange between the surface of object and the  air circulating in surrounding is convection type heat transfer. The heat transfer from the wall surface to the atmosphere or other body through electromagnetic waves is radiation heat transfer.

The overall heat transfer rate is mainly considered to study different geometry for heat transfer. It is addition the of the conduction heat transfer coefficient and convection heat transfer coefficient (h). It is the total sum of individual heat transfer rate.

It is helpful to identify the problem of individual heat transfer and modify the system. If the flow rate is high, the velocity generates higher eddies in the system. The higher eddies are responsible for the enhancement in the heat transfer.

## Does heat transfer increase with flow rate?

These three modes of heat transfer through the body

The rate heat transfer ΔQ is vary linearly with the flow rate. The flow rate could be either mass flow rate (m°) or volume flow rate (m°). The heat transfer always increases with the increase in flow rate.

Heat transfer has a direct relationship with flow rate. So it is increased or decreased corresponding change in the flow rate.

Deepakkumar Jani

I am Deepak Kumar Jani, Pursuing PhD in Mechanical- Renewable energy. I have five years of teaching and two-year research experience. My subject area of interest are thermal engineering, automobile engineering, Mechanical measurement, Engineering Drawing, Fluid mechanics etc. I have filed a patent on "Hybridization of green energy for power production". I have published 17 research papers and two books. I am glad to be part of Lambdageeks and would like to present some of my expertise in a simplistic way with the readers. Apart from academics and research, I like wandering in nature, capturing nature and creating awareness about nature among people. Let's connect through LinkedIn - https://www.linkedin.com/in/jani-deepak-b0558748/. Also refer my You-tube Channel regarding “Invitation from Nature”