How to Calculate Thermal Energy Transfer in Heat Exchangers: A Comprehensive Guide

Calculating the thermal energy transfer in heat exchangers is a crucial step in the design and optimization of these essential devices. Heat exchangers are widely used in various industries, including power generation, chemical processing, HVAC systems, and refrigeration, to efficiently transfer thermal energy between two or more fluids. This comprehensive guide will walk you through the step-by-step process of calculating the thermal energy transfer in heat exchangers, covering the key parameters, formulas, and practical examples.

Understanding the Fundamentals of Heat Exchangers

Heat exchangers are devices that facilitate the transfer of thermal energy between two or more fluids, typically with different temperatures. The primary purpose of a heat exchanger is to either heat or cool one fluid by transferring thermal energy to or from another fluid. The efficiency of this process is determined by various factors, including the flow rates, specific heat capacities, and temperature differences of the fluids involved.

Calculating the Heat Load

The first step in determining the thermal energy transfer in a heat exchanger is to calculate the heat load, which represents the amount of thermal energy being transferred. The formula for calculating the heat load (P) is:

P = m × c_p × δt

Where:
– P = Heat load (BTU/h)
– m = Mass flow rate (lb/h)
– c_p = Specific heat (BTU/lb °F)
– δt = Temperature difference between inlet and outlet on one side (°F)

To illustrate this, let’s consider an example:

Suppose we have a heat exchanger with a hot fluid flowing at a rate of 1000 lb/h, with a specific heat of 0.5 BTU/lb °F and an inlet temperature of 200 °F and an outlet temperature of 100 °F. The cold fluid is flowing at a rate of 2000 lb/h, with a specific heat of 1 BTU/lb °F and an inlet temperature of 80 °F and an outlet temperature of 120 °F.

We can calculate the heat load as follows:

P = m_hot × c_p_hot × δt_hot
P = 1000 lb/h × 0.5 BTU/lb °F × (200 °F – 100 °F)
P = 50,000 BTU/h

This means that the heat exchanger is transferring 50,000 BTU/h of thermal energy from the hot fluid to the cold fluid.

Determining the Heat Transfer Coefficient

The heat transfer coefficient (k) is a measure of the rate of heat transfer between the two fluids and the heat transfer surface. It is defined by the following equation:

k = α_1 + α_2 + δ / (1 / α_1 + δ / λ + 1 / α_2)

Where:
– α_1 = Heat transfer coefficient between the warm medium and the heat transfer surface (BTU/ft² h °F)
– α_2 = Heat transfer coefficient between the heat transfer surface and the cold medium (BTU/ft² h °F)
– δ = Thickness of the heat transfer surface (ft)
– λ = Thermal conductivity of the material separating the medias (BTU/ft h °F)

Assuming the following values:
– α_1 = 200 BTU/ft² h °F
– α_2 = 150 BTU/ft² h °F
– δ = 0.1 ft
– λ = 20 BTU/ft h °F

We can calculate the heat transfer coefficient as:

k = 200 + 150 + 0.1 / (1 / 200 + 0.1 / 20 + 1 / 150)
k = 349.6 BTU/ft² h °F

Calculating the Log Mean Temperature Difference (LMTD)

The log mean temperature difference (LMTD) is a crucial parameter in determining the heat transfer area required for a heat exchanger. It is calculated using the inlet and outlet temperatures of both the hot and cold sides:

LMTD = [(T1 – T4) – (T2 – T3)] / ln[(T1 – T4) / (T2 – T3)]

Where:
– T1 = Inlet temperature – hot side
– T2 = Outlet temperature – hot side
– T3 = Inlet temperature – cold side
– T4 = Outlet temperature – cold side

Plugging in the values from the previous example:

LMTD = [(200 °F – 120 °F) – (100 °F – 80 °F)] / ln[(200 °F – 120 °F) / (100 °F – 80 °F)]
LMTD = 70 °F

Determining the Required Heat Transfer Area

Finally, we can calculate the required heat transfer area (A) using the following formula:

A = P / (k × LMTD)

Substituting the values from the previous calculations:

A = 50,000 BTU/h / (349.6 BTU/ft² h °F × 70 °F)
A = 22.3 ft²

Therefore, a heat exchanger with a heat transfer area of at least 22.3 ft² would be required to transfer the thermal energy between the hot and cold fluids in this example.

Additional Considerations

• Fluid Properties: The specific heat capacity and density of the fluids involved can significantly impact the heat transfer calculations. Accurate data on these properties is crucial for precise calculations.
• Flow Arrangement: The flow arrangement (parallel, counter-current, or cross-flow) of the heat exchanger can affect the heat transfer efficiency and should be considered in the calculations.
• Fouling Factors: Fouling of the heat transfer surfaces can reduce the overall heat transfer coefficient over time, and this should be accounted for in the design process.
• Pressure Drop: The pressure drop across the heat exchanger can impact the pumping power requirements and should be evaluated as part of the overall system design.
• Heat Exchanger Types: Different heat exchanger designs, such as shell-and-tube, plate-and-frame, or compact heat exchangers, may have unique calculation methods and considerations.

Conclusion

Calculating the thermal energy transfer in heat exchangers is a crucial step in the design and optimization of these essential devices. By understanding the key parameters, formulas, and practical examples, you can effectively determine the heat load, heat transfer coefficient, log mean temperature difference, and required heat transfer area for your specific heat exchanger application. This comprehensive guide provides a solid foundation for mastering the calculations involved in heat exchanger thermal energy transfer analysis.

References

1. Plate heat exchanger calculation method – Alfa Laval
2. Temperature Change and Heat Capacity | Physics – Lumen Learning
3. Quantifying Heat and Work – Chemistry LibreTexts
4. Shell and Tube Heat Exchangers – Basic Calculations – PDH Online
5. Heat Exchange – an overview | ScienceDirect Topics