Sizing a Parallel Flow and Counter Flow Heat Exchangers: Detailed Calculation Guide

Detailed steps to determine the necessary length of the parallel flow heat exchanger. 

In this tutorial, we'll explore how to size a parallel flow concentric heat exchanger.  

Here, hot oil is cooled by water that jackets it.

The given information includes:

Oil:

Enters at 100°C and leaves at 60°C

Mass flow rate: 0.15 kg/s (kilograms per second)

Heat capacity: 2131 J/kg°C (joules per kilogram degrees Celsius)

Convective heat transfer coefficient: 38.8 W/m²°C (watts per meter squared degrees C)

Water: Enters at 25°C and leaves at 50°C

Convective heat transfer coefficient: 2250 W/m²°C (watts per meter squared degrees C)

 

We aim to determine the length of the tube required for the necessary cooling. We'll make a couple of assumptions: negligible heat loss to the surroundings and a thin wall between the fluids, implying no conductive heat resistance between them.

 

Governing Equation

Our heat transfer rate (𝑄) is given by the equation:

Q=U×A×ΔT log mean

​

 

Where:

𝑄 is the heat transfer rate.

𝑈 is the overall heat transfer coefficient.

𝐴 is the wetted surface area.

Δ𝑇log mean is the log mean temperature difference.

We'll rewrite this equation in terms of the length (𝐿) of the heat exchanger.

 

Step-by-Step Calculation

Calculate Heat Transfer Rate (𝑄)

 

𝑄=𝑚˙×𝐶𝑝×Δ𝑇

𝑄=0.15 kg/s×2131J/kg°C×(100°𝐶−60°𝐶)

𝑄=12,786W

 

 

Overall Heat Transfer Coefficient (𝑈):

𝑈=(1/ℎoil+1/ℎwater)^-1

​ 𝑈=(1/38.8W/m2°C+1/2250W/m2°C)⁻¹

 

 

Log Mean Temperature Difference ΔT log mean

 

ΔT 1  (entrance): 100°𝐶−25°𝐶=75°𝐶

Δ𝑇2   (exit):              60°𝐶−50°𝐶=10°𝐶

 

Δ𝑇log mean=((Δ𝑇1−Δ𝑇2)/ln(Δ𝑇1/Δ𝑇2))

Δ𝑇log mean=((75°𝐶−10°𝐶)/ ln (75°𝐶/10°𝐶))

 

Δ𝑇log mean≈32.2°𝐶

 

Calculate Length L                                             

𝐿=((12,786 W)/(38.1 W/m2°C)(𝜋)(0.03 m)(32.2°𝐶))

𝐿≈110.6 meters

 

Conclusion

The length of the parallel flow heat exchanger required to achieve the necessary cooling is approximately 110.6 meters. This calculation considers the specific parameters and assumptions outlined above.

Sizing a Counter-Flow Heat Exchanger

Detailed steps to determine the necessary length of the cross flow heat exchanger. 

We are going to look at a concentric counter-flow heat exchanger. 

 

In this type of heat exchanger, the hot fluid (in our case, oil) enters the heat exchanger in a direction opposite to the cooling fluid, which is water. The water enters the heat exchanger at one end while the oil exits it at the other end, counterflow to the water.

 

Analysis and Calculation

We’ll perform an analysis similar to that for a parallel flow heat exchanger, focusing on finding the length of the heat exchanger. The key difference lies in the counterflow arrangement.

 

We will use the governing equation:

Q=U×A×ΔT log mean

​

 Where:

Q is the heat transfer rate.

U is the overall heat transfer coefficient.

A is the heat transfer area.

ΔT log mean is the log mean temperature difference.

 

We will rewrite this equation in terms of the length of the heat exchanger.

 

Log Mean Temperature Difference (LMTD)

In a counterflow heat exchanger, the calculation of Δ𝑇log mean differs from that in a parallel flow heat exchanger. Here’s how we determine it:

 

Calculate Δ𝑇1

ΔT 1 =T oil in​ −T water out​

Δ𝑇1=100∘𝐶−50∘𝐶=50∘𝐶

 

Calculate Δ𝑇2

ΔT 2 :Δ𝑇2=𝑇 oil out−𝑇 water in

Δ𝑇2=60∘𝐶−25∘𝐶=35∘𝐶

 

Calculate Δ𝑇 log mean

Δ𝑇 log mean=Δ𝑇1−Δ𝑇2/ln(Δ𝑇1/Δ𝑇2)

Δ𝑇log mean =50∘𝐶−35∘𝐶/ln(50∘𝐶/35∘𝐶)≈42∘𝐶

 

Length Calculation

Using the values from a similar heat exchanger with parallel flow:

 

Heat transfer rate (Q): 12,786 watts.

Overall heat transfer coefficient (𝑈): 38.1 W/m²°C.

Diameter (𝐷): 0.03 meters.

Δ𝑇log mean : 42°C.

The length (L) of the heat exchanger is calculated as:

𝐿=𝑄/(𝑈×𝜋×𝐷×Δ𝑇log mean)

 

𝐿=12,786 watts /( 38.1 W/m2°C×𝜋×0.03 m×42∘𝐶)

L≈84.8 meters

 

 

 

Comparative Analysis

When compared to the length of a parallel flow heat exchanger (110.6 meters), the counterflow heat exchanger is shorter. This difference arises because the temperature difference is greater along the length of the tube in a counterflow arrangement, requiring less surface area for the same amount of heat transfer.

 

Final Thoughts

Understanding the differences between counterflow and parallel flow heat exchangers and accurately calculating the required length is crucial for efficient heat exchanger design. The counterflow design often proves more efficient due to the greater temperature gradient, resulting in a shorter and more compact heat exchanger.