Find Outlet Temp of Cold Stream of Counterflow in Double Pipe Heat Exchanger

[kyta]

Given the mass flow, Cp, temp of the inlet streams of both hot and cold streams.
As well as being given the inner pipe diametre of the double pipe heat exchanger.
Also knowing the setting is at counterflow and that the overall heat transfer coefficient and that the temp difference between the two liquids is no less than 10C at any point in the exchanger.

How would you go about finding the outlet temp of the cold stream?

What equations would you use?

 

[stewartcs]

Given the mass flow, Cp, temp of the inlet streams of both hot and cold streams.
As well as being given the inner pipe diametre of the double pipe heat exchanger.
Also knowing the setting is at counterflow and that the overall heat transfer coefficient and that the temp difference between the two liquids is no less than 10C at any point in the exchanger.

How would you go about finding the outlet temp of the cold stream?

What equations would you use?

Conservation principles (energy and mass).

CS

 

[oswaler]

To find the outlet temperature of the cold stream in a counterflow double pipe heat exchanger, I would use the heat transfer equation:

Q = UAΔTlm

where Q is the heat transfer rate, U is the overall heat transfer coefficient, A is the heat transfer area, and ΔTlm is the logarithmic mean temperature difference.

First, I would calculate the logarithmic mean temperature difference using the equation:

ΔTlm = (ΔTh1 - ΔTc1) / ln(ΔTh1/ΔTc1)

where ΔTh1 is the temperature difference between the hot stream inlet and outlet, and ΔTc1 is the temperature difference between the cold stream inlet and outlet.

Next, I would use the heat transfer equation to solve for the unknown outlet temperature of the cold stream:

Q = mCpΔTc2

where m is the mass flow rate of the cold stream, Cp is the specific heat capacity of the cold stream, and ΔTc2 is the temperature difference between the cold stream inlet and outlet.

Finally, I would rearrange the equation to solve for ΔTc2 and then add this value to the inlet temperature of the cold stream to find the outlet temperature.

ΔTc2 = Q / (mCp)

Outlet temp of cold stream = Inlet temp of cold stream + ΔTc2

Overall, the equations used to find the outlet temperature of the cold stream in a counterflow double pipe heat exchanger are the heat transfer equation and the logarithmic mean temperature difference equation. It is important to ensure that the temperature difference between the two streams is no less than 10C at any point in the exchanger to maintain efficient heat transfer.