Counter-flow double pipe Heat Exchanger

[heatmass]

Homework Statement

see attachment

Homework Equations

C for cold side = mass flow rate of cold*Cp
Cp is specific heat

1.) NTU=UA/Cmin
2.) ε=q/qmax
3.) qmax=Cmin*(T hot,in - T cold,in)
4.) NTU=(1/(Cr-1))*ln((ε-1)/(ε*Cr-1)) (Cr<1)
5.) Cr= Cmin/Cmax

for the two small exchangers, assumptions.
6.) (T_oe1 + T_oe2)/2=85
7.) U is the same as first single heat exchanger, and for both heat exchangers.
8.) Cp is assumed to be constant and independent of temperature.
9.) Mass flow rate is considered to be the same for both hot and cold portions.

The Attempt at a Solution

First for the one large heat exchanger simulation we used the log mean temperature difference method to calculate the area needed to achieve a specific heat flow rate or q. This will be used to compare with the double heat exchanger setup while comparing area to heat transfer rate.

for the second portion, we were looking for an equation to relate the heat transfer rate to the total surface area for both smaller heat exchangers. To do this we symbolically expressed the NTU method with variables for the middle temperature of the water, and the outlet temperatures of each exchanger for the oil. The hope being to calculate the needed efficiency to gain the correct temperatures, and from there knowing the NTU value, and from this calculating the area needed.

Is any of this correct? Or could you point us in the right direction.

 

[KataKoniK]

Hello!

I would like to offer some input on your solution attempt.

Your approach seems to be on the right track, but there are a few things that could be improved. First, I would suggest using a more systematic and organized approach to solving the problem. This will make it easier to identify any errors and to communicate your solution clearly.

One suggestion would be to start by clearly defining the problem and the given information. This includes stating the desired heat transfer rate, the temperatures and heat capacities of the hot and cold streams, and any assumptions that are being made. This will help to ensure that all relevant information is considered and that the problem is approached correctly.

Next, I would recommend using a systematic method to solve the problem. For example, you could start by using the log mean temperature difference method to calculate the area needed for the single large heat exchanger. Then, you could use the NTU method to calculate the heat transfer rate for the two smaller exchangers. Finally, you could use this information to calculate the area needed for the two smaller exchangers.

In addition, I would advise being careful with assumptions. While they can be useful in simplifying the problem, they should be clearly stated and justified. For example, in your solution attempt, you assume that the heat capacity is constant and that the mass flow rate is the same for both hot and cold streams. These assumptions may not be accurate in all situations, so it would be important to justify them or to consider their potential impact on the solution.

Overall, I would suggest taking a step back and reviewing your approach to ensure that all necessary information is considered and that the problem is approached systematically. I hope this helps and good luck with your solution!