Counter-flow double pipe Heat Exchanger

1. Dec 11, 2011

heatmass

1. The problem statement, all variables and given/known data

see attachment

2. Relevant 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.) (Toe1 + Toe2)/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.

3. 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.

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