How Does the Log Mean Temperature Difference Affect Heat Exchanger Efficiency?

[tehallchemist]

Hi Physics Forum-ers, long time reader, first time poster.

I've been given the task to do a simulation for the cooling of a motor from 50C to 20C. The motor is cooled using a water cooling system, and a 3.5kW heat exchanger.

I've done some quick preliminary calculation, but I'm getting stuck on the limits of the heat exchanger. My current formula looks like:

Twater(1) = Twater(0) + Heat From motor(~2kW) - Heat Removed From exchanger (~3.5kW)

(I know I should use heat capacities and such, this is a simple model)

Now, the heat exchanger we are using is specced to remove 3.5kW of heat. I was told that using this value independent of temperature is an acceptable assumption, but if I were to assume that this will continuously remove 3.5kW, the water temperature would eventually drop below freezing, and I don't think this is correct. What type of function should I be using to describe the heat removed by the exchanger?

Other information:
Refrigerant Conditions BXD: 16bar, 52C
Refrigerant Conditions Suction: 3bar, 7K
Coolant temperature 35C

 

[anorlunda]

The relationship you lack is called log mean temperature difference. It allows you to relate the heat removed to temperatures. It works for both parallel flow and counter flow heat exchangers.

https://en.wikipedia.org/wiki/Logarithmic_mean_temperature_difference