# Average Nusselt number or heat transfer coefficient to compare better heat transfer?

I'm simulating different arrays for cylinders in a simple cross flow heat exchanger (cylindrical pipes) as shown below: Inlet temperate(300K) is constant and the cylinders are at constant temperature(400K).

I'm simulating different arrays for cylinders.

I've calculated average Nusselt on each pipe then summed all of them and finally divided it by the number of cylinders (9).

This gives me an average Nusselt number for heat exchanger. Let's call it $$Nu_{av}$$. $$Nu_{av}=\frac{\sum Nu_{cylinder}}{9}$$

I also calculated the heat transfer coefficient of heat exchanger using the following equation: $$\dot{m}c(T_o-T_i)=UA(T_s-T_i)$$

$$\dot{m}$$: Mass flow of fluid passing the heat exchanger

$$c$$: Specific heat of fluid

$$T_o$$: Average outlet temperature

$$T_i$$: Average inlet temperature

$$U$$: Heat exchanger coefficient

$$A$$: Total surface of all cylinders

$$T_s$$: Cylinders surface temperature

I've simulated a lot of arrays. In some cases, the average Nusselt number($$Nu_{av}$$) is bigger and in some others, the average outlet temperature and so, the heat exchanger coefficient($$U$$) is bigger.

My question is: Which one should be my criteria to compare cases? Average Nusselt number or heat exchanger coefficient?

• Which one transfers the most power? Which one causes the lowest pressure drop? – Solar Mike Sep 9 '19 at 3:13
• What is the purpose of comparing these cases? The answer to that question should drive selection criteria. Generally in industry, U is a more widely needed design or evaluation parameter if you are forced to look at only one parameter. – J. Ari Sep 9 '19 at 18:05

## 1 Answer

While this is not a direct answer, I would not use just the average Nusselt number or the overall heat exchanger coefficient. I would take this a step further and determine the heat exchanger efficiency, which is the ratio of heat transferred to the maximum amount of heat transferred. This way, you have a standardized basis to compare heat exchanger models. As SolarMike indicated, you should look at the pressure drop each heat exchanger inflicts on the flow. You could have an extremely efficient unit with a significant pressure drop. This would be detrimental from a system perspective. For example, a pump/compressor would need to input more work to compensate for the pressure loss or a downstream expander would suffer a loss of potential work. I highly recommend the book Design of Fluid Thermal Systems by William S. Janna.