Refrigeration Heat Exchanger Area Ratio Optimization

[recreated]

The equation for heat transfer is:

1. Q = U.A.(TL-T1)

Where:

Q= heat transferred (W).
U= overal h.t. coefficient.
A= area of heat exhanger (m^2).
TL= Temp. of refrigerated space (Kelvin)
T1= Low temp. of refrigerant= refrigerant in evaporator (K)

I want to eventually find the maximum heat removed from the refrigerated space: QL, corresponding to the optimal heat exchanger area ratio: Xa.

2. QL,max. =

(Click for clear version)3. Xa,optimum =

I know all values in parts 1. 2. and 3. except for A, U and QL,m(QL max). My question:

I want to find a reasonable value for A and U (the values will be theoretical but must be realistic, and I only need these results so I can show how using a optimised area ratio will improve them). After that I will optimize the system using the QL max and Xa optimum equations, from 2. and 3. above, respectively. Does this make sense to you? I have many doubts, such as when I sub in a reasonable value for A, I do not find a reasonable value for U, even though I trust my other values are correct.

What other equations for U are there, so I might be able to find this oppose to estimate?

Thanks for your time

 

[KataKoniK]

.Dear scientist,

Thank you for your forum post and for reaching out for advice. Your approach to optimizing the heat transfer system seems reasonable and it is important to consider both the QL,max. and Xa,optimum equations in order to find the best solution.

In terms of finding a reasonable value for A and U, there are a few things to consider. Firstly, A is the area of the heat exchanger, which can vary depending on the design and size of the system. It is important to ensure that the area you choose is practical and feasible for your specific application.

As for U, the overall heat transfer coefficient, it is a measure of the ability of a material to conduct heat. It takes into account the thermal conductivity of the material, the thickness of the material, and the surface area. In order to estimate a reasonable value for U, you can use the following equation:

U = (k / d) * (1/h1 + 1/h2)

Where:
k = thermal conductivity of the material
d = thickness of the material
h1 and h2 = heat transfer coefficients on either side of the material

This equation can give you a rough estimate for U, but keep in mind that it may vary depending on the specific materials and design of your heat exchanger.

Additionally, there are other equations for U that take into account specific heat transfer mechanisms such as convection, conduction, and radiation. You can do some further research on these equations to see if they may be more applicable for your specific system.

I hope this helps and best of luck with your optimization process!