Heat exchanger for high-performance computing. I built (assembled) a gaming

computer that I want to use to run Transport simulations. These computers come with an advanced cooling system because the processor and electronics will warm up a lot during operation. The cooling system is crucial for optimum performance of the computer. The system consists of a tube that runs through the main computer body, housing, (it is a desktop computer) and that contains a liquid as a refrigerant. I now want to have an initial steady-state heat transfer model that helps me find the best material for the tube considering the local heat transfer coefficient of the refrigerant to optimize the cooling of the computer. So, I need an equation that gives me the amount of heat flowing through the wall of the tube from the inside of the computer housing to the refrigerant in the main section of the tube. Note: the air inside the computer housing is constantly warmed up when the electronics are running. The tube is positioned horizontally and has a length L. The model needs to have the thermal conductivity of the wall of the tube and the local heat transfer coefficient of the refrigerant. The tubing has an inner radius of R0 and an outer radius of R1 (small radius compared to its length). I want to test tubes of different materials but all of them have constant k. The inner fluid has a local heat transfer coefficient of . The air outside the tube (inside the computer housing) is known to be at an average temperature far away from the tube and higher than the temperature of the refrigerant Trefri. The local heat transfer coefficient of the air is the typical . The temperature at the surface of the tube will be known because I have a thermocouple placed at the outer wall (R1) of the tube (Tout). I cant put a thermocouple inside the tube. There is no heat generation inside the tube. The refrigerant can be considered an incompressible pure Newtonian liquid.

a) Establish appropriate boundary conditions.

b) Obtain a 1D model for the appropriate vector component of the heat flux.

c) Obtain a 1D model for that describes the temperature variations inside your control volume.

d) Obtain an equation for the heat flow through the control volume.