Finding thermal contact resistance of a cold plate

I am currently working on a project that includes designing a water cooled system for industrial scale infrared heating modules.

A cold plate which is directly radiated by IR radiations is to be cooled simultanously with water cooling techniques, having water passed through the tubes that run inside the plate. In order to design the tube, the Overall thermal resistance of the plate is to be determined which requires me to find out the thermal contact resistance between the Cu tube and the Aluminium plate.

Since the temperature at the Surface is non uniform, I need some guidance as to what areas to be used in my calculations to solve the problem at Hand. To my understanding, I can not use the complete area of the plate and tube since the Surface temperature is known only at the inlet and outlet and both water and Surface temperatures are varied throughout the plate.

Please see the attached file for understanding

Thanks

The value for Rc will vary greatly depending on how the copper and aluminum are in contact, and whether the aluminum is oxidized/anodized or polished. How is the copper tube attached to the aluminum? Does the application require that they be easily separated?

It would be a lot better to eliminate the pipe altogether. Redesign the aluminum plate so that water runs directly in contact with the channels cut in the aluminum.

If the copper pipe must be kept, it would be best to provide continuous contact by soldering the two together.

If a non-permanent connection is required, at least use a thermally conductive paste to displace the air between the copper and aluminum. Polish or etch the surface of the aluminum so the oxide layer is as thin as possible. Also clamp the two together to increase the pressure at the asperities which will improve thermal conductivity.