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