Analytical solution of conjugate heat transfer and optimum configurations of flat-plate heat exchangers with circular flow channels

An analytical solution is developed for conjugate heat transfer in a flat-plate heat exchanger with circular embedded channels. The analysis was carried out for fully-developed conditions in the circular tube and uniform heat flux at the plate boundary. The results are applicable to cooling channels that are 50 μm or more in diameter with a large length–diameter ratio. The thermal characteristics of the heat exchanger have been examined for a wide range of the relevant independent parameters and optimum designs for three different sets of constraints have been presented. It was found that the overall thermal resistance increases with the depth of the tube from the heated surface, as well as the spacing between the tubes. For a given combination of tubes’ depth and spacing, there is a certain tube diameter at which the thermal resistance attains a minimum value.