The optimal spacing of parallel plates cooled by forced convection

This paper reports the optimal board-to-board spacing and maximum total heat transfer rate from a stack of parallel boards cooled by laminar forced convection. The optimal spacing is proportional to the board length raised to the power 1/2, the property group (μα) 1 4 , and (ΔP)− 1 4 , where ΔP is the pressure head maintained across the stack. The maximum total heat transfer rate is proportional to (ΔP) 1 2 , the total thickness of the stack (H), and the maximum allowable temperature difference between the board and the coolant inlet. Board surfaces with uniform temperature and uniform heat flux are considered. It is shown that the surface thermal condition (uniform temperature vs uniform heat flux) has a minor effect on the optimal spacing and the maximum total heat transfer rate.