Optimization of Parallel, Horizontal, and Laminar Forced Air-Cooled Heat Generating Boards

The objective of this study is to predict numerically the optimal spacing between parallel heat generating boards. The isothermal boards are stacked in a fixed volume of electronic package enclosed by insulated lateral walls, and they are cooled by laminar forced convection of air with prescribed pressure drop. In the numerical procedure, governing equations for the solution of forced convection of constant property incompressible flow through one rectangular channel are solved. Resulting flow and temperature fields in each rectangular channel yield the optimal board-to-board spacing by which maximum heat dissipation rate from the package to the air is achieved. Next, generalized correlations for the determination of the maximum heat transfer rate from the package and optimal spacing between boards are derived in terms of prescribed pressure difference, board length, and density and kinematic viscosity of air. Finally, corresponding correlations are compared with the available two-dimensional studies in literature for infinite parallel plates.