Effects of Boundary Conditions and Source Dimensions on the Effective Thermal Conductivity of a Printed Circuit Board

Abstract

The heat conduction equation and its boundary conditions were used to show that the planar and normal thermal conductivities of an orthotropic model of a printed circuit board were functions of source to board size ratio, top and bottom side boundary conditions, and thickness and thermal conductivity of each layer. Numerical solutions of the heat conduction equation were used to quantify the dependence on source to board size ratio and top and bottom boundary conditions. It was shown that the thermal conductivities were stronger functions of the source to board size ratio for smaller values of this ratio. This dependence was more pronounced for boards with stronger convection heat transfer on their top side, and for boards with thicker component side copper layer. The thermal conductivities were less sensitive to the variation of the convection heat transfer on the bottom side of the board.