On the effect of nonlinear boundary conditions for heat conduction in diamond heat spreaders with temperature-dependent thermal conductivity

Abstract

For steady-state heat conduction in diamond heat spreaders with temperature-dependent thermal conductivity, we examine the valid range of the commonly used approximate solution against a rigorous solution which we have recently formulated. The basic difference between our work and the approximate solution lies in the boundary condition (bc) of the transformed temperature over the spreader-sink interface-we use a nonlinear bc whereas the bc in the approximate solution has been assumed to be linear. We point out that the valid range of the approximate solution is determined by the temperature difference above the ambient over the interface. The discrepancy between the two solutions becomes severe (>10%) for devices of radius around 50 m involving high power dissipation (>20 W).Index Terms-Diamond heat spreader, microwave diode package, temperature-dependent thermal conductivity.