Steady-state heat sink analysis for two-terminal microwave oscillator devices with temperature dependent thermal conductivity

Abstract

A theoretical analysis to calculate the steady-state temperature distribution within a cylindrical heat sink configuration, where the thermal conductivity is dependent on the temperature, is outlined. The analysis applies to any heat sink arrangement that can be treated as one or more homogeneous solid cylinders mounted on a semi-infinite heat sink, where the heat flux incident on both faces of each cylinder is uniform over a given centralized circular region. The model is used to analyse the temperature distribution within the heat sink configurations used commonly to package two-terminal semiconductor devices that are operated as sources of electromagnetic radiation in microwave oscillators. Results are presented that show how the maximum temperature rise within commercially available heat sink packages, depends on the input heat flux and the dimensions and thermal conductivity of the materials. Furthermore, results that show how the temperature rise varies across the interfaces of given heat sink configurations, similar to those used commercially, are given also.

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

“…T HE problem of high power density heat dissipation (of order 10 W cm ) from a small semiconductor device (with area of about 10 cm ) has attracted considerable interest in the literature [1]- [6], because of the practical difficulties involved in efficiently conducting the heat out into the environment. Diamond heat spreaders with copper studs are commonly used as means to solve this kind of thermal dissipation problem.…”

“…To avoid solving the nonlinear boundary value problem for , the linear continuity equation (4) is often employed to replace the nonlinear boundary condition (3). Batchelor [1] calculated the temperature distributions of 1070-9886/97$10.00 © 1997 IEEE cylindrical heat dissipation system for microwave oscillators using this linear continuity equation without any justification. In a later paper, Batchelor and Postoyalko [2] extended the same approach to rectangular gold heat spreaders with circular surface heat source.…”