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.