Thermal constriction resistance of an axisymmetric plate subjected to a circular heat source and mixed boundary conditions. Semi-analytical solutions and simple and accurate correlations

This article deals with a complex problem of thermal constriction induced by mixed boundary conditions. Recently (Laraqi et al., 2021) [1], we have developed a set of new analytical solutions to solve some thermal constriction problems for the particular case of semi-infinite axisymmetric media under mixed boundary con-ditions. In this article, we propose a study extended to media of finite thickness to cover other applications related to thermal problems such as electronic cards equipped with chips, and other assemblies involving thin plate. The problem of finite thickness is much more complex to solve. In this article we consider a plate subjected to a circular heat flux density while the rest of the same face is isothermal. Two configurations concerning the rear face are studied. In the first one the surface is adiabatic and in the second one it is isothermal. The analytical developments are carried out until obtaining a Fredholm integral equation of the second kind with finite limits and explicit and converging kernel. Its resolution is done numerically in an easy way (a simple linear system to solve). Comparison with some available results is performed and shows an excellent agreement. Furthermore, on the basis of a judicious study of the asymptotic behavior, simple and accurate correlations are proposed to calculate the thermal constriction resistance for the both considered configurations.

Automated summary

This article tackles the complex problem of thermal constriction caused by mixed boundary conditions and proposes new analytical solutions. It extends the study from semi-infinite axisymmetric media to finite thickness media and provides simple and accurate correlations for calculating thermal constriction resistance.