New developments and explicit results for the thermal constriction resistance of a circular contact under mixed axisymmetric boundary conditions

This article presents a study of the thermal constriction resistance developed in a semi-infinite medium subjected to a circular heat source with mixed boundary conditions. The problem is considered axisymmetric and stationary. Two cases of mixed boundary conditions are considered. The contact area can be subjected to a nonuniform axisymmetric heat flux density while the remainder of the surface is isothermal, or the contact is subjected to a non-uniform axisymmetric surface temperature while the remainder of the surface is adiabatic. The thermal constriction resistance is determined analytically. It takes a simple form and can be used for various problems. To offer a wide choice of applications, a general distribution law for the heat flux density or the temperature of the contact area is considered. Verifications of the proposed solutions are carried out by comparison with some analytical results available in the literature. An analysis of the results according to the kind of boundary conditions and the curvature of the axisymmetric source is also performed.

Automated summary

This study investigates the thermal constriction resistance developed in a semi-infinite medium subjected to a circular heat source with mixed boundary conditions. The thermal constriction resistance is determined analytically and takes a simple form, applicable to various problems. The proposed solutions are verified through comparison with analytical results in the literature, and an analysis based on different boundary conditions and the curvature of the axisymmetric source is also conducted.