Thermal constriction resistance of a functionally graded material plate heated by a circular disc heat source on one face and isothermal on the opposite face

Abstract

This article presents a study of the thermal constriction phenomenon for the Functionally Graded Materials (FGM). The studied configuration is that of a plate subjected to a circular disc heat source. The study is carried out under steady-state conditions, considering axisymmetric heat conduction. An analytical solution is developed to calculate the temperature and thermal constriction resistance. Thermal conductivity, which varies as a function of position in the depth direction of the plate, is modeled by a law that allows to consider several possible evolutions (slow, rapid or linear). The thermal constriction resistance resulting from these thermal conductivity evolutions is studied and analyzed as a function of the geometric and physics parameters of the problem. As a verification, we compared the proposed solution with the same configuration but in the asymptotic case of homogeneous conductivity. Both solutions lead to the same result. In a second step, a homogeneous apparent thermal conductivity, which would be that measured by conventional methods, is introduced. It is shown that the calculation of thermal constriction resistance using a homogeneous apparent thermal conductivity differs from that of a calculation using the full developed analytical solution. This difference is small in the case of very thin plates but becomes very significant with increasing plate thickness.