Exact Solution of Heat Conduction in Composite Materials and Application to Inverse Problems

Abstract

Calculation of temperature in high-temperature materials is of current interest to engineers, e.g., the aerospace industry encounters cooling problems in aircraft skins during the flight of high-speed air vehicles and in high-Mach-number reentry of spacecraft. In general, numerical techniques are used to deal with conduction in composite materials. This study uses the exact series solution to predict the temperature distribution in a two-layer body: one orthotropic and one isotropic. Often the exact series solution contains an inherent singularity at the surface that makes the computation of the heat flux difficult. This singularity is removed by introducing a differentiable auxiliary function that satisfies the nonhomogeneous boundary conditions, Finally, an inverse heat conduction technique is used to predict surface temperature and/or heat flux.