A method for the identification of nonlinear components of the thermal conductivity tensor for anisotropic materials

A method is proposed for the numerical solution of coefficient inverse problems on nonlinear heat transfer in anisotropic materials used for heat shielding in the aerodynamic heating of hypersonic craft (HC). The main characteristics of anisotropic heat-shielding materials at high temperatures are the components of a nonlinear thermal conductivity tensor that are to be restored based on the results of the experimental measurements of the temperature in space-time nodes. The proposed method is based on the alternating direction method with extrapolation of the numerical solution of heat transfer problems, the method of parametric identification, and the gradient descent method. The results have been obtained for the reconstruction of components of a thermal conductivity tensor for carbon-carbon composite material using the experimental values of the nonlinear heat conduction of these materials. The method can be employed for restoring other numerous thermophysical characteristics of composite materials. The obtained results of the numerical experiments on the identification of components of a thermal conductivity tensor of composite materials in a two-dimensional space are presented and discussed.