A methodology for solving inverse coefficient problems of determining nonlinear thermophysical characteristics of anisotropic bodies

A methodology is proposed for solving inverse coefficient thermal-conductivity problems of defining the thermal-conductivity tensor components that depend on the temperature by introducing a quadratic residual functional, its linearization, a minimization iteration algorithm, and a method of parametric identification considering errors in determining the experimental temperature values. The existence and uniqueness of the solution to inverse coefficient problems of nonlinear thermal conductivity in anisotropic bodies at moderate constraints on the descent parameters and the sensitivity matrix norms are proven. The results obtained for carbon-carbon composites support the entire methodology for numerical solution to inverse coefficient problems with an allowable error of the experimental temperature values. The proposed methodology can be applied to define both linear and nonlinear characteristics of anisotropic heat-protection materials used in aircraft and space engineering.