Solution of the inverse problems of heat admittance in order to derive characteristics of anisotropic materials

A solution of the inverse problem in order to determine the principal coefficients and principal axes angles of the heat conduction tensor of an anisotropic material is proposed in this paper. It is based upon a previously found solution of the heat conduction problem in an anisotropic half-space heated with a thermal flow. The technique is based upon expansion of the discrepancy composite function into Taylor series and determination of differential vectors of the target coefficients, which are then used for application of iterative gradient descent algorithms. The results have proved fine convergence even if the initial approximation of the coefficients vector is different from the target by more than one hundred percent. The proposed method can be applied to determination of thermophysical characteristics of composite materials used for thermal protection of hypersonic flying vehicles.