The inverse boundary thermal conductivity problem of recovery of heat fluxes to the boundries of anisotropic bodies

A method for solution of the inverse boundary thermal conductivity problem of recovery of the heat fluxes to the structural components of aircraft fabricated of anisotropic materials is proposed. The method is based on a previously obtained analytical solution of a $2\text{D}$ nonstationary thermal conductivity problem in an anisotropic fin under boundary heat transfer. The method consists in parametric identification and finite-element approximation of the dependence of the heat flux on the spatial variable. A regularizing algorithm is developed that permits identification of heat fluxes with large, up to $10\%$, errors in the experimental temperature values. The results obtained in numerical experiments are analyzed.