Reconstruction of the aerothermal heat flux in a fractional thermal protection system model

This paper examines the inverse problem associated with a thermal protection system, which is modelled through the use of fractional derivatives. A three-layer system, representing a comprehensive thermal protection system, is taken into account. The material parameters present in this model are temperature-dependent. Thermal resistances at the interfaces between the layers are also considered. Furthermore, due to the porosity of the third layer, the heat flow within it is modelled utilizing the Caputo derivative. The focus of the inverse problem is to replicate the aerothermal heating on the exterior surface of the space vehicle. An additional input, essential for solving the inverse problem, is the temperature specified at a chosen point within the thermal protection system. To address the posed problem, the Levenberg-Marquardt method is employed to minimize the constructed functional that defines the error of the approximate solution. Meanwhile, the direct problem, which must be resolved to compute the minimized functional value, is tackled using the implicit scheme of the finite difference method. The innovation of this research lies in the introduction of an algorithm designed to address the inverse problem associated with a thermal protection system model utilizing the fractional-order derivative.