Analytical Inverse Analysis Methodological Approach for Thermo-Physical Parameters Estimation of Multilayered Medium Terrain with Homogenized Sampled Measurements

The current paper presents results of the inverse theory approach utilized for the analytical estimation of thermo-physical properties for a multi-layered medium terrain with homogenized experimental measurements. We demonstrate the derivation steps of the exact solution for the heat transfer problem with third-kind boundary conditions due to natural convection on the outlets posed for the considered experimental domain. There are received analytical expressions. Initially, we illustrate the homogenization of the boundary conditions. We then discuss the process of derivation for the analytical solution of the posed problem with the help of key elements of the Fourier method. We provide an algorithm for applying the contact condition to extend received expressions for multiple layers. After that we demonstrate the major steps for the construction of nonlinear systems of equations to be solved in order to obtain exact values of key thermo-physical and geometrical parameters of the investigated medium with the help of received exact analytical expressions. Along with analytical procedures, we present a posed experimental design and discuss an algorithm of numerical exploitation for a suggested method, outlining its advantages and possible limitations in terms of initial approximations.