Analytical calculation of non-stationary temperature field of a flat body with variable thermal conductivity

Analytical formulas describing the non-stationary temperature field in inhomogeneous structures are obtained. In practice, such structures are most often multilayer, which makes it difficult to obtain a mathematically acceptable solution for practical calculations. A feature of this problem is the significant dependence of thermal conductivity on spatial coordinate. In the case where this dependence is exponential, it is possible to obtain a rigorous analytical solution.