Abstract
Most of the time the surface of materials presents profiles of physical properties that are variable along the depth. The heat diffusion equation of current thermophysical profiles rarely accepts analytical solutions that can be introduced in a rapid minimization scheme. A thermal Riccati equation is defined in case of any continuous profiles, the solutions of which are shown to be the limit of the exact solutions for simple staircase multilayer modellings when the layers are taken thinner and thinner. Thanks to the use of iterative methods based on the thermal wave or the quadrupole descriptions, it is shown that the choice of the multilayer approach to describe continuous depth profiles of materials leads to exact solutions of the problem.
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