Modeling and evaluation of multilayer coating effects on the thermal behavior of semi-infinite solids

This study proposes a method for assessing the applicability of the homogenization model with microlocal parameters in determining the thermophysical properties of multilayer coatings constructed from representative cells consisting of two homogeneous isotropic materials. The investigation is based on solving a two-dimensional quasi-steady-state heat conduction problem for a semi-infinite solid with an insulation coating subjected to a moving heat source. Two models are considered for the coating analysis: one that accounts for the actual layered structure of the coating and another that represents a homogenized coating with continuously varying properties. The solutions are constructed using the Fourier integral transform and two different approaches for approximating the homogenized coating, i.e., by substituting it with a set of homogeneous transversely isotropic layers, and by constructing an approximate solution with modeling functions. It is shown that both approaches ensure a high level of accuracy for specific geomerties, while the latter one is more efficient computationally. Conditions under which the homogenized model adequately simulates the actual layered structure are frameworked. In particular, when the ratio of the representative cell thickness to the heating area width is below 10⁻², the homogenized model provides results acceptable for engineering applications. The approach also enables the correct estimation of local heat fluxes within individual components of the coating, enhancing thereby its applicability for modeling real gradient coatings in thermomechanical analyses.