On a temperature distribution in a nonhomogeneous half-space caused by a moving heated circle

The quasi-stationary three-dimensional problem of the heat conduction for a nonhomogeneous half-space heated by heat fluxes distributed at a circle and moving with constant speed is investigated. The nonhomogeneous body is composed of a homogeneous half-space and a periodically two-layered coating. The considered problem is formulated using two approaches: (1) by a direct boundary value problem of heat conduction (an exact description), (2) by an application of the homogenized model with microlocal parameters` to the description of the layered coating. The obtained solutions of both approaches are compared and some applicability criterion of the homogenized model is presented.