A numerical-analytical solution to the mixed boundary-value problem of the heat-conduction theory for arbitrarily inhomogeneous coatings

This paper presents a technique for the solution of mixed-type axisymmetric heat-conduction problems for an inhomogeneous half-space consisting of an arbitrarily inhomogeneous coating and a homogeneous substrate. The boundary surface of the half-space is thermally insulated with except for a circular area, where either the heat flux or temperature is given. For the case of mixed-type boundary conditions, the bilateral asymptotic method was employed in order to construct the numerical-analytical solutions to the arising dual integral equations, whose kernels have been operated by means of the method of modeling functions. Numerical analysis of the temperature and transversal heat flux in the inhomogeneous half-space has been performed for different variations of the heat-conduction coefficient within the thickness of the inhomogeneous coating.