Analytical-Numerical Methods for Solving Heat Conduction Problems for Half-Spaces with Gradient Coating

Five analytical-numerical algorithms for solving problems for a body with a functionally gradient coating (FGM) are compared. The study is carried out on the example of an axisymmetric heat conduction problem about local heating of the surface of a coated half-space. The algorithms are based on the use of the Hankel integral transformation. In three approaches, the coating with continuously varying properties is replaced by a package of homogeneous or inhomogeneous layers. An analytical solution is constructed in each layer of the package. In the fourth approach, the boundary value problem arising in the space of the Hankel transform is solved by approximating the derivatives by known difference formulas. The fifth algorithm uses the approximation of the solution in the FGM coating using modeling functions.