Analytical solution of heat conduction problem for a multilayer assembly arising in photothermal reliability testing

An analytical solution of a two-dimensional heat conduction problem is obtained for a multilayer thin coating-substrate assembly irradiated by a laser beam. A method of solution is based on expansion of Laplace and Hankel transforms of temperature distribution in terms of a small parameter which is equal to the ratio of a coating thickness to a laser beam radius. It is shown that the boundary value problem of the second kind reduces to a generalized characteristic equation. It includes as particular cases the known in heat conduction theory characteristic equations which have been obtained for the one-dimensional boundary value problems of the second and third kinds. Also an asymptotic expression for a temperature distribution in a substrate is derived for the case of small values of Fourier number.