Non-stationary thermal field in the system layer-half-space generated by moving heat source (Q2759525)

A layer overlaying a half-space with different thermal-physical characteristics is considered. The heat source is moving along the layer surface with constant velocity. The problem is reduced to the integration of two non-stationary equations of heat conduction under proper boundary conditions and conditions of ideal thermal contact at the interface. A solution is obtained using the Laguerre transform with respect to time and the Fourier transform with respect to the spatial variable in the direction of motion of the heat source. The general solution of the problem is represented in the form of series containing the Laguerre polynomials. A numerical example is considered, and temperature plots are presented.