The heat transfer problem of a moving heat source along the surface of a half space was studied analytically and numerically. For the 2D problem, the heat source was a strip moving source and for the 3D problem, the heat source was a square moving source. Analytical solutions are available only for adiabatic conditions as given by Carslaw and Jaeger [H.S. Carslaw, J.C. Jaeger, Conduction of Hea...