Analytical solution for the 3D steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling

Abstract

Heating of solids, e.g. by friction or welding, plays an important role in the thermomechanical behaviour of materials. An analytical model to compute the three-dimensional temperature distribution in a solid, subjected to a moving rectangular heat source with surface cooling is proposed in this article. A frequential integral transform and a finite cosine Fourier integral transform are used to solve the advection–diffusion equation related to this problem. The obtained solution is explicit and does not impose any restriction on the speed, the dimensions and the heat convection coefficient. It is presented in series form which converges rapidly. To cite this article: T. Osman, A. Boucheffa, C. R. Mecanique 337 (2009).