ABSTRACT
Many scientific problems and industrial applications, such as welding, ablation, and specific surface treatments like laser hardening operations of materials, involve a moving heat source. Modeling of these processes for precise prediction of thermal effects is essential to understand the physics of the processes and to optimize process parameters [1-3]. From a thermal engineering point of view, such a process is a heat conduction problem containing a moving-heat-source term and can be expressed as analytical equations. The heat source can be applied internally (volumetric heating) or at the surface (boundary heating) in many manufacturing processes. In the case of constant thermophysical material properties, the problem is governed by a linear differential equation, and it is possible to use analytical methods such as separation of variables, integral transformations, or Green’s function method (GFM) [4,5]. Although analytical methods may be limited and may include some mathematical challenges (determining the eigenvalues of complex matrices, difficult-to-calculate integral expressions, etc.), modern symbolic solution tools such as Mathematica, Maple, MatLab may extend existing limits of analytical solution strategies.
