Semi-analytical solutions for the transient temperature fields induced by a moving heat source in an orthogonal domain

A semi-analytical solution has been derived for the transient temperature fields that are generated in a three-dimensional solid body when it is subjected to one or more moving heat sources. The solution was derived using the Green's function method, and is applicable to any orthogonal domain that is subject to arbitrary boundary conditions. The solution can account for any linear combination of double-ellipsoidal or double-ellipsoidal-conical (DEC) heat sources. It can therefore be applied in situations ranging from an electric arc moving across a flat plate, to partial-penetration or full-penetration welding either with a laser or an electron beam. In this work, full penetration electron beam welds in 30 mm and 130 mm thick sections of SA508 steel were used as experimental test cases. The solution was shown to offer improved accuracy and dramatic reductions in solution times when compared with numerical methods, thereby lending itself to real-time in process monitoring of fusion welding processes.