A semi-analytical solution has been derived for the transient temperature elds
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 at 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 oer 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.