A unified approach to closed-form solutions of moving heat-source problems

A closed-form model for the computation of temperature distribution in an infinitely extended isotropic body with a time-dependent moving-heat sources is discussed. The temperature solutions are presented for the sources of the forms: (i) Q(01)(t) = Q(0) exp(-lambda t), (ii) Q(02)(t) = Q(0)(t/t*) exp(-lambda t), and Q(03)(t) = Q(0)[1 + acos(omega t)], where lambda and omega are real parameters and t* characterizes the limiting time. The reduced (or dimensionless) temperature solutions are presented in terms of the generalized representation of an incomplete gamma function Gamma(alpha, x; b) and its decomposition C-Gamma and S-Gamma. The solutions are presented for moving, -point, -line, and -plane heat sources. It is also demonstrated that the present analysis covers the classical temperature solutions of a constant strength source under quasi-steady state situations.