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) Q̇₀₁(t) = Q̇₀exp(-λt), (ii) Q̇₀₂(t) = Q̇₀(t/t*)exp(-λt), and Q̇₀₃(t) = Q̇₀[1 + a cos(ωt)], where λ and ω 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 Γ(α, x; b) and its decomposition C_Γ and S_Γ. 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.