HEAT-CONDUCTION IN A SEMIINFINITE SOLID SUBJECT TO TIME-DEPENDENT SURFACE HEAT FLUXES - AN ANALYTICAL STUDY

A closed-form model for the computation of the transient temperature a nd heat flux distribution in the case of a semi-infinite solid of cons tant properties is investigated. The temperature and heat flux solutio ns are presented for time-dependent, surface-heat flux of the forms: ( i) Q1 (t) = Q0 (t/t)nu-1, (ii) Q2 (t) = Q0 exp (- lambdat), and (iii) Q3 (t) = Q0(t/t) exp(-lambdat), where lambda is a real number and nu is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker funct ion, the generalized representation of an incomplete Gamma function I( alpha) (b, x) which can also be expressed by the complementary error f unctions. It is also demonstrated that the present analysis covers som e well known (classical) solutions as well as a family of new solution s for the heat transfer through a semi-infinite solid.