HEAT-CONDUCTION IN A SEMIINFINITE SOLID SUBJECT TO STEADY AND NONSTEADY PERIODIC-TYPE SURFACE HEAT FLUXES

An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investi gated. The solutions are presented for time-dependent, surface hear fl uxes of the forms: (i) Q(1) (t) = Q(0)(1 + a cos omega t); and (ii) Q( 2)(t) = Q(0)(1 + bt cos omega t), where a and b are controlling factor s of the periodic oscillations about the constant surface heat flux Q( 0). The dimensionless (or reduced) temperature and heat Aux solutions are presented in terms of decompositions C-Gamma and S-Gamma of the ge neralized representation of the incomplete Gamma function. It is demon strated that the present analysis covers the limiting case for large t imes which is discussed in several textbooks, for the case of steady p eriodic-type surface heat fluxes. in addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.