TEMPERATURE AND HEAT-FLUX SOLUTIONS DUE TO STEADY AND NONSTEADY PERIODIC-TYPE SURFACE TEMPERATURES IN A SEMIINFINITE SOLID

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 tempera tures of the forms: (i) T1(t) = T0(1 + a cos omega t), and (ii) T2(t) = T0(1 + b t cos omega t), where a and b are controlling factors of th e periodic oscillations about the constant surface temperature T0. The dimensionless (or reduced) temperature and heat flux solutions are pr esented in terms of decompositions C(GAMMA) and S(GAMMA) of the genera lized representation of the incomplete Gamma function. It is demonstra ted that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady perio dic-type surface temperatures.