RESPONSE FUNCTION FOR TRANSIENT HEAT-CONDUCTION IN SEMI-INFINITE MEDIA

The concept of response function is used to investigate the transient heat conduction in a semi-infinite medium, when the temperature of the surface is an arbitrary function of time. First, the response of the system to a unit step function of surface temperature T//s(t) is obtained. The temperature distribution in the medium corresponding to arbitrary surface temperature T//s(t) is then expressed in terms of the response function and convolution integral. The analytical solution of the convolution integral is obtained for a periodic variation of T//s(t). The resulting expression for T(x, t) is identical with that obtained by the usual periodic analysis. Numerical computations are carried out to investigate the dependence of the accuracy of numerical results on the upper limit of time (t//0) in the convolution integral.