APPROXIMATE SOLUTIONS TO GOVERNING HEAT CONDUCTION EQUATIONS WITH UNIFORM HEAT GENERATION IN SEMI-INFINITE PLATES

In a previous paper, we introduced a new methodology for using integral methods to solve governing linear partial differential equations in the undergraduate heat transfer course [1]. In it, we considered heat conduction problems solely over finite domains. In this paper, we extend our approach to the case of linear transient heat conduction problems with a uniform internal energy generation over semi-infinite domains. In particular, we use the superposition principle and the heatbalance integral to determine the transient response of a semi-infinite solid with a volumetric heat generation that may be constant or time-dependent over the domain subject to prescribed uniform initial and boundary-surface temperatures. In effect, we construct approximate analytic solutions to the problem in question with accuracy acceptable by most engineering standards.