An explicit finite difference solution of the generalized equation for unsteady state heat transfer in solids with radiation at one boundary

Abstract

The numerical results of a theoretical investigation of an explicit finite difference solution of the generalized equation for unsteady state heat transfer in solids with radiation at one boundary are presented. Results of this investigation are divided into three groups: first, the case where the end of a plate is suddenly exposed to a constant-temperature radiant heat source; second, the case where the internal conductance of a plate approaches infinity as the end of the plate is suddenly exposed to a constant-temperature heat source or sink; and finally, the case where a plate, which is in initially at some constant-temperature, is allowed to radiate to a sink temperature of zero degrees absolute. The generalized equations for the different cases cited are put into normalized form and are solved on the IBM 709 digital computer. For this investigation one end of a plate was exposed to a constant-temperature radiant heat source or sink, while the other end was insulated. The plate was divided into ten equal segments and an energy balance was performed on each segment. Temperature ratios for the boundaries and all interior points, for the first 25 step calculations, are presented in tabular form for each of the typical cases investigated. Numerical results are presented in the form of curves plotted by using dimensionless parameters on semi-logarithmic paper. Due to computer time limitations, results for the different cases of this investigation are shown only in part. Curves extending to the region of steady state conditions are not shown. Computer programs for each of the cases studied in this investigation are presented in the Appendix.