THE SYMBOLIC OPERATOR REPRESENTATION APPLIED TO THE DERIVATION OF SOLUTIONS OF UNSTEADY HEAT DIFFUSION-PROBLEMS

The method of the Symbolic Operator Representation, first introduced b y Lord Rayleigh in the solution of the wave equation, is applied to th e unsteady heat conduction problem. The general equations for the temp erature field around particle of arbitrary shape are expressed in term s of a symbolic operator Xi. Hence, the analytical solution for the te mperature field around a sphere and for the rate of heat transfer from a spherical particle are obtained, when the temperature of the partic le is a time-dependent function. As an example for the use of this met hod, analytic solution is derived in an explicit. form for the case of a linear field around the spherical particle. The solutions obtained by this method are exact.