The Symbolic Operator Representation applied to the Derivation of Solutions of Unsteady Heat Diffusion Problems

摘要

The method of the Symbolic Operator Representation, first introduced by Lord Rayleigh in the solution of the wave equation, is applied to the unsteady heat conduction problem. The general equations for the temperature field around particle of arbitrary shape are expressed in terms of a symbolic operator Ξ. Hence, the analytical solution for the temperature field around a sphere and for the rate of heat transfer from a spherical particle are obtained, when the temperature of the particle is a time-dependent function. As an example for the use of this method, 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.