Green's functions and numbering system for transient heat conduction

Abstract

A numbering system for transient heat conduction is proposed in connection with Green's functions. A tabulation of Green's functions for rectangular coordinates is given that can be used for a total of 220 different sets of boundary conditions; one-, two-, and three-dimensional cases are included. This total can be further extended for additional terms in the heat conduction equation. The proposed numbering system has a number of advantages, including the efficient tabulation and location of Green's functions and exact heat conduction solutions. Such a numbering system provides a framework for the computer cataloging and retrieval of a heattransfer data base in diffusion and heat conduction. Nomenclature c = specific heat / = nonhomogeneous boundary condition term F = initial temperature distribution g — volume energy source G = Green's function h —heat-transfer coefficient k = thermal conductivity m — coefficient in Eq. (7) n — outward-pointing normal coordinate r = radial coordinate r_ = general coordinates R = region s = number of boundary conditions s' = surface coordinate S = surface t = time T — temperature