Green's functions and numbering system for transient heat conduction

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 locating of Green's functions and exact heat conduction solutions. Such a numbering system provides a framework for the computer cataloging and retrieval of a heat transfer data base in diffusion and heat conduction.