Transient and Steady Heat Conduction in Arbitrary Bodies with Arbitrary Boundary and Initial Conditions

Abstract

A method of analysis is described which yields closed-form solutions for two-dimensional heat conduction problems for bodies of arbitrary shape. Three-dimensional problems can also be treated without basic conceptual changes. The method accommodates rather general thermal boundary conditions including arbitrary spatial variations in surface temperature or in surface heat flux, or a convective (or linearized radiative) exchange with a fluid having spatially varying temperature and heat transfer coefficient. For transient problems, the initial temperature may be arbitrarily distributed. Once the solution method has been developed, its practical realization is rather direct, being facilitated by the use of widely available computer routines. A numerical example to illustrate the method is worked out.