Use of Boundary Sources in Problems of Heat Conduction

Abstract

A method is presented for solving problems of one-dimensional heat flow in regions with plane, spherical, or cylindrical boundaries. It is based on the physical concept of a uniform continuous-source distribution on the boundary, whose strength varies with time in such a way as to meet the prescribed boundary condition. Examples of the method are given, including the solution for the temperature in a half-space with an initial steady gradient of temperature and the boundary condition (∂T/∂x) − w(∂T/∂t) − hT = − hθ.