A shape factor scheme for point source configurations

Abstract

Shape factors for steady heat conduction from single bodies and for various configurations of such bodies are often presented in heat transfer textbooks. These presentations are not always clear. Using a single sphere in an infinite medium as an example, a scheme is developed to obtain the shape factor for the hemisphere, for two spheres, a sphere near an isothermal surface and near an adiabatic surface. This scheme can also be applied to other bodies such as ellipsoids, circular discs, pieces of wire and ribbons. The introduction of a “shape resistance”, as the reciprocal of the shape factor, and of a “distance function”, characterizing the influence of the mutual distance of the bodies, simplifies the presentation of the scheme. The overall shape resistance of a configuration can be obtained additively from the shape resistance of a single body and from the distance function. Shape resistance and distance function for various bodies are presented in diagrams.