Steady temperature in multilayer bodies

Summary

The general solution of fundamental problems of conduction of heat in composite solids is known¹)²)³). The mathematical deductions are, of course, of considerable difficulty and solutions in closed form are not readily to be found in literature, despite their great practical importance. We give here closed formulae for steady temperature fields in multilayer bodies whose surface is kept at a constant temperature, or when radiation takes place at the surface into a medium with a prescribed temperature. The author has not found in the literature a closed form of solution like the one obtained in this article. Also the common way of treating all three fundamental cases (slabs, cylinders and spheres) may very likely be regarded as a now one. Industrial significance of the following considerations is evident. The paper is divided into two main parts. First comes the general solution of the basic mathematical problem, the second part applies theoretical results to special cases.