Classical heat flow problems applied to induction billet heating

THE AUTHOR has often referred to the solutions of certain classical heat-flow problems as a method of analyzing the more practical heat-flow problems of induction heating. Certainly others have done the same but surprisingly little has been published on the subject. Several difficulties confront the average engineer considering such an approach. In the first place, the mathematics used in the solution of classical heat flow problems is rather formidable and strange to many. Like anything else, the mathematics becomes understandable and appears simple enough when one masters it, but this requires time and effort and is a deterrent to the practicing engineer. An even greater deterrent is the fact that the numerical evaluation of the solution is often tedious or may even involve an arbitrary function which must be integrated for the special case of the problem at hand before numerical evaluation is possible. Two classical heat-flow problems are selected in this paper for evaluation and use in the analysis of induction billet heating. To overcome the difficulties cited, the solutions are reduced to simple formulas and dimensionless curves. The general plan of presentation is 1. to evaluate and extend the classical solutions to obtain working formulas and curves, and 2. to show how these may be used to analyze the relationships involved in induction billet heating. As usual, it will be necessary occasionally to introduce logical approximations in applying the classical solutions.