Induction heating of long cylindrical charges

With the remarkable expansion of induction heating applications during recent years, a growing number of persons is being involved in the design and operation of induction heating equipment. While the general principle of induction heating is obvious to most, the concepts of certain important peculiarities such as skin effect, including its bearing on the intensity of heat generation, are not as widely understood. One reason for this state lies in the classic approach by partial differential equations^1,2 involving operations with which many engineers interested in induction heating are not familiar. A previous paper by the author offered a new approach for the analysis of the induction heating effect by using concepts commonly applied to a-c engineering and not involving differential equations.³ A limitation of that paper consisted in the assumption that the radius of the charge will be very large in comparison with the so-called depth of penetration. It is the object of this paper to cast off this limitation and hence provide an analysis which is valid for any size of the radius of the charge and the depth of penetration. The generated heat is expressed in terms of rapidly converging series. The analysis is applied finally to the case where the charge is subdivided into a number of cylindrical rods. It is shown that for one certain radius of the individual rods, the inductor efficiency reaches a maximum. While in the case of a single (not subdivided) charge, the inductor efficiency cannot increase over a certain limit depending on the material of the charge, the subdivision of the charge removes such limitation, and inductor efficiencies can approach asymptotically 100 per cent for any material.