Surface Heating by Induction

Induction heating offers a method for heating of electrical conductors such as steel, brass, graphite, by exposing them to a varying magnetic field. The application of induction heating to melting, forging, surface hardening, and other uses is becoming increasingly common, resulting in a mounting interest for a physical concept of the heating effect itself. This effect has been previously analyzed by means of partial differential equations whose solutions are Bessel functions.¹ It is the object of this paper to analyze the induction-heating effect by using concepts commonly applied to a-c engineering without involving differential equations. It was found that ordinary vector diagrams lead to quantitative expressions for the penetration of the magnetic field into the charge, for the distribution of eddy currents and generated heat, as well as for the impedance of the loaded inductor. The analysis is limited to the heating of a body of cylindrical shape, surrounded by a uniform alternating magnetic field; this limitation is the same as commonly applied when partial differential equations are used for the analysis. Another limitation is introduced by the assumption that the depth of penetration is very small compared to the radius of the charge. This assumption greatly simplifies the mathematical treatment without sacrifice to the physical concept. If the depth of penetration is five per cent of the radius of the charge, the expression for the generated heat in the load will deviate only 3.