Resistance Heating of a Circular Billet - Two Simple Analytic Models

Two simple models are presented for calculating the ac-dc resistance ratio and power factor of a resistance heated magnetic biliet of circular cross section. The step-function magnetization model yields a normalized ac-dc resistance ratio graph applicable to any homogeneous magnetic billet for which the magnetization characteristic is known. The coupled-circuit model yields a set of unidirectionally coupled algebraic equations that may be solved serially. For the case of a billet of radially inhomogeneous conductivity and permeability both of which are linear, the system may be solved in one pass. When the permeability is a function of field strength an iterative solution is required.