Author(s)

A. E. Taigbenu

Abstract

The nonlinear coupled differential equations that govern the problem when materials are electrically heated are solved with a flux-based Green element formulation that has significantly enhanced computational features in comparison to previous Green element formulations. The flux-based Green element formulation takes advantage of the ability of the boundary element theory to correctly calculate the normal derivative of the primary variable by implementing the theory in a finite element sense so that enhanced accuracy is achieved with coarse discretization. The complete solution information (temperature, electric potential and their normal derivatives) are made available by the flux-based formulation in each element so that refined solutions at any point, when needed, are calculated using only the element in which the point is located. The closure problem associated with having more unknowns than discretized equations at internal nodes is addressed in a novel manner by a compatibility relation for the normal derivatives of the primary variable that has universal appeal. The computational accuracy of the flux-based Green element formulation is demonstrated with a numerical example of nonlinear electromagnetic heating problem. Keywords: electromagnetic heating, nonlinear diffusion-advection, nonlinear Poisson equation, Green element method. 1 Introduction The food and related industries are very interested in addressing the problems associated with the heating of food substances by electrical currents. Of

Keywords

electromagnetic heating, nonlinear diffusion-advection, nonlinear Poisson equation, Green element method.