Simulation of Radiation Heat Transfer in a VAR Furnace Using an Electrical Resistance Network

Abstract

The use of electrical resistance networks to simulate heat transfer is a well known analytical technique that greatly simplifies the solution of radiation heat transfer problems. In a VAR furnace, radiative heat transfer occurs between the ingot, electrode, and crucible wall; and the arc when the latter is present during melting. To explore the relative heat exchange between these elements, a resistive network model was developed to simulate the heat exchange between the electrode, ingot, and crucible with and without the presence of an arc. This model was then combined with an ingot model to simulate the VAR process and permit a comparison between calculated and observed results during steady state melting. Results from simulations of a variety of alloys of different sizes have demonstrated the validity of the model. Subsequent simulations demonstrate the application of the model to the optimization of both steady state and hot top melt practices, and raises questions concerning heat flux assumptions at the ingot top surface.