Transient numerical simulation of a thermoelectrical problem in cylindrical induction heating furnaces

Abstract

This paper concerns the mathematical modelling and numerical solution of thermoelectrical phenomena taking place in an axisymmetric induction heating furnace. We formulate the problem in a two-dimensional domain and propose a finite element method and an iterative algorithm for its numerical solution. We also provide a family of one-dimensional analytical solutions which are used to test the two-dimensional code and to predict the behaviour of the furnace under special conditions. Some numerical results for an industrial furnace used in silicon purification are shown.

Steel heat treating: mathematical modelling and numerical simulation of a problem arising in the automotive industry

“…Since electromagnetic fields generated by high frequency currents are sinusoidal in time, both the electric potential, φ, and the magnetic potential field, A, take the form ( [1,2,14,15]…”

Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms

“…This example has been taken from Refs. [6] and [21] where it was used to analyze a similar problem in harmonic regime. In what follows we describe briefly the test; we refer the reader to the above mentioned references for further details.…”

Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace

“…From the mathematical point of view, and in order to perform a numerical simulation of the furnace, the physical process is expressed as a coupled non-linear system of partial differential equations arising from the thermo-electromagneto-hydrodynamic problem. In the past years several papers have been published dealing with the thermo-electromagnetic problem [5,7,8,14,16,22], with the electromagneto-hydrodynamic problem [18,24] or with the thermo-electromagneto-hydrodynamic problem [17,21], but not fully coupled because materials properties are supposed to be independent of temperature.…”

“…Based on this idea, different kinds of induction furnaces can be designed depending on the application. Thus, in the past years, with the growth of the photovoltaic industry and the increasing request for high purity silicon, greater efforts have been made to design operative induction furnaces devoted to the silicon purification [7][8][9].…”