Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-26T19:08:59.651Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence of a solution for a free boundary problem in the thermoelectrical modelling of an aluminium electrolytic cell

Published online by Cambridge University Press:  09 May 2003

L. CONSIGLIERI  and
M. C. MUÑIZ
L. CONSIGLIERI
Affiliation:
CMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal email: glieri@lmc.fc.ul.pt
M. C. MUÑIZ
Affiliation:
Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago, Spain email: mcarmen@usc.es
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a coupled system of elliptic equations describing the steady state of the thermoelectrical behaviour of an aluminium electrolytic cell. The thermal model is a free boundary problem which consists of the heat equation with Joule heating as a source. We neglect the Joule heating in the ledge, and allow for temperature-dependent electrical conductivity. We also formulate a numerical approximation using a finite element method. An iterative algorithm and numerical results are presented. The existence of a weak solution is also proved.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 14 , Issue 2 , April 2003 , pp. 201 - 216
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This work has been supported by AI#E-12/00, HP1999-0027 and Xunta de Galicia (PGIDT00PXI20701PR).