# IJPAM: Volume 63, No. 2 (2010)

**MODELING OF TWO-FLUID FLOW AND**

HEAT TRANSFER WITH SOLIDIFICATION IN

CONTINUOUS STEEL CASTING PROCESS

UNDER ELECTROMAGNETIC FORCE

HEAT TRANSFER WITH SOLIDIFICATION IN

CONTINUOUS STEEL CASTING PROCESS

UNDER ELECTROMAGNETIC FORCE

Department of Mathematics

Faculty of Science

Mahidol University

272, Rama 6 Road, Rajthevee, Bangkok, 10400, THAILAND

e-mail: scbww@mahidol.ac.th

Department of Mathematics and Statistics

Curtin University of Technology

Perth, WA 6845, AUSTRALIA

e-mail: yhwu@maths.curtin.edu.au

**Abstract.**This paper is concerned with the two-fluid flow and heat transfer in the continuous steel casting process under electromagnetic (EM) force. The governing equations consist of the Navier-Stokes equations, the continuity equation, and the energy equation. The influence of the EM field on the flow pattern, the meniscus shape, and temperature distribution in the EM caster is modeled by the addition of the EM force and the surface tension force in the Navier-Stokes equations. The EM force is defined by the cross product of current density and magnetic flux density obtained from the Maxwell's equations. A surface tension force is a function of the level set function which can be solved from the level set equation. A complete set of governing equations is solved by the level set finite element method. The numerical results demonstrate that the EM field applied to the system has significant effect on the two-fluid flow, meniscus profile, and temperature distribution.

**Received: **June 23, 2010

**AMS Subject Classification: **35Q60, 74A50, 74F15, 74S05, 83C50

**Key Words and Phrases: **electromagnetic stirring, continuous steel casting process, two-fluid flow, heat transfer, level set finite element method

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2010

**Volume:** 63

**Issue:** 2