Numerical Analysis of Natural Convection of Thermoelectrically Conducting Fluids in a Square Cavity under a Uniform Magnetic Field (Estimation of Induced Heating Term)

摘要

The applications of MHD (magnetohydrodynamics) devices have been rapidly developed in recent years. Thermoelectrically conducting fluid has been increasingly used in the manufacturing process of semiconducting materials such as silicon crystal. In the present paper, we propose a new GSMAC (generalized simplified marker and cell) finite-element method coupled with the B method. The present scheme efficiently satisfies both conservation laws of mass and magnetic flux. In order to verify the present scheme, we discuss the natural convection of thermoelectrically conducting fluids in a square cavity under a uniform magnetic field. The numerical results obtained here agreed well with previous experimental and numerical results. Moreover, we estimate the effect of the induced heating term on a temperature field.