MHD Convection of an Electrically Conductive Fluid with Variable Thermal Conductivity

Abstract

The effect of temperature-dependent thermal conductivity on the magneto-convection in a low Prandtl number liquid is investigated numerically. The liquid is contained in a closed square cavity with isothermal vertical walls kept at different temperatures. The top and bottom walls are assumed to be insulated. To solve the governing non-linear differential equations (mass, momentum and energy) a finite volume code based on SIMPLER algorithm is utilized. The results for different Rayleigh numbers (Ra), Hartmann numbers (Ha) and temperature coefficient of thermal conductivity (η) are presented in form of streamlines, isotherms and Nusselt number. It is found that the heat transfer decreases appreciably across the cavity with a decrease in thermal conductivity. It is observed that at low Hartmann number (Ha=30) the thermal boundary layer is formed near the side walls and as η increases the thickness of these boundaries decreases. Also it is found that as non-dimensional thermal conductivity increases the peak of velocity profile increases; however, this phenomenon is very weak at high Hartmann number.