Numerical study of steady magneto-convection around an adiabatic body inside a square enclosure in low Prandtl numbers

In this paper, the effects of Prandtl number on the steady magneto-convection around a centrally located adiabatic body inside a square enclosure are numerically investigated. Two-dimensional nonlinear governing equations are discretized using the control volume method and hybrid scheme. The equations are solved using SIMPLER algorithm. The results are displayed in the form of streamlines and isotherms when the Rayleigh number varies between 10³ and 10⁶, the Hartmann number changes between 0 and 100 and the Prandtl number ranges between 0.005 and 0.1. The ratio of the buoyancy force to the Lorentz force (Ra/Ha ²) is introduced as an index to compare the contribution of natural convection and magnetic field strength on heat transfer. The results obtained from numerical modeling show that the Prandtl number has not considerable effect on heat transfer at low Rayleigh numbers. The effect of magnetic field strength on convection is increased by increasing Prandtl number. The effect of Prandtl number on the average Nusselt number in the presence of a magnetic field is less than the case without a magnetic field.