Numerical study of magnetohydrodynamic mixed convection in a partially heated rectangular enclosure with elliptic block

Abstract

Magnetohydrodynamic mixed convection fluid flow and heat transfer in a partially heated rectangular enclosure with elliptic block has been investigated numerically in this study. The left wall of the enclosure has been supposed to high temperature, Th whereas the right wall has been maintained at low temperature, Tc while the remaining walls have been kept adiabatic. The top adiabatic wall has been kept lid-driven with constant velocity parallel to the positive x-direction. A uniform magnetic field of strength, B0 is applied parallel to the x-axis. The Physical problem has been presented mathematically by different sets of governing differential equations (such as mass, momentum and energy equations) along with the corresponding initial and boundary conditions. By using appropriate transformations, the governing equations along with the boundary conditions have been transformed into non-dimensional form, which have been then solved by employing a finite-element scheme based on the Galerkin method of weighted residuals. Numerical results have been obtained for a wide range of dimensionless parameters such as Richardson number, Hartmann number, Prandtl number, Reynolds number and the physical parameter namely area of elliptical block. Also, these results have been presented graphically in the form of streamlines, isothermal contours, and average Nusselt number along the heated section of the vertical left wall at the three values of Richardson number (Ri), varying from 0.1 to 10. This range of Ri have been selected on the basis of calculation covering pure forced convection, pure mixed convection and free convection dominated regimes. In mixed convection dominated region, the heat transfer decreases 4.74, 16.58, and 44.16% with increasing Hartmann number from Ha = 0 to 10, 20, and 50, respectively. On the other hand, the heat transfer increases 51.34, 89.52, and 118.82% with increasing Reynolds number from Re = 50 to 100, 150, and 200, respectively.