Magnetohydrodynamics Opposing Mixed Convection in Two-Sided Lid-Driven Differentially Heated Parallelogrammic Cavity

Abstract

Mixed convection in a two-sided anti-parallel lid-driven differentially heated parallelogrammic cavity with the presence of magnetic field has been investigated and solved numerically using the finite volume method. The top and bottom walls of the cavity are horizontal and thermally insulated, whereas the left and right moving walls are maintained at different hot and cold constant temperatures, respectively. Both the lid-driven left and the right sidewalls of the cavity are allowed to move in an anti-parallel motion with the same sliding velocity. Calculations have been made for a wide range of Richardson numbers from 0.01-100, Hartman numbers from 0-75 and various inclination angles with gravitational direction (-60o≤Φ≤60o). Effort is focused on the interaction of force convection with natural convection in presence of magnetic field is subjected in the horizontal direction, while the gravitational force acts in the vertical direction. The working fluid is air, so that the Prandtl number equals to 0.71. Flow and heat transfer characteristics inside the cavity have been presented and discussed in terms of streamtraces, isotherms and average Nusselt number along the heated wall for various combinations of different governing parameters. The accuracy of the numerical method is checked by comparisons with previously published works and the results showed an excellent agreement. The obtained results showed that the positive values of Φ cause a greater increase in local Nusselt number than the same negative values of Φ, and both of them have great effects on the heat transfer and fluid flow phenomenon in the parallelogrammic cavity.Keywords: Magneto-hydrodynamic, Mixed convection, two-sided, lid-driven, parallelogrammic cavity, finite volume, MHD.