Combined surface tension and buoyancy-driven convection in a rectangular open cavity in the presence of a magnetic field

Abstract

A numerical study is conducted to understand the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054). The two side walls are maintained at uniform but different temperatures θ_h and θ_c (θ_h > θ_c), while the horizontal top and bottom walls are adiabatic. A finite difference scheme consisting of the ADI (Alternating Direction Implicit) method, which incorporates upwind differencing for non-linear convective terms and the SLOR (Successive Line Over Relaxation) method are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Grashof number Gr ranging from 2 × 10⁴ to 2 × 10⁶, Marangoni number Ma from 0 to 10⁵ and Hartmann number Ha from 0 to 100. The detailed flow structure and the associated heat transfer characteristics inside the cavity are presented. At large Ma, two counter-rotating cells are formed at the upper half and lower half of the enclosure. As Ha increases, the temperature field resembles that of a conduction type and the streamlines are elongated in nature in the horizontal direction. The upper cell is crowded and stretched along the free surface. The average Nusselt number increases with Ma but decreases with Ha.