High-resolution simulations of magnetohydrodynamic free convection in an enclosure with a transverse magnetic field using a velocity–vorticity formulation

The differential quadrature method (DQ) is employed to simulate the effect of a transverse magnetic field on buoyancy-driven magnetohydrodynamic (MHD) flow in an enclosure. The DQ numerical procedure is adopted for solving the velocity–vorticity form of Navier–Stokes equations in two dimensions. These equations together with respective (appropriate) boundary conditions are solved numerically using a DQ method by a coupled algorithm for the velocity–vorticity–temperature coupled together with a bi-conjugate gradient iterative solver technique. The velocity–vorticity formation is properly utilized to obtain results in the range of Grashof numbers (104 ≤ Gr ≤ 105), Hartmann numbers (0 ≤ Ha ≤ 100), and Prandtl numbers (0.01 ≤ Pr ≤ 10), as well as aspect ratios A = L/H varying from 1 to 3 in a differentially heated cavity with a transverse magnetic field. The algorithm is then employed to compute the average Nusselt numbers and flow parameters for all the cases. With support from the present simulations of the heat transfer characteristics for a constant value of Gr within the cavity, the heat transfer rate is at its maximum for higher Pr and in the absence of MHD effects (Ha = 0), while it is lower with increase in external magnetic field strength in the lower region of the Prandtl number.