Numerical calculations of the 2D steady incompressible magnetohydrodynamic (MHD) driven cavity flow and heat transfer are presented. The Navier−Stokes equations in the stream function and vorticity formulation, and the energy equation are solved numerically using a uniform mesh of size 601 × 601. The effect of magnetic field in terms of the Hartmann number (Ha ≤ 1000) are studied for steady incompressible driven cavity flow for various Prandtl numbers (0.001 < Pr < 10). Contours of stream function, vorticity, and temperature, and profiles of centerline velocities and Nusselt number (Nu) at the hot boundary are presented to assess the MHD effects. While the magnetic field makes all flows one-dimensional with stretching observed in the direction of the magnetic field, its effect on heat transfer is more pronounced only with increased Pr.
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