Numerical Simulations of Mhd Fluid Flow and Heat Transfer in a Lid-Driven Cavity at High Hartmann Numbers

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 \u3c Pr \u3c 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

Accurate and Efficient Numerical Simulations of Magnetohydrodynamic (MHD) Mixed Convection at High Hartmann Numbers

Massively parallel numerical calculations of 2-D steady incompressible magnetohydrodynamic (MHD) mixed convection heat transfer at high-Hartmann numbers (Ha) are conducted in a square cavity using a scalable computational implementation developed here. The mixed convection phenomena is a result of the forced convection from an adiabatic and moving top wall, and natural convection from buoyant effects in a domain that has hot and cold walls on each side. The Navier-Stokes equations in the form of a vorticity-streamfunction formulation, and the energy equation, are solved numerically using a uniform mesh of size 1200 × 1200, and simulations are conducted on up to 256 parallel computing cores. The effects of magnetic field in terms of Ha ≤ 1000 are studied for flows at various Richardson numbers (0.1 ≤ Ri ≤ 100). Contours of streamfunction, vorticity and temperature, and profiles of centerline velocities are presented to assess the MHD effects. While the magnetic field makest 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 Ri