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

Abstract

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.