Numerical study of MHD suppression of secondary motion in buoyancy-driven flows

A recently developed numerical method is employed for computing the numerical solutions of the incompressible Navier-Stokes equations and energy equation with Boussinesq approximation in the presence of a magnetic field. The method is based on the Harlow and Welch approach and employs a regular grid finite-volume variable arrangement instead of the usual staggered grid. The key feature of the algorithm is that the transport equations of the magnetic field with solenoidal condition are similar to the momentum and continuity equation and hence can be solved in a similar fashion. This allows for a unified computational framework for the solution of incompressible viscous magnetohydrodynamic flows. Implemented in a second-order-accurate finite-volume code, the algorithm is used to compute the fully developed magnetohydrodynamic flow in a pipe with combined free- and forced-convection at various Hartman and Grashof numbers. Computations show that the magnetic field inhibits the secondary motion in buoyancy-driven flows.