Mixed convection of a low Prandtl fluid with spatially periodic lower wall heating in the presence of a wall-normal magnetic field

Numerical simulations of the combined natural and forced convection flow in a horizontal channel have been carried out for a fluid of low Prandtl number in the presence of a uniform wall-normal magnetic field. The upper wall is maintained at a constant temperature, while a spatially periodic temperature is imposed at the lower wall. A stability diagram is created based on the results from two- and three-dimensional numerical simulations in order to examine whether the present two-dimensional flows are unstable to three-dimensional disturbances. At the range of parameters studied (5000⩽Ra⩽150,0005000⩽Ra⩽150,000-Rayleigh number, 5⩽Re⩽5005⩽Re⩽500-Reynolds number, and 0⩽Ha⩽200⩽Ha⩽20-Hartmann number), no stable two-dimensional unsteady flow is observed. All mixed convection flows are suppressed by the action of sufficiently strong electromagnetic forces and, in contrast to the hydrodynamic cases, the direct transition to unsteadiness is favored with an apparent lack of steady three-dimensional magnetohydrodynamic flows. The velocity and temperature features of the various flow regimes are discussed, addressing also the differences in the predictions produced by the two- and three-dimensional numerical simulations.