Magnetic control of natural convection in the horizontal Bridgman configuration using a spectral method: transversal plan

The present study investigates the electromagnetic braking of buoyancy convective flows occurring in differentially heated cavities, filled with low Prandtl, dilute, incompressible and electrically conducting alloys, and subjected to a constant horizontal temperature gradient. In practice, such flows known as ‘Hadley circulation’ are relevant in material processing technologies, such as the horizontal Bridgman configuration. A collocation spectral numerical method is developed to solve the two-dimensional Navier–Stokes equations, modelling the flow phenomena occurring in such configurations, using a vorticity–stream function formulation. The two components of the velocity are deduced from the stream function and the temperature distribution is obtained through the resolution of the energy conservation equation. The results in terms of velocity and temperature distributions for a given Grashof number are obtained for various Hartmann numbers and show that as the Hartmann number increases, the electromagnetic braking of the flow is observed. Moreover, the results illustrate the changes affecting the flow structure which becomes quasi-parallel in the core region of the cavity for sufficiently high values of Ha and the onset of the Hartmann and parallel layers along the boundaries. Also, with increasing Ha, the isotherms are less affected by the convective flow and become parallel to the vertical walls indicating that heat transfer is mainly achieved by conduction.