Unconfined Flow and Heat Transfer around a Square Cylinder at Low Reynolds and Hartmann Numbers

The forced convection heat transfer is analyzed through a two- dimensional numerical simulation following a finite volume approach for the hydromagnetic flow around a square cylinder at low Reynolds numbers. The cylinder is placed in an unconfined medium and acted upon by the magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conductive fluid. The magnetic field is applied either along the streamwise or transverse directions. Fictitious confining boundaries are considered on the lateral sides of the simulation domain to make the problem computationally feasible. The simulation is carried out for the range of Reynolds number 10 <= Re <= 50 with Hartmann number 0 <= Ha <= 10 and with a fixed Prandtl number, P r = 0.02 (liquid metal) and a blockage parameter, beta = d / H = 5 %. The flow is steady and stable for the above range of conditions. The magnetic field provides additional stability to the flow as a result of which the wake region behind the cylinder reduces with increasing magnetic field strength at any Reynolds number. The critical magnetic field strength is also computed for which the separation is completely suppressed for the Reynolds number range in case of transversely applied magnetic field. The rate of heat transfer is found almost invariant at low Reynolds number whereas it increases slightly for higher Reynolds number with the applied magnetic field. The heat transfer increases as usual with the Reynolds number for all Hartmann numbers.