Heat transfer in a high Hartmann number MHD duct flow with a circular cylinder placed near the heated side-wall

Abstract

The heat transfer from the side-wall of a duct through which an electrically conducting fluid flows within a strong transverse magnetic field is investigated. A circular cylinder aligned with the magnetic field is offset from the duct centerline. In this configuration the flow is well described by a quasi-two-dimensional model and is therefore solved on a two-dimensional domain. The effects of blockage ratio, gap ratio and Reynolds number on the flow and heat transfer are considered. An optimal cylinder position is determined using an efficiency index defined as the ratio of heat transfer enhancement to pressure drop penalty resulting from insertion of the cylinder in the channel. Cylinder placement with gaps to the heated wall of between 0.83 and 1.4 diameters performed best, achieving at least 95% of the peak efficiency indices for each blockage ratio. These gap ratios corresponded to the periodic shedding of alternating-sign vortices into the wake which interacted with the heated side-wall boundary layer to form counter-rotating vortex pairs carrying hot fluid into the duct interior. By offsetting the cylinder from the wake centreline, heat transfer enhancement of up to 48% compared to the centreline placement is achieved with only a modest increase in the pressure head losses from cylinder drag.