Transient Laminar MHD Natural Convection Cooling in a Vertical Cylinder

Abstract

A numerical study is presented of transient laminar natural convection cooling of an electrically conductive fluid, placed in a vertical cylinder in the presence of an axial magnetic field. The cylindrical wall is suddenly cooled to a uniform temperature, thus setting the fluid to motion. The cooling process starts with the development of momentum and thermal boundary layers along the cylindrical cold wall, followed by the intrusion of the cooled fluid into the bulk, and finally, by fluid stratification. A range of Hartmann, Rayleigh, and Prandtl numbers are studied for which the flow remains laminar in all stages. It is found that the increase of the magnetic field reduces the heat transfer rate and decelerates the cooling process. This can be attributed to the damping of the fluid motion by the magnetic field, which results in the domination of conduction over convection heat transfer. The increase of the Rayleigh number enhances heat transfer, but the cooling process lasts longer due to the higher temperature of the hot fluid. The flow deceleration and the reduction of heat transfer are less intense for fluids with low Prandtl number.