Magnetic field effect on the cooling of a low-Pr fluid in a vertical cylinder

Abstract

Results of direct numerical simulations are presented for the transient and turbulent natural convection cooling of an initially isothermal quiescent liquid metal placed in a vertical cylinder in the presence of a vertical magnetic field. The electrically conductive low-Prandtl number fluid is put to motion when the cylindrical wall is suddenly cooled to a uniform lower temperature. For this particular cooling process, the flow is characterized by three sequential almost discrete stages: (a) development of momentum and thermal boundary layers along the cylindrical cold wall, (b) intrusion of the cooled fluid into the main fluid body, and (c) flow and thermal stratification. The selected Rayleigh numbers in the present study are high enough so that turbulent convection is established. The numerical results show that the magnetic field has no observable effect at the initial stage of the vertical boundary layer development and conduction heat transfer is favored during the intrusion stage. An interesting effect of the magnetic field during the stratification stage is the deceleration of the cooling process for low Rayleigh numbers and its acceleration for high ones. This dependence of the magnetic field effect on the Rayleigh number was found to be related to the cold vortices emanating from the vertical boundary layer. In contrast with the hydrodynamic cooling, the magnetic field was also found to accelerate the cooling near the bottom of the cylinder.