Magnetohydrodynamic mixed convection flow of liquid metals in a vertical channel: A stability analysis

Abstract

The impact of applied magnetic field on liquid metal flows has good prospects for the industry. For a better understanding of flow dynamics, the stability analysis of liquid metal flows through a confined transverse magnetic field is of fundamental importance in designing advanced magnetohydrodynamic (MHD) devices for the next generation. In this paper, we report the linear stability analysis of mixed convection flow of electrically conducting liquid metals with low Prandtl number (Pr) in a vertical channel under a transverse magnetic field. The flow is described by quasi-static MHD approximation. The instability properties are examined numerically through a spectral collocation method. The influence of magnetic field on instability mechanism is examined for a good range of Pr. The results demonstrate that the growth of the infinitesimal disturbance decreases with increasing strength of the applied magnetic field due to the effective Lorentz force exerted on the flow, i.e., stability of the flow increases. In contrast, the stability of the basic flow decreases on increasing the value of Pr, except for a small range of Pr, where it increases. The kinetic energy balance shows that for very small values of Pr, the shear instability dominates the flow, whereas for relatively larger values of Pr, thermal-buoyant instability plays a significant role in the instability mechanism. The dissipation of energy in the kinetic energy balance occurs prominently due to the presence of the applied magnetic field. The secondary flow pattern shows that the applied magnetic field suppresses the disturbance in the vicinity of channel walls. In contrast, a decrease in thermal diffusivity provokes instability by inviting a strong disturbance cell in the middle portion of the channel. The energy dissipation in the kinetic energy balance occurs mainly due to the presence of the magnetic field.