Finite-amplitude instability of magnetohydrodynamic mixed convection flow of liquid metals in a vertical channel

Abstract

The study of mixed convective liquid metal flow under a magnetic field has good potential for designing the next generation of advanced magnetohydrodynamic (MHD) devices. Flow instabilities play a crucial role in understanding flow dynamics in different applications. This paper reports the finite-amplitude instability of MHD mixed convection flow of electrically conducting liquid metals in a vertical channel under a transverse magnetic field. The cubic Landau equation is derived to determine the subcritical/supercritical bifurcations in the flow. The weakly nonlinear stability results are examined for a good range of Ha and Pr in the vicinity and far from the linear stability critical point (bifurcation point) at Reynolds number Re = 5000. The finite-amplitude results give only the supercritical type of instability for the considered range of Ha and Pr. The equilibrium amplitude increases by increasing the strength of the applied magnetic field. The impact of the nonlinear interaction of different harmonic modes on friction coefficient, heat transfer rate, and wave speed is also examined for the linearly unstable region. The results show that the distorted mean flow's heat transfer rate is higher than that calculated by the laminar basic state. Like linear stability analysis, the nonlinear analysis shows that the applied magnetic field stabilizes the basic flow. The supercritical instability shows that the linearly unstable flow shows a smooth transition.