Magnetohydrodynamic thermal instability in a conducting fluid layer with throughflow

An analysis is made of the effect of vertical throughflow on the onset of thermal convection in a horizontal layer of an electrically conducting fluid contained between two rigid permeable plates and heated from below in the presence of a uniform vertical magnetic field. The constant throughflow is measured by Peclet number Q and at both boundaries heat flux is held constant. It is found that when both boundaries are perfectly electrically conducting, the critical value of Rayleigh number Rct at the onset of steady convection increases with increase in Q for given values of the magnetic parameter Rh, the Prandtl number p1 and the magnetic Prandtl number p2 with p1>p2p1>p2. It is observed that the magnetic field inhibits the onset of steady convection. The analysis further reveals that Rct is independent of the sign of Q. When the lower plate is electrically non-conducting and the upper plate is perfectly electrically conducting, Rct is greater than the corresponding value of Rct for perfectly conducting plates for given values of Q, Rh, p1 and p2. It is also found that the positive throughflow (Q>0Q>0) is more stabilizing than the negative one (Q<0)Q<0). The results are exemplified by considering some realistic cases e.g., liquid sodium and gallium.

► Explore the possibility of controlling magnetohydrodynamic thermal instability by throughflow.
► The layer is heated from below and heat flux at both the plates is held constant.
► Rtd attains its minimum value at a  =0 when walls are perfectly conducing if (Rhp2/14p1)≤8Rhp2/14p1)≤8.
► Lower wall non-conducting, upper wall conducting, Rtc occurs at a  =0 if p2⪡p1p2⪡p1, moderate value of Rh.
► Rtc is found to be independent of the sign of throughflow in the case of perfectly conducing walls.