Stability of modulated-gravity-induced thermal convection in magnetic fields.
A stability analysis is presented of modulated-gravity-induced thermal convection in a heated fluid layer subject to an applied magnetic field. The nearest correction to the critical Rayleigh number for both single and multiple frequency oscillating-gravity components is obtained by solving the linearized magnetohydrodynamic equations using the small parameter perturbation technique. The correction depends on both the applied magnetic field and the oscillating frequency. In the absence of an applied magnetic field, the correction depends on the Prandtl number only when the exciting frequency is small. However, it asymptotically approaches zero as the frequency increases, with or without the presence of a magnetic field. The heated fluid layer is more stable with gravity modulation than with any type of wall temperature modulation. The difference becomes smaller with decreasing Prandtl number Pr. This finding is of critical importance in that ground-based experiments with appropriate wall temperature modulations may be conducted to simulate the oscillating-gravity effects on the onset of thermal convection in lower-Prandtl-number fluids. For conducting melts considered for microgravity applications, it is possible to apply an external magnetic field to further inhibit the onset of modulated-gravity-induced thermal convection. This effectiveness increases with the Hartmann number Ha. For large Ha, the nearest correction term R02 approximately Ha2 as the magnetic Prandtl number Pm<<1. However, R02 approximately Ha(4/3) for Ha>>1 and Pm>>1, provided that Ha<0.5pi(Pm/Pr(3/2)), which is satisfied by a majority of space melt experiments. Thus, under normal laboratory conditions applied magnetic fields are more effective in stabilizing a conducting fluid subject to an oscillating-gravity field than one subject to a constant field. If Ha>0.5pi(Pm/Pr(3/2)), R02 approximately -Ha2 for Ha>>1 and Pm>>1 and the magnetic field becomes less effective in stabilizing thermal convection driven by oscillating gravity than that driven by the constant gravity. This is in contrast with the existing studies on thermal convection stability in a magnetic field, which show that marginal stability is independent of Pm and always increases with increasing applied field.
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School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99163, USA.