Combined effect of temperature and gravity modulations on the onset of magneto-convection in weak electrically conducting micropolar liquids

Abstract

The combined effect of time-periodic boundary temperature (TBT, also called temperature modulation) and time-periodic body force (TBF, also called gravity modulation) of small amplitude on magneto-convection in a micropolar liquid is investigated by making a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of subcritical motions. The individual results of TBT and TBF are obtained as limiting cases of the present study. The Venezian [1] approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitudes of TBT and TBF. In the case of synchronous TBT and TBF for moderate frequency values, the role of Prandtl, Chandrasekhar, Rayleigh numbers, micropolar heat conduction parameters and ratio of amplitudes in inducing subcritical instability is delineated. The TBF and synchronous TBT are shown to give rise to subcritical instability. The system is shown to be most stable with respect to asynchronous TBT and TBF. Comparison is made between the effects of temperature, gravity and combined (temperature + gravity) modulations.