Effect of Gravity Modulation on the Onset of Rayleigh-Bénard Convection in a Weak Electrically Conducting Couple Stress Fluid with Saturated Porous Layer

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The effect of time-periodic body force (TBF, also called gravity modulation) of small amplitude in a weak electrically conducting couple stress fluid with saturated porous layer is investigated by using a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number. The Venezian approach is adopted in arriving at the critical Rayleigh and wave number for small amplitudes of TBF. The effect of roles of Couple stress parameter, Hartmann number, Darcy number, Porous parameter and Prandtl number on the onset of convection is studied. It is found that TBF leads to delay in convection. Also the results suggest that instead of taking electrically non-conducting fluid it is better to consider electrically conducting fluid with weak electrical conductivity as this ensures a stable environment in the presence of a magnetic field. The system is most stable with respect to TBF.