Linear and Weakly Nonlinear Analyses of Magneto-Convection in a Sparsely Packed Porous Medium under Gravity Modulation

This paper deals with the linear stability analysis and weakly non-linear analysis of Magneto-convection in a sparsely packed porous medium with constant vertical Magnetic field and gravity modulation. A linear stability analysis reported here and shows that the gravity modulation has significant effect on the stability limits of the system. The gravity modulation is know to have effect and is treated by a perturbation expansion in powers of the amplitude of modulation. The shift in the critical Rayleigh number is evaluated and depends on the prandtl number and frequency of modulation, using the Venezian method. It is also shown that the onset of convection can be advance or delay by the regulation of various parameters. Weakly nonlinear analysis is performed based on the method of power series, where the disturbance is expressed in terms of power series. A nonlinear Ginzburg-Landau equation to investigate the three different types of gravity modulation on heat transfer is derived as part of this work. Heat transfer have been shown to depend on Nusselt number, further the effect of different types of parameter on heat transport have been studied graphically. Nusselt number graph is also shown for different parameter and explain in detail. The effect of magnetic prandtl number and Chandrasekhar number are stabilize the system. The control of convection is a major issue in systems with fluids as a working media. This is all the more difficult if the fluid system is housed in a porous medium. The paper presents three mechanisms of controlling onset of convection and thereby the heat transfer in such fluid systems. In order the modulation effect is effective in its role, we have considered the system to be a fluid-saturated porous media.