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Magneto-double diffusive convection in an electrically conducting-fluid-saturated porous medium with temperature modulation of the boundaries. (English) Zbl 1191.80006
Summary: Thermal instability in an electrically conducting two component fluid-saturated-porous medium has been investigated, considering temperature modulation of the boundaries. The porous medium is confined between two horizontal surfaces subjected to a vertical magnetic field; flow in the porous medium is characterized by Brinkman-Darcy model. Making linear stability analysis and applying perturbation procedure, the correction in the critical Darcy Rayleigh number is calculated. It is found that the correction in the critical Darcy Rayleigh number is a function of frequency of modulation, solute Rayleigh number, diffusivities ratio, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number and the non-dimensional group number $\chi$. Also the effects of various parameters on thermal instability have been studied; we found that these parameters may have stabilizing or destabilizing effects, thus may advance or delay the onset of convection. A comparison between the results from the present model has been made with that of Darcy model.
##### MSC:
 80A20 Heat and mass transfer, heat flow 76W05 Magnetohydrodynamics and electrohydrodynamics 76S05 Flows in porous media; filtration; seepage 76R50 Diffusion (fluid mechanics)