The Onset of Multi-Diffusive Convection Analyzed for Suspended Particles in a Rotating Dusty Porous Layer: A Brinkman Model

Abstract

Thermal convective instability of a horizontal layer of fluid heated from below has several applications in geophysics, earth science, and oceanography and extensive reviews of this subject can be found in Chandrasekhar [1]. The onset of multi-diffusive convection is analyzed to include the effects of suspended particles and rotation through a porous medium. In the present chapter, the Brinkman model is considered for the porous medium. The variations in fluid density are due to the variation in (n+1) stratifying components having different thermal and solute diffusivities. Linear stability analysis procedure along with normal mode method is employed to obtain a dispersion relation for the stationary convection and it is found that the parameters porosity, permeability and suspended particle have destabilizing effects whereas, rotation and Darcy-Brinkman number have stabilizing effects and the results are also shown both numerically and graphically. A sufficient condition for the validity of the principle of exchange of stabilities (PES) is also obtained using Rayleigh-Ritz and Cauchy-Schwartz inequality.