Thermal Convection of Micropolar Fluid in the Presence of Suspended Particles in Hydromagnetics

Abstract

The onset of instability is investigated in a micropolar fluid layer heated from below in the presence of suspended particles (fine dust) and uniform vertical magnetic field ${H}\left(0, 0, H\right)$. Using the Boussinesq approximation, the linearized stability theory and normal mode analysis method, the exact solutions are obtained for the case of two free boundaries. It is found that the presence of coupling between thermal and micropolar effects, the suspended particles number density, the magnetic field intensity and the micropolar coefficients bring oscillatory modes and over stability in the system which were non--existent in their absence. The behaviour of the Rayleigh numbers for the stationary convection and the case of over stability are computed numerically using Newton-Raphson method through the software Fortran-90 and Mathcad. The graphs show that Rayleigh number for the case of over stability and stationary convection increase with increase in magnetic field intensity ${H}\left(0, 0, H\right)$ and decrease with increase in micropolar coefficients (the dynamic microrotation viscosity $\kappa$ and coefficient of angular viscosity $\gamma'$), for a fixed wave-number, implying thereby the stabilizing effect of magnetic field intensity and destabilizing effect of micropolar coefficients on the thermal convection of micropolar fluids.