Thermal convection of micropolar fluid in the presence of suspended particles in rotation

Abstract

A study has been made of the convection of micropolar fluids heated from below in the presence of suspended particles (fine dust) and uniform vertical rotation Ω ­(0; 0;­ Ω ). The effect of Coriolis forces on the stability is chosen along the direction of the gravitational field. It is found that the presence of coupling between thermal and micropolar effects, rotation parameter and suspended particles may introduce overstability in the system. Using the Boussinesq approximation, the linearized stability theory and normal mode analysis, the exact solutions are obtained for the case of two free boundaries. Graphs have been plotted by giving numerical values to the parameters accounting for rotation Ω­ (0; 0;­ Ω ­) and the dynamic microrotation viscosity kappa and coefficient of angular viscosity γ' to depict the stability characteristics, for both the cases of stationary convection and overstability. It is found that Rayleigh number for the case of overstability and stationary convection increases with increase in rotation parameters and decreases with increase in micropolar coefficients, for a fixed wave number, showing thereby the stabilizing effect of rotation parameters and destabilizing effect of micropolar coefficients on the thermal convection of micropolar fluids. Thus there is a competition between the stabilizing effect of rotation parameters and destabilizing effect of micropolar coeffcients and the suspended particles. It is also found from the graphs that the Rayleigh number for the case of overstability is always smaller than the Rayleigh number for the case of stationary convection, for a fixed wave number.