Effect of Dust Particles on Rotating Micropolar Fluid Heated From Below Saturating a Porous Medium

This paper deals with the theoretical investigation of the effect of dust particles on a layer of rotating micropolar fluid heated from below saturating a porous medium. A dispersion relation is obtained for a flat fluid layer contained between two free boundaries using a linear stability analysis theory and normal mode analysis. The principle of exchange of stabilities is found to hold true for the micropolar fluid saturating a porous medium heated from below in the absence of dust particles, rotation and micropolar heat conduction parameter. The oscillatory modes are introduced due to the presence of the dust particles and rotation, which were non-existence in their absence. The presence of micropolar heat conduction parameter may also introduce oscillatory modes. For the case of stationary convection, the effect of various parameters like medium permeability, rotation, dust particles, coupling parameter, micropolar coefficient (A) and micropolar heat conduction parameter has been analyzed. The thermal Rayleigh number for the onset of instability is also determined numerically and results are depicted graphically. In the present paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability

Ferromagnetic Convection in a Rotating Medium with Magnetic Field Dependent Viscosity. A Correction Applied

The effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferrofluid layer, heated from below, has been investigated in the simultaneous presence of a uniform vertical magnetic field and a uniform vertical rotation. A correction is applied to Vaidyanathan et al. (Ind. J. Pure Appl. Phy., 2001, 40, 159165), which is very important in order to predict the correct behavior of MFD viscosity. A linear stability analysis has been carried out for stationary modes and oscillatory modes separately. The critical wave number and critical Rayleigh number for the onset of instability, for the case of free boundaries, are determined numerically for sufficiently large values of the magnetic parameter ??1. Numerical results are obtained and are illustrated graphically. It is shown that MFD viscosity has a destabilizing effect on the system for the case of stationary mode and stabilizing effect for the case of oscillatory mode, whereas magnetization has a destabilizing effect. Further, it is also shown that rotation has a stabilizing effect on the system

Ferromagnetic convection in a rotating ferrofluid saturated porous layer

The effect of Coriolis force on the onset of ferromagnetic convection in a rotating horizontal ferrofluid satd. porous layer in the presence of a uniform vertical magnetic field is studied. The boundaries are considered to be either stress free or rigid. The modified Brinkman-​Forchheimer-​extended Darcy equation with fluid viscosity different from effective viscosity is used to characterize the fluid motion. The condition for the occurrence of direct and Hopf bifurcations is obtained anal. in the case of free boundaries, while for rigid boundaries the eigenvalue problem has been solved numerically using the Galerkin method. Contrary to their stabilizing effect in the absence of rotation, increasing the ratio of viscosities, Λ, and decreasing the Darcy no. Da show a partial destabilizing effect on the onset of stationary ferromagnetic convection in the presence of rotation, and some important observations are made on the stability characteristics of the system. Moreover, the similarities and differences between free-​free and rigid-​rigid boundaries in the presence of buoyancy and magnetic forces together or in isolation are emphasized in triggering the onset of ferromagnetic convection in a rotating ferrofluid satd. porous layer. For smaller Taylor no. domain, the stress-​free boundaries are found to be always more unstable than in the case of rigid boundaries. However, this trend is reversed at higher Taylor no. domain because the stability of the stress-​free case is increased more quickly than the rigid case

Effect of Horizontal Magnetic Field and Horizontal Rotation on Thermosolutal Stability of a Dusty Couple-Stress Fluid through a Porous Medium: a Brinkman Model

The problem of the onset of double diffusive convection in a couple-stress fluid saturated with a porous medium is studied under the effects of magnetic field, rotation and suspended dust particles. Linear stability analysis based on the method of perturbations of infinitesimal amplitude is performed using the normal mode technique for the case of free-free boundaries. The governing hydrodynamic and hydromagnetic equations of fluid flow are governed by the Brinkman model. The stability analysis examines the effects of various embedded parameters for the stationary mode both analytically and graphically. The principle of exchange of stabilities holds good in the absence of solute gradient parameter. Also, the sufficient conditions responsible for the existence or non-existence of overstability are obtained

Effect of Rotation on Double-Diffusive Convection in a Magnetized Ferrofluid with Internal Angular Momentum

This paper deals with the theoretical investigation of the effect of rotation in a magnetized ferrofluid with internal angular momentum, heated and soluted from below subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset of convection. The influence of various parameters like rotation, solute gradient, magnetization and internal angular momentum parameters (i.e. coupling parameter, spin diffusion parameter and heat conduction parameter) has been analyzed on the onset of stationary convection. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter M1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferrofluid with internal angular momentum heated from below in the absence of rotation, coupling between vorticity and spin, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the rotation, coupling between vorticity and spin, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability

Effects of Radiation Absorption and Thermo-diffusion on MHD Heat and Mass Transfer Flow of a Micro-polar Fluid in the Presence of Heat Source

An analysis of the heat and mass transfer effects on an unsteady flow of a micro-polar fluid over an infinite moving permeable plate in a saturated porous medium in the presence of a transverse magnetic field, radiation absorption and thermo-diffusion were studied. The governing system of partial differential equations was transformed to dimensionless equations using suitable dimensionless variables. The dimensionless equations were then solved analytically using perturbation technique to obtain the expressions for the velocity, micro-rotation, temperature and concentration. With the help of graphs, the effects of the various important parameters such as the translational velocity, micro-rotational velocity, temperature and concentration fields within the boundary layer entering into the problem were discussed. Also the effects of the pertinent parameters on the skin friction coefficient, couple stress coefficient and rates of heat and mass transfer in terms of the Nusselt number and Sherwood numbers were presented numerically in tabular form. The results showed that the observed parameters have a significant influence on the flow, heat and mass transfer