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

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

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

A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source

Rayleigh�Bénard convection in nanoliquids is studied in the presence of volumetric heat source. The present analytical work concerns twenty nanoliquids. Carrier liquids considered are water, ethylene glycol, engine oil and glycerine and with them five different nanoparticles considered are copper, copper oxide, silver, alumina and titania. Expression for the thermophysical properties of the nanoliquids is chosen from phenomenological laws or mixture theory. Heat source is characterized by an internal nanoliquid Rayleigh number (Formula presented.). Heat source adds to the energy of the system and hence an advanced onset is observed in this case compared to the problem with no heat source. In the case of heat sink, however, heat is drawn from the system leading to delay in onset. The individual effect of all the nanoparticles is to advance convection. Enhanced heat transport situation is observed in each of the nanoliquids with engine-oil-silver transporting maximum heat and water-titania the least. Additional Fourier modes are found not to have any profound effect on the results predicted by minimal modes. The connection between the Lorenz model and the Ginzburg�Landau model is clearly shown in the paper. © 2017 Korean Society for Computational and Applied Mathematic