Veena Sharma

Thermosolutal convection of micropolar fluids in hydromagnetics

The thermosolutal convection in a layer of electrically conducting micropolar fluids heated and soluted from below in the presence of a uniform vertical magnetic field is considered. The presence of coupling between thermosolutal and micropolar effects may bring overstability in the system. The magnetic field also introduces oscillatory modes in the system and the Rayleigh number is found to increase with the increase in magnetic field. The possibility of oscillatory motions and the increase in Rayleigh number with increase in magnetic field is depicted graphically.

Hall Effect on Magneto-Thermal Stability of Rivlin-Ericksen Ferromagnetic Fluid Saturating A Porous Medium

This paper deals with the electrically conducting and numerical investigation of the effect of Hall currents on the thermal stability of a ferromagnetic viscoelastic fluid heated from below saturating porous medium. The rheology of the fluid in described by the Rivlin-Ericksenian. The boundaries are considered to be stress-free. The eigen-value problem obtained using linear stability theory and normal mode technique is solved numerically using the Galerkin technique and the software MATHEMATICA by assuming the trial functions satisfying the boundary conditions. A dispersion relation governing the effects of medium permeability, a uniform horizontal magnetic field, magnetization and Hall currents is derived. For the case of stationary convection, it is found that the magnetic field and magnetization have a stabilizing effect on the system, as such their effect is to postpone the onset of thermal instability, whereas the Hall currents are found to hasten the onset of convection under certain conditions.

Numerical Investigations of Electro-Thermal Convection in Dielectric Nanofluid Layer

The numerical investigations of a dielectric nanofluid under the simultaneous action of an Alternating Current electric field and a uniform adverse temperature gradient has been studied using the linear theory and normal mode analysis. The eigen-value problem is solved analytically and numerically using the Galerkin technique. Effect of various non-dimensional parameters on thermal Rayleigh number Ra for the stationary convection has been determined. The boundaries are considered to be stress-free. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability using the software-MATHEMATICA Version 5.2. Numerical results are presented graphically. The thermal Rayleigh number decreases linearly as the concentration Rayleigh number Rn increases. Moreover for stability motion, the value of thermal Rayleigh number Ra occurs only for negative values of Rea and it is positive. The value of critical thermal Rayleigh number Ra decreases with decreasing the value of Rea. It is observed that the role of electric field is not of much sinificance the convection in the fluid layer in case of stability motions. In case of stability, the thermal Rayleigh number is independent of Prandtl number and hence Prandtl number has no role to play.

Deformation due to expanding ring load in modified couple stress thermoelastic diffusion in time and frequency domain

ABSTRACT The two-dimensional problem of expanding ring load in a modified couple stress theory of thermoelastic diffusion with heat sources in time and frequency domains is investigated. The mathematical formulation prepared for thermoelastic diffusion solids with one and two relaxation times using Laplace and Hankel transforms. The displacements, stress components, temperature change, and chemical potential are obtained in a transformed domain. Numerical computation is performed for these quantities and the resulting quantities are shown graphically for the time and frequency domains. Comparisons are made with the results predicted by the two theories and different values of time and frequency. Particular cases of interest are also deduced.

A problem of thick circular plate in modified couple stress thermoelastic diffusion with phase-lags

Purpose The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model. Design/methodology/approach The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Findings The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter. Originality/value Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

Analytical/numerical investigations of Kelvin-Helmholtz instability of superposed non-viscous fluids in the presence of magnetic field

The instability of two immiscible superposed, non-viscous, electrically conducting and counter-streaming fluids with upper fluid layer lighter than the lower fluid layer in the presence of uniform magnetic field has been investigated numerically. Using the linear theory and normal mode analysis, the exact solutions of eigen value problem have been obtained for stress free bounding surfaces and the dispersion relation so obtained has been analysed to examine the effects of magnetic field and velocity of streaming fluids on the growth rates of the unstable mode of perturbation on the physical system. It has been found that the magnetic field has a slight stabilizing effect on the system; whereas the velocity of the counter-streaming fluids has a large enough stabilizing effect towards neutral stability.

Stability of Stratified Rivlin-Ericksen Fluid in the Presence of Horizontal Magnetic Field and Uniform Horizontal Rotation in Porous Medium

The influence of viscosity, viscoelasticity and medium permeability on the stability of stratified Rivlin-Ericksen viscoelastic fluid is examined for viscoelastic polymeric solutions in the simultaneous presence of a uniform horizontal magnetic field (H, 0, 0) and uniform horizontal rotation (Ω,0,0). These solutions are known as Rivlin-Ericksen fluids and their rheology is approximated by the Rivlin-Ericksen constitutive relations, proposed by Rivlin and Ericksen [13]. The effects of Coriolis forces on the stability is chosen along the direction of the magnetic field and transverse to that of the gravitational field (o,o,-g). The system is found to be stable for all wave numbers for stable stratifications and unstable for unstable stratifications for the stratifications in density, viscosity, viscoelasticity, medium permeability and medium porosity. The system can be completely stabilized by large enough magnetic field, which was unstable in the absence of magnetic field; provided the initial configuration is top-heavy density wise. The kinematic viscosity and kinematic viscoelasticity have damping effects on the growth rates with the increase in kinematic viscosity and kinematic viscoelasticity, respectively, for a fixed wave number. The medium permeability has enhancing effects on the growth rates with its increase for a fixed wave number. The above results have also been shown graphically.

Stability of Stratified viscoelastic Rivlin-Ericksen Fluid/Plasma in the presence of variable Horizontal Magnetic Field

A study has been made of the instability of an electrically conducting stratified viscoelastic Rivlin-Ericksen fluid/plasma arranged in a horizontal strata to include a variable horizontal magnetic field. Applying the linear stability theory and normal mode technique to a set of partial differential equations, the solutions of an eigen value problem have been obtained by assuming exponential vertical stratifications in density, neutral gas density, viscosity, viscoelasticity and magnetic field. Using these solutions, the dispersion relation so obtained has been analysed numerically. It has been found that viscosity, viscoelasticity, collisional frequency and magnetic field have stabilizing effects on the growth rates for unstable configuration under certain wave-number band.