Research Journal of Science and Technology

Veena Sharma ¹, Sumit Gupta ²

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171 005, IN
2 Department of Mathematics, Govt. Degree College Diggal Distt. Solan-173 218, IN

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) in a porous medium. 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, medium permeability 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) medium permeability, dynamic microrotation viscosity K 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 parametre and decreases with increase in micropolar coefficients and medium permeability, for a fixed wave number, showing thereby the stabilizing effect of rotation parametre , destabilizing effect of micropolar coefficients and medium permeability on the thermal convection of micropolar fluids.

Keywords

Micropolar Fluid, Rotation, Suspended Particles (Fine Dust), Medium Permeability, Microrotation, Coefficient of Angular Viscosity.

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Veena Sharma ¹, Kavita ², Sumit Gupta ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, IN
2 Department of Mathematics, Govt. Degree College Diggal, Distt. Solan (H.P), IN

Abstract

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.

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Veena Sharma ¹, Ashwini Kumar ¹, Abhilasha ², Abhishek Sharma ³

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, IN
2 SDWG Govt. College Beetan, Distt. Una (H.P), IN
3 Govt. College Beetan, Distt. Una (H.P), IN

Abstract

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 R_a 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 R_n increases. Moreover for stability motion, the value of thermal Rayleigh number R_a occurs only for negative values of R_ea and it is positive. The value of critical thermal Rayleigh number R_a decreases with decreasing the value of R_ea. 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.

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Veena Sharma ¹, Renu Kumari ¹, Sumit Gupta ¹, Radhe Shyam ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171 005, IN

Abstract

Quantum effects on the Rayleigh-Taylor Instability in an inhomogeneous stratified incompressible, viscoelastic Walters' (model B') fluid/plasma are investigated. The linear growth rate is derived for the case where a plasma with exponential density, viscosity, viscoelasticity and quantum parameter distribution is confined between two rigid planes at z=0, z=d. The solution of the linearized equations of the system together with the boundary conditions leads to derive the dispersion relation (the relation between the normalized growth rate and square normalized behavior wave number) using normal mode technique to explain the roles that play the variables of the problem. The behavior of growth rates with respect to the quantum effect and kinematic viscoelasticity are examined in the presence of kinematic viscosity.

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Veena Sharma ¹, Sumna Devi ¹, Anukampa ¹, Monika Sharma ²

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, IN
2 ABVGIET, Pragatinagar, Shimla (H.P), IN

Abstract

The numerical investigations of a viscoelastic fluid layer to include the effect of AC electric field on the onset of instability heated from below saturating a porous media for the free-free boundaries has been studied. The theology of the fluid is described by the Maxwell model. In the Stationary convection it is observed that Maxwellian fluid acts like ordinary fluid, since the viscoelasticity parameter vanishes with the vanishing of the growth rate. The eigen-value problem obtained using linear stability theory and normal mode technique is solved numerically using the software MATHEMATICA by assuming the trial functions satisfying the boundary conditions. For the case of stationary convection electric Rayleigh number and Darcy number both have destabilizing effect on the stability of the system. Also for the over stability, the stress-relaxationtime parameter has destabilising effect on the stability of the system.

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