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Dhiman, Joginder Singh
- Quantum Effects on the Magnetogravitational Instability of Viscoelastic Fluid through a Porous Medium
Authors
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 199-205Abstract
In the present analysis, the effect of quantum corrections on the gravitational instability of a viscoelastic fluid through porous medium in the presence of uniform magnetic field has been studied in the transverse and longitudinal mode of wave propagation. For the mathematical formulation of the physical problem Generalized Hydrodynamic and Hass model have been used. A general dispersion relation has been derived by using the normal mode analysis. The general dispersion relation is discussed separately for both the modes of wave propagation under the strongly and weakly coupling limits. It is found that the porosity of the medium and quantum effects modifies the Jeans criterion of instability for both the modes of wave propagation under the strongly and weakly coupling limits. Further, the effects of various parameters on the growth rate of gravitational instability has been numerically studied and depicted graphically.
- On the Effect of Non-Uniform Magnetic field on the Jeans Instability of a Viscoelastic Medium
Authors
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 7-12Abstract
In the present paper the problem of Jeans instability of a self gravitating viscoelastic medium in the presence of nonuniform magnetic field for both longitudinal and transverse mode of wave propagation under the kinetic and hydrodynamic limits has been investigated, using the generalized hydrodynamic model. It is found that magnetic field has no effect on the Jeans criterion for the onset of gravitational instability in case of longitudinal mode of wave propagation, whereas it modifies the Jeans criterion in the case of transverse mode of wave propagation and has stabilizing effect on the onset of instability. Further, it is observed that the magnetic field has no effect on the growth rate of Jeans instability of a viscoelastic medium. The effects of shear viscosity, bulk viscosity and Mach number on the Jeans criterion and on the growth rate of Jeans instability have also been studied numerically and the obtained results are depicted graphically, for both strongly coupled plasma (SCP) and weakly coupled plasma (WCP).Keywords
Jeans Instability, Viscoelastic Medium, Non-Uniform Magnetic Field, Wave Propagation, Coupled Plasma.- On the Effect of Non-Uniform Temperature Gradients on the Stability of Modified Thermal Convection Problem
Authors
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla (H.P.)-171005, IN
2 Govt. Degree College, Sunni, Distt. Shimla (H.P.)-171301, IN
3 Govt. Degree College, Kullu (H.P.)-175101, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-6Abstract
The aim of the present paper is to study the effect of non-uniform basic temperature gradients on the onset of modified thermal convection in a layer of fluid heated from below for different combinations of rigid and dynamically free boundary conditions. It is shown that the principle of exchange of stabilities (PES) is valid when the temperature gradient is monotonically decreasing upward, which means that the instability sets in as stationary mode. The expressions for the Rayleigh numbers for each combination of rigid and dynamically free boundary conditions for the stationary case of instability are derived using Galerkin method. The effects of non-uniform temperature gradients and the modification factor which arises due to modified theory of Banerjee et al on the instability are studied from the values of the critical Rayleigh numbers calculated numerically for various temperature profiles and the coefficient of specific heat variation due to temperature variation for the given values of other parameters. It is observed from these values that the Cubic temperature profile is more stabilizing than the inverted parabolic temperature distribution profile. Further, it is also found that the critical Rayleigh numbers for thermally insulating boundaries are lower than those for the corresponding isothermal cases.
Keywords
Thermal Convection, Modified Theory, Temperature Gradient, Stationary Convection, Galerkin Method, Rayleigh Numbers, Boundary Conditions.- Onset of Triply-Diffusive Convection in a Fluid Layer with Suspended Particles and Temperature Dependent Viscosity
Authors
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-5Abstract
The present paper mathematically investigates the triply-diffusive convection problem with suspended particles by considering the viscosity to be temperature dependent. The temperature gradient is considered to be destabilizing whereas the solute gradients may be stabilizing or destabilizing. A sufficient condition for the validity of principle of exchange of stabilities (PES) is obtained and a bound for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable, is derived for this general problem. Various consequences of the above results are discussed and the analogous results under the individual effect of suspended particles, solute gradients and viscosity variations are also deduced.