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Veena Sharma ¹, Abhilasha ², Sumit Gupta ³

Affiliations
1 Department of Mathematics $ Statistics, H.P.University, Shimla-5, IN
2 Govt. Degree College, Amb, Una (H.P.), IN
3 APG University, Solan (H.P.), IN

Abstract

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.

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Veena Sharma ¹, Priti Bala ¹, Sumit Gupta ¹, Radhe Shyam ¹

Affiliations
1 Department of Mathematics and Statistics, H.P. University, Shimla-5, IN

Abstract

An investigation is made on the onset of thermal instability in a triply diffusive three dimensional fluid layer in porous medium , since there are important fluid mechanical systems in which the density depends on three or more stratifying agencies having different diffusivities, in which the onset of convective instability in isothermal ternary and non-isothermal ternary fluids is termed as triple diffusion. Special attention is given to systems with k₁ >>k₂ , k₃ and p₁ >>K₂/K₃ where K_i is the molecular diffusivity of the ith component and Pis the molecular diffusivity of the ith component and p₁ is the thermal Prandtl number. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydrodynamic equations to derive a characteristic equation. For the stationary convection, the stable solute gradients are found to have stabilizing effects on the system, due to which the onset of instability is postponed and the medium permeability parameter has a destabilizing effect on the system..The presence of stable solute gradients and medium permeability parameter also introduce oscillatory modes which were nonexistent in their absence. The case of overstability (with increasing amplitude of perturbations) is also considered and the sufficient conditions for the non existence of stable solutions are derivedr. These analytical results are confirmed numerically and the effects of various parameters on the stability analysis for both the cases of stationary convection and overstability are depicted graphically using the software Mathematica version 2007.

Keywords

Thermal Instability, P₁, Thermal Prandtl Number, Solute Rayleigh Numbers, Medium Permeability.

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Shesh Prakash Maurya ¹, Ashima ¹, Sibadatta Das ¹, Nimerpreet Kaur ¹, Indira Bairy ², Sumit Gupta ²

Affiliations
1 SHKM Government Medical College, Mewat, Haryana, IN
2 Department of Microbiology, Kasturba Medical College, Manipal University, Madhav Nagar, Manipal, Karnataka, IN

Abstract

Bacterial diarrhoea is a major health problem in developing countries and travellers to these countries. Various herbal and traditional medicines have been tried to treat infectious diarrhoea, with variable success. Here, we screened different fruit juices for the possible anti-microbial activity against intestinal bacterial pathogens isolated from acute gastroenteritis cases. Seven fruit juices [apple, orange, pineapple, grape, pomegranate, sweet lime and lemon water] were tested against 11 bacterial enteropathogens including Vibrio cholerae, Salmonella spp. and Shigella spp. via agar diffusion method. Pomegranate juice showed the highest anti microbial activity against enteropathogens. The results with grape juice, orange juice and lemon water were also appreciable but variable with pH changes. Apple juice showed least and negligible activity. Pomegranate juice can provide a dual benefit of rehydration and anti bacterial therapy in infectious gastroenteritis.

Keywords

Diarrhoea, Fruit Juice, Pomegranate, Intestinal Pathogen.

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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, 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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