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Singh, Virender
- On Rotatory Hydrodynamic Triply Diffusive Convection in Porous Medium
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 113-117Abstract
Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for rotatory hydrodynamic triply diffusive convection in a porous medium is derived. It is analytically proved that the principle of the exchange of stabilities, in rotatory triply diffusive convection in a porous medium, is valid in the regime R1E1σ/2τ21π4 + R2E2σ/2τ22π4 + Ta/π2ΛDa-1 ≤ 1, where R1 and R2 are the concentration Raleigh numbers, and τ1 and τ2 are the Lewis numbers for the two concentration components respectively, Ta is the Taylor number, σ is the Prandtl number, Da is the Darcy number, E1 and E2 are constants.Keywords
Triply Diffusive Convection, Porous Medium, Darcy-Brinkman Model, the Principle of the Exchange of Stabilities, Taylor Number, Concentration Rayleigh Number.
- Linear Stability Analysis of Multicomponent Convection
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla – 171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 118-122Abstract
Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for multicomponent convection is derived.Keywords
Multicomponent Convection, The Principle of the Exchange of Stabilities, Oscillatory Motions, Complex Growth Rate, Concentration Rayleigh Number.- Heat and Mass Transfer in Three Dimensional Free Convective Oscillatory Flow in Porous Medium with Constant Heat and Mass Flux in Presence Radiation for an Optically Thin Fluid
Authors
1 Department of Mathematics, Government College, Shahpur (H.P) 176206, IN
2 Department of Mathematics, Government College, Jawalamukhi (H.P) 176031, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 175-184Abstract
A theoretical analysis of free convective flow of viscous incompressible fluid through a porous medium bounded by a flat porous plate subject to periodic suction and constant heat and mass flux has been presented. The flow becomes three dimensional due to variation of suction velocity in transverse direction. Analytical expression for velocity, temperature, concentration and skin friction are obtained using perturbation technique. Numerical solutions are obtained for different values Grash of number (Gr), mass Grashof number(Gc), Prandtl number (Pr), Schmidt number (Sc) and Radiation (R). It is found that non-dimensional velocity increases with increase of Gr, Gc and Sc and decreases with increase of R, non-dimensional temperature decreases with increasing of R, Concentration decreases with increase of Sc. and skin friction co-efficient increases with increase of Gr and R but effect of Gr is more than R.Keywords
Free Convection, Oscillatory Flow, Sinusoidal Suction, Mass Transfer, Radiation.- Thermal Instability of Ferromagnetic Fluid in the Presence of Hall Effect and Suspended Particle under Varying Gravity Field
Authors
1 Department of Mathematics, Govt. College, Haripur (Manali) (H,P.) – 175136, IN
2 Department of Mathematics, Jwalaji Degree College, Jwalamukhi (H,P.) – 176031, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-9Abstract
In this paper we consider theoretical investigation of the effect hall current and the suspended particle under varying gravity field on the thermal instability of ferromagnetic fluid heated from below. For a fluid layer between two free boundaries and exact solution is obtained using a linearized stability theory and normal mode analysis. A dispersion relation governing the effect of hall current and the suspended particle is obtained. For the case of stationary convection it is found that the magnetic field has a stabilizing the system when the gravity is increasing upward i.e. (λ>0), where as the hall current and suspended particle are found to have the destabilizing effect on the system when the gravity is increasing upward i.e. (λ>0). The critical Rayleigh numbers and wave numbers of the associated disturbances for the onset of stability as stationary convection are obtained. The principle of exchange of stabilities is not valid for the problem under consideration, whereas in the absence of Hall currents hence magnetic field, it is valid under certain conditions.
Keywords
Hall Currents, Suspended Particles, Ferromagnetic Fluid and Varying Gravity Field.- Upper Limits to the Complex Growth Rates in Triply Diffusive Convection in Porous Medium
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
2 Department of Physics, MLSM College, Sundernagar, H.P., IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-3Abstract
The paper mathematically establishes that the complex growth rate (pr,pi ) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer in porous medium (Darcy Model) with one of the components as heat with diffusivity , must lie inside a semicircle in the right- half of the (pr,pi)-plane whose centre is origin and radius equals √(R1+<R2)σ where R1 and R2 are the Raleigh numbers for the two concentration components with diffusivities k1 and k2 (with no loss of generality, k > k1> k2 ) and is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.Keywords
Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Porous Medium.- On the Characterization of Nonoscillatory Motions in Triply Diffusiveconvection in Porous Medium
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
Source
International Journal of Technology, Vol 4, No 1 (2014), Pagination: 1-3Abstract
The present paper mathematically establishes that 'the principle of the exchange of stabilities' for triply diffusive convection in porous medium (Darcy model) is valid in the regime (R_1 σ)/(2〖ι_1〗^2 π^4 )+(R_2 σ)/(2〖ι_2〗^2 π^4)≤1, where R_1 and R_2 are the Rayleigh numbers for the two concentration components, ι_1 and ι_2 are the Lewis numbers for the two concentration components and σ is the thermal Prandtl number. It is further proved that the above result is uniformly valid for any combination of rigid and free boundaries.