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Prakash, Jyoti
- 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.- On the Onset of Stationary Convection in Double-Diffusive Binary Viscoelastic Fluid Saturated Anisotropic Porous Layer
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla 171005, IN
2 Department of Physics, M.L.S.M. College, Sunder-Nagar, Distt. Mandi (H.P.), IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 223-226Abstract
Linear stability of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer has been studied analytically. A sufficient condition for the occurrence of stationary convection has been derived in terms of the parameters of the system alone. It is further proved the above result is uniformly valid for any combination of the bounding surfaces.Keywords
Double-Diffusive Convection, Viscoelastic Fluid, The Principle of the Exchange of Stabilities, Porous Medium.- A Characterization Theorem in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations
Authors
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN
Source
International Journal of Technology, Vol 6, No 2 (2016), Pagination: 81-86Abstract
The paper mathematically establishes that magnetohydrodynamic triply diffusive convection, with variable viscosity and with one of the components as heat with diffusivity κ, cannot manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R1 and R2, the Lewis numbers τ1 and τ2 for the two concentrations with diffusivities k1 and k2 respectively (with no loss of generality κ > κ1 > κ2), μmin (the minimum value of viscosity μ in the closed interval [0,1]) and the Prandtl number σ satisfy the inequality R1 + R2 ≤ 27π4/4{μmin+(τ1+τ2)/σ/1+τ1/τ22 provided D2μ is positive everywhere. It is further proved that this result is uniformly valid for any combination of rigid and/or free perfectly conducting boundaries.Keywords
Triply Diffusive Convection, Variable Viscosity, Concentration Rayleigh Number, Oscillatory Motion, Initially Bottom Heavy Configuration and Chandrasekhar Number.- An Energy Relationship in Multicomponent Convection Problem
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: 99-102Abstract
analogous to magnetohydrodynamic thermohaline convection problem of Veronis (1965) type has been established. It is shown that the total kinetic energy associated with a disturbance exceeds the sum of its total magnetic and concentration energies in the parameter regime Qσ1/π2 + R1σ/4τ21π4 + R2σ/4τ22π4 + ⋯+ Rn-1σ/τ2n-1π4 ≤ 1, where Q,σ,σ1,τ1,τ2,…,τn-1,R1,R2,…,Rn-1 represent Chandrasekhar number, Prandtl number, magnetic Prandtl number, Lewis number for first concentration component, Lewis number for second concentration component, Lewis number for (n − 1)th concentration component, concentration Rayleigh number for first component, concentration Rayleigh number for second component, concentration Rayleigh number for (n - 1)th component respectively. Further, this result is uniformly valid for any combination of rigid or free boundaries whether perfectly conducting or insulating.Keywords
Multicomponent Convection, Chandrasekhar Number, Lewis Number, Prandtl Number, Rayleigh Number.- Characterization of Magnetorotatory Thermohaline Instability in Porous Medium:Darcy Model
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: 32-36Abstract
The present paper prescribes upper bounds for oscillatory motions of neutral or growing amplitude in magnetorotatory thermohaline configurations of Veronis (Veronis, G., J. Mar. Res., 23(1965)1) and Stern types (Stern, M.E., Tellus 12(1960)172) in porous medium (Darcy model) in such a way that also result in sufficient conditions of stability for an initially bottom-heavy as well as initially top-heavy configuration.
Keywords
Thermohaline Instability, Oscillatory Motions, Initially Bottom-Heavy Configuration, Initially Topheavy Configuration, Porous Medium.- 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.- Upper Bounds for the Complex Growth Rate of Thermohaline Convection of Veronis and Stern Types with Viscosity Variations
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: 1-4Abstract
Upper bounds for the complex growth rate of an arbitrary oscillatory perturbation which may be neutral or unstable of thermohaline convection of Veronis (G.Veronis, J.MarineRes., 23, (1965) 1-17) type with the viscosity variation effects included heated from below are obtained which in particular yield sufficient condition for the validity the "principle of the exchange of stabilities" for this configuration. Similar results are also obtained for thermohaline convection of Stern (ME Stern, Tellus, 12,(1960), 171-175) type with the viscosity variation effect included. The results obtained herein are uniformly valid for all combinations of dynamically free and rigid boundaries.
Keywords
Thermohaline Instability, Veronis Type, Stern Type, Oscillatory Motions, Variable Viscosity.- 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.
Keywords
Triply Diffusive Convection, Nonoscillatory Motions, Principle of the Exchange of Stabilities, Concentration Rayleigh Number, Porous Medium, Darcy Model.- A Semi-Circle Theorem in Triply Diffusive Convection
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: 1-4Abstract
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 with one of the components as heat with diffusivity k, must lie inside a semicircle in the right- half of the (Pr, Pi)-plane whose centre is origin and radius equals
√(R1+R2)σ-27/4π4τ22
where R1 and R2are the Rayleigh numbers for the two concentration components with diffusivities κ1and κ2(with no loss of generality, κ > κ1> κ2) and σ is the Prandtl number. The bounds obtained herein, in particular, yield a sufficient condition for the validity of 'the principle of the exchange of stability'. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.