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Kumar, Rajeev
- A Characterization Theorem in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN
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.- Upper Bounds for the Complex Growth Rate of Thermohaline Convection of Veronis and Stern Types with Viscosity Variations
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Authors
Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN
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.