International Journal of Technology

Jyoti Prakash ¹, Rajeev Kumar ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, IN

Abstract

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), μ_min (the minimum value of viscosity μ in the closed interval [0,1]) and the Prandtl number σ satisfy the inequality R₁ + R₂ ≤ 27π⁴/4{μ_min+(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.

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Jyoti Prakash ¹, Rajeev Kumar ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, IN

Abstract

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.

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