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An Energy Relationship in Multicomponent Convection Problem


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

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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 Qσ12 + R1σ/4τ21π4 + R2σ/4τ22π4 + ⋯+ Rn-1σ/τ2n-1π4 ≤ 1, where Q,σ,σ112,…,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.
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  • An Energy Relationship in Multicomponent Convection Problem

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Authors

Jyoti Prakash
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
Pankaj Kumar
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
Shweta Manan
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

Abstract


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 Qσ12 + R1σ/4τ21π4 + R2σ/4τ22π4 + ⋯+ Rn-1σ/τ2n-1π4 ≤ 1, where Q,σ,σ112,…,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.