Journal :   International Journal of Technology

Volume No. :   6

Issue No. :  2

Year :  2016

Pages :   81-86

ISSN Print :  2231-3907

ISSN Online :  2231-3915


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A Characterization Theorem in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations



Address:   Jyoti Prakash, Rajeev Kumar*
Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005
*Corresponding Author
DOI No: 10.5958/2231-3915.2016.00012.2

ABSTRACT:
The paper mathematically establishes that magnetohydrodynamic triply diffusive convection, with variable viscosity and with one of the components as heat with diffusivity ?, cannot manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R_1 and R_2, the Lewis numbers t_1 and t_2 for the two concentrations with diffusivities ?_1 and ?_2 respectively (with no loss of generality ?> ?_(1 )> ?_2), µ_min (the minimum value of viscosity µ in the closed interval [0,1]) and the Prandtl number s satisfy the inequality R_1+R_2=(27p^4)/4 {(µ_min+((t_1+t_2 ))/s)/(1+t_1/(t_2^2 ))} provided D^2 µ 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.
Cite:
Jyoti Prakash, Rajeev Kumar. A Characterization Theorem in Magnetohydrodynamic Triply Diffusive Convection with Viscosity Variations. Int. J. Tech. 2016; 6(2): 81-86.
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