Journal :   International Journal of Technology

Volume No. :   4

Issue No. :  1

Year :  2014

Pages :   210-213

ISSN Print :  2231-3907

ISSN Online :  2231-3915


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A Semi-circle Theorem in Triply Diffusive Convection



Address:   Jyoti Prakash*, Sanjay Kumar Gupta, Renu Bala, Kanu Vaid
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
*Corresponding Author
DOI No:

ABSTRACT:
The paper mathematically establishes that the complex growth rate (p_(r ),p_i ) 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 ?, must lie inside a semicircle in the right- half of the (p_(r ),p_i )-plane whose centre is origin and radius equals v((R_1+R_2)s-27/4 p^4 t_2^2 ) where R_1 and R_2 are the Rayleigh numbers for the two concentration components with diffusivities ?_1 and ?_2 (with no loss of generality, ?>?_1>?_2 ) and s 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.
KEYWORDS:
Triply Diffusive convection; Oscillatory motions; complex growth rate; Principle of the exchange of Stability.
Cite:
Jyoti Prakash, Sanjay Kumar Gupta, Renu Bala, Kanu Vaid. A Semi-circle Theorem in Triply Diffusive Convection. Int. J. Tech. 4(1): Jan.-June. 2014; Page 210-213
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