ISSN

2231-3915 (Online)
2231-3907 (Print)


Author(s): Jyoti Prakash, Sanjay Kumar Gupta, Renu Bala, Kanu Vaid

Email(s): jpsmaths67@gmail.com , sanjay6571@gmail.com

DOI: Not Available

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

Published In:   Volume - 4,      Issue - 1,     Year - 2014


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.


Cite this article:
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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DOI: 10.5958/2231-3915 


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