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Z. Naturforsch. 67a, 1 – 9
(2012)
doi:10.5560/ZNA.2011-0045
Gravity Modulation of Thermal Instability in a Viscoelastic Fluid Saturated Anisotropic Porous Medium
1 Department of Applied Mathematics and Statistics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
2 Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005, India
3 Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PC 123, Al Khod, Muscat, Sultanate of Oman
Received November 22, 2010 / revised June 22, 2011
Reprint requests to: B. S. B.; E-mail:
drbsbhadauria@rediffmail.com
The present paper deals with a thermal instability problem in a viscoelastic fluid saturating an anisotropic porous medium under gravity modulation. To find the gravity modulation effect, the gravity field is considered in two parts: a constant part and an externally imposed time-dependent periodic part. The time-dependent part of the gravity field, which can be realized by shaking the fluid, has been represented by a sinusoidal function. Using Hill's equation and the Floquet theory, the convective threshold has been obtained. It is found that gravity modulation can significantly affect the stability limits of the system. Further, we find that there is a competition between the synchronous and subharmonic modes of convection at the onset of instability. Effects of various parameters on the onset of instability have also been discussed.
Key words: Viscoelastic Fluid; Thermal Rayleigh Number; Gravity Modulation; Anisotropic Porous Medium; Floquet Theory.