A study of thermal instability driven by buoyancy force is carried out in an initially quiescent infinitely extended horizontal rotating fluid layer. The temperature at the boundaries has been taken to be time-periodic, governed by the sinusoidal function. A weakly nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the complex form of Ginzburg–Landau equation (CGLE), is calculated. The influence of external controlling parameters such as amplitude and frequency of modulation on heat transfer has been investigated. The dual effect of rotation on the system for the oscillatory mode of convection is found either to stabilize or destabilize the system. The study establishes that heat transport can be controlled effectively by a mechanism that is external to the system. Further, the bifurcation analysis also presented and established that CGLE possesses the supercritical bifurcation.

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# Weakly Nonlinear Oscillatory Convection in a Rotating Fluid Layer Under Temperature Modulation

Palle Kiran

,
Palle Kiran

Assistant Professor

Department Mathematics,

Rayalaseema University,

Kurnool 518002, Andhra Pradesh, India

e-mail: kiran40p@gmail.com

Department Mathematics,

Rayalaseema University,

Kurnool 518002, Andhra Pradesh, India

e-mail: kiran40p@gmail.com

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B. S. Bhadauria

B. S. Bhadauria

Professor

Department of Mathematics,

Faculty of Sciences,

Banaras Hindu University,

Varanasi 221005, Uttar Pradesh, India

e-mail: mathsbsb@yahoo.com

Department of Mathematics,

Faculty of Sciences,

Banaras Hindu University,

Varanasi 221005, Uttar Pradesh, India

e-mail: mathsbsb@yahoo.com

Search for other works by this author on:

Palle Kiran

Department Mathematics,

Rayalaseema University,

Kurnool 518002, Andhra Pradesh, India

e-mail: kiran40p@gmail.com

B. S. Bhadauria

Department of Mathematics,

Faculty of Sciences,

Banaras Hindu University,

Varanasi 221005, Uttar Pradesh, India

e-mail: mathsbsb@yahoo.com

*J. Heat Transfer*. May 2016, 138(5): 051702 (10 pages)

**Published Online:**February 3, 2016

Article history

Received:

May 14, 2014

Revised:

October 4, 2015

Citation

Kiran, P., and Bhadauria, B. S. (February 3, 2016). "Weakly Nonlinear Oscillatory Convection in a Rotating Fluid Layer Under Temperature Modulation." ASME. *J. Heat Transfer*. May 2016; 138(5): 051702. https://doi.org/10.1115/1.4032329

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