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Research Papers: Forced Convection

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

[+] Author and Article Information
Palle Kiran

Assistant Professor
Department Mathematics,
Rayalaseema University,
Kurnool 518002, Andhra Pradesh, India
e-mail: kiran40p@gmail.com

B. S. Bhadauria

Professor
Department of Mathematics,
Faculty of Sciences,
Banaras Hindu University,
Varanasi 221005, Uttar Pradesh, India
e-mail: mathsbsb@yahoo.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 14, 2014; final manuscript received October 4, 2015; published online February 3, 2016. Assoc. Editor: Gennady Ziskind.

J. Heat Transfer 138(5), 051702 (Feb 03, 2016) (10 pages) Paper No: HT-14-1312; doi: 10.1115/1.4032329 History: Received May 14, 2014; Revised October 04, 2015

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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Figures

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Fig. 2

The characteristic curves representing the marginal stability limit with respect to overstable convection

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Fig. 1

Physical representation of the problem

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Fig. 3

(a) Finite amplitude results for oscillatory convection, variation of the nonlinear term coefficient, lr as a function of Pr for Ta = 5000, identifying the tricritical point where lr changes sign. For values of Pr below the tricritical point, the bifurcation is forward while for the above bifurcation is inverse. (b) Bifurcation diagram for super critical bifurcation given by steady solution. (c) Supercritical Hopf bifurcation.

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Fig. 4

Nu versus s for different values of (a) Pr and (b) Ta

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Fig. 5

Nu versus s for different values of (a) Pr, (b) Ta, (c) δ1, and (d) ωf

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Fig. 6

Nu versus s for different values of (a) Pr, (b) Ta, (c) δ1, and (d) ωf

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Fig. 7

(a) Comparison among different temperature profiles and (b) comparison between stationary and oscillatory case

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Fig. 8

Effects of resonance ωf and forcing frequency ω on Nu and A

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