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Natural and Mixed Convection

Nonlinear Thermal Instability in a Rotating Viscous Fluid Layer Under Temperature/Gravity Modulation

[+] Author and Article Information
B. S. Bhadauria

Department of Applied Mathematics,  Babasaheb Bhimrao Ambedkar University, Lucknow, Indiamathsbsb@yahoo.com

P. G. Siddheshwar

Department of Mathematics,  Bangalore University, Central College Campus, Bangalore, Indiamathdrpgs@gmail.com

Om P. Suthar

Department of Mathematics,  Bangalore University, Central College Campus, Bangalore, Indiaompsuthar@aol.com

J. Heat Transfer 134(10), 102502 (Aug 07, 2012) (9 pages) doi:10.1115/1.4006868 History: Received May 17, 2011; Revised May 16, 2012; Published August 06, 2012; Online August 07, 2012

In the present paper, the effect of time-periodic temperature/gravity modulation on the thermal instability in a rotating viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of modulation, which has been assumed to be small. The amplitude equation, viz., the Ginzburg–Landau equation, for the stationary mode of convection is obtained and using the same, the effect of temperature/gravity modulation on heat transport has been investigated. The stability of the system is studied and the stream lines are plotted at different slow times as a function of the amplitude of modulation, Rossby number, and Prandtl number. It is found that the temperature/gravity modulation can be used as an external means to augment/diminish heat transport in a rotating system. Further, it is shown that rotation can be effectively used in regulating heat transport.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Physical configuration of the temperature modulation problem

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Figure 2

Physical configuration of the gravity modulation problem

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Figure 3

Nu versus τ for temperature modulation, for different values of Ro and Pr with δ1  = 0.05, ω*  = 5

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Figure 4

Stream lines for Ro = 0.1 (- -) and Ro = 0.5 (—) in the OPM case (δ1  = 0.05, ω*  = 5, Pr = 7)

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Figure 5

Nu versus τ for gravity modulation case for different values of Ro and Pr with δ2  = 0.05, ω*  = 5

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Figure 6

Stream lines for Ro = 0.1 (- -) and Ro = 0.5 (—) in the gravity modulation case (δ2  = 0.05, ω*  = 5, Pr = 7)

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