0
Natural and Mixed Convection

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

[+] Author and Article Information

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

## Abstract

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.

<>

## Figures

Figure 1

Physical configuration of the temperature modulation problem

Figure 2

Physical configuration of the gravity modulation problem

Figure 3

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

Figure 4

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

Figure 5

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

Figure 6

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

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections