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RESEARCH PAPERS: Natural and Mixed Convection

# On the Role of Coriolis Force in a Two-Dimensional Thermally Driven Flow in a Rotating Enclosure

[+] Author and Article Information

Department of Applied Mechanics, IIT Delhi, New Delhi, INDIA-110016nadhasan@gmail.com

Sanjeev Sanghi1

Department of Applied Mechanics, IIT Delhi, New Delhi, INDIA-110016sanghi@am.iitd.ernet.in

1

Corresponding author.

J. Heat Transfer 129(2), 179-187 (Aug 15, 2006) (9 pages) doi:10.1115/1.2402176 History: Received October 25, 2005; Revised August 15, 2006

## Abstract

In this work the role of Coriolis forces in the evolution of a two-dimensional thermally driven flow in a rotating enclosure of arbitrary geometry is discussed. Contrary to the claims made in some of the studies involving such class of flows that there is an active involvement of the these forces in the dynamics of the flow, it is shown that the Coriolis force does not play any role in the evolution of the velocity and temperature fields. This is theoretically demonstrated by recognizing the irrotational character of the Coriolis force in such class of flows. It is further shown that the presence of the irrotational Coriolis force affects only the pressure distribution in the rotating enclosure. The theoretical deductions apply quite generally to any geometry and thermal boundary conditions associated with the enclosure. The numerical results for the problem of two-dimensional thermally driven flow of air $(Pr=0.71)$ in a circular rotating enclosure provide direct evidence of the theoretical deductions.

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## Figures

Figure 5

Profiles of v velocity along the horizontal diameter (y=0) for (RaΩ=103,Ta=105) at (a)ϕg=3π∕2, (b)ϕg=π, (c)ϕg=π∕2, and (d)ϕg=0

Figure 6

Profiles of θ along the horizontal diameter (y=0) for (RaΩ=103,Ta=105) at (a)ϕg=3π∕2, (b)ϕg=π, (c)ϕg=π∕2, and (d)ϕg=0

Figure 7

Time histories of v velocity for (RaΩ=103,Ta=105) at (a)(−0.72,0) and (b)(0.72,0)

Figure 10

Time histories of v velocity for (RaΩ=1.7×103,Ta=1.7×105) at (a)(−0.72,0) and (b)(0.72,0)

Figure 9

Distribution of (a)Peff and (b) magnitude of gradient of Peff with and without coriolis force for (RaΩ=103,Ta=105) at ϕg=3π∕2

Figure 8

Pressure distributions with and without coriolis force for (RaΩ=103,Ta=105) at (a)ϕg=3π∕2, (b)ϕg=π, (c)ϕg=π∕2, and (d)ϕg=0

Figure 4

Profiles of u velocity along the vertical diameter (x=0) for (RaΩ=103,Ta=105) at (a)ϕg=3π∕2, (b)ϕg=π, (c)ϕg=π∕2, and (d)ϕg=0

Figure 3

Geometry of the problem of two-dimensional thermally driven flow in a rotating horizontal cylinder

Figure 1

Generic configuration of two-dimensional thermally driven flow in an arbitrary cross-sectional rotating enclosure

Figure 11

Time histories of v velocity for (RaΩ=1.9×103,Ta=1.9×105) at (a)(−0.72,0) and (b)(0.72,0)

Figure 2

Geometry and thermal boundary conditions of the problem in Ref. 18

## Errata

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