Bénard Convection With Rotation And A
Periodic Temperature Distribution
Author(s)
S. J. D. D’Alessio & K. A. Ogden
Abstract
This study investigates the effects of a sinusoidally varying temperature
distribution and rotation on free convection between two rigid plates. The domain
is assumed to be much larger in the horizontal direction than in the vertical
direction, which naturally introduces a small parameter. An approximate analytical
solution for the steady-state flow is derived by expanding the flow variables in
the small parameter. The steady-state solution was also determined numerically
using the commercial CFD software package CFX. A comparison of the results
shows that the form of the steady-state flow pattern is indeed captured by the
approximate analytical solution. Unsteady numerical calculations are also carried
out for various sets of parameters to determine when the flow destabilizes, how the
modulated temperature boundary condition and rotation affect the critical Rayleigh
number, and also to illustrate the flow pattern that develops when the flow becomes
unstable.
Keywords: Bénard convection, rotation, sinusoidally varying boundary condition,
shallow flow, analytical, numerical.
1 Introduction
The problem of free convection within a long, rotating rectangular domain driven
by a sinusoidally varying bottom temperature is studied. This problem is an
extension of traditional Bénard convection to account for both rotation and a
periodic temperature distribution along the bottom plate. Numerous studies have
been devoted to Bénard convection. One previous related study is the work by
Pascal and D’Alessio [1], which addresses the stability of the flow with rotation
and a quadratic equation of state. Schmitz and Zimmerman [2] studied the effects
of a spatially varying temperature condition together with wavy boundaries, but
Keywords
Bénard convection, rotation, sinusoidally varying boundary condition,
shallow flow, analytical, numerical.
Related Book
Other papers in this volume
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