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Natural convection in an enclosure having a vertical sidewall with time-varying temperature

Published online by Cambridge University Press:  26 April 2006

Ho Sang Kwak  and
Jae Min Hyun
Ho Sang Kwak
Affiliation:
Space Environment Laboratory, Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229, Japan
Jae Min Hyun
Affiliation:
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon 305-701, South Korea
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Abstract

A numerical study is performed for time-varying natural convection of an incompressible Boussinesq fluid in a sidewall-heated square cavity. The temperature at the cold sidewall Tc is constant, but at the hot sidewall a time-varying temperature condition is prescribed, $ T_H = \overline{T_H} + \Delta T^{\prime} \sin ft $. Comprehensive numerical solutions are found for the time-dependent Navier–Stokes equations. The numerical results are analysed in detail to show the existence of resonance, which is characterized by maximal amplification of the fluctuations of heat transfer in the interior. Plots of the dependence of the amplification of heat transfer fluctuations on the non-dimensional forcing frequency ω are presented. The failure of Kazmierczak & Chinoda (1992) to identify resonance is shown to be attributable to the limitations of the parameter values they used. The present results illustrate that resonance becomes more distinctive for large Ra and Pr ∼ 0(1). The physical mechanism of resonance is delineated by examining the evolution of oscillating components of flow and temperature fields. Specific comparisons are conducted for the resonance frequency ωr between the present results and several other previous predictions based on the scaling arguments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 329 , 25 December 1996 , pp. 65 - 88
Copyright
© 1996 Cambridge University Press

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