Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-08T22:00:19.539Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bark, F. H., Alavyoon, F. & Dahlkild, A. A. 1992 On steady free convection in vertical slots due to prescribed fluxes of heat or mass at the vertical walls. J. Fluid Mech. 235, 665–689.Google Scholar
Chenoweth, D. R. & Paolucci, S. 1986 Natural convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech. 169, 173–210.Google Scholar
Davis, G. DE VAHL & Jones, I. P. 1983 Natural convection in a square cavity - a comparison exercise. Intl J. Num. Methods Fluids 3, 227–248.Google Scholar
Hayase, T., Humphery, J. A. C. & Grief, R. 1992 A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures. J. Comput. Phys. 98, 108–118.Google Scholar
Hyun, J. M. 1994 Unsteady buoyant convection in an enclosure. Adv. Heat Transfer 34, 277–320.Google Scholar
Ivey, G. N. 1984 Experiments on transient natural convection in a cavity. J. Fluid Mech. 144. 389–401.Google Scholar
Iwatsu, R., Hyun, J. M. & Kuwahara, K. 1992 Convection in a differentially-heated square cavity with a torsionally-oscillating lid. Intl J. Heat Mass Transfer 35, 1069–1076.Google Scholar
Jischke, M. C. & Doty, R. T. 1975 Linearized buoyant motion in a closed container. J. Fluid Mech. 71, 729–754.Google Scholar
Kazmjerczak, M. & Chinoda, Z. 1992 Buoyancy-driven flow in an enclosure with time-periodic conditions. Intl J. Heat Mass Transfer 35, 1507–1518.Google Scholar
Lage, J. L. & Bejan, A. 1991 The Ra-Pr domain of laminar natural convection in an enclosure heated from the side. Numer. Heat Transfer A 19, 21–41.Google Scholar
Lage, J. L. & Bejan, A. 1993 The resonance of natural convection in an enclosure heated periodically from the side. Intl J. Heat Mass Transfer 36, 2027–2038.Google Scholar
Le quere, P. 1990 Transition to unsteady natural convection in a tall water-filled cavity. Phys. Fluids A 2, 503–514.Google Scholar
Le Quéré, P. & Alziary de roquetfort, T. 1986 Transition to unsteady natural convection of air in differentially heated vertical cavities. Proc. ASME Winter Annual Meeting, Anaheim, California. ASME HTD, Vol. 60, pp. 29–36.
Ostrach, S. 1982 Natural convection heat transfer in cavities and cells. Proc. 7th Intl Heat Transfer Conf., Munich, Vol. 6, pp. 365–379.
Paolucci, S. 1990 Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity. J. Fluid Mech. 215, 229–262.Google Scholar
Paolucci, S. & Chenoweth, D. R. 1989 Transition to chaos in a differentially heated vertical cavity. J. Fluid Mech. 201, 379–410.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.
Patterson, J. & Armfield, S. W. 1990 Transient features of natural convection in a cavity. J. Fluid Mech. 219, 469–497.Google Scholar
Patterson, J. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.Google Scholar
Sakurai, T. & Matsuda, T. 1972 A temperature adjustment process in a Boussinesq fluid via a buoyancy-induced meridional circulation. J. Fluid Mech. 54, 417–421.Google Scholar
Schladow, S. G., Patterson, J. & Street, R. L. 1989 Transient flow in a side-heated cavity at high Rayleigh number: a numerical study. J. Fluid Mech. 200, 121–148.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Vasseur, P. & Robillard, L. 1982 Natural convection in a rectangular cavity with wall temperature decreasing at a uniform rate. Warme-u. Stoffubertr. 16, 199–207.Google Scholar
Xia, Q., Yang, K. T. & Mukutmoni, D. 1995 Effect of imposed wall temperature oscillations on the stability of natural convection in a square enclosure. Trans. ASME C: J. Heat Transfer 117, 113–120.Google Scholar
Yewell, R., Poulikakos, D. & Bejan, A. 1982 Transient natural convection experiments in shallow enclosures. Trans. ASME C: J. Heat Transfer 104, 533–538.Google Scholar