Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T07:01:25.338Z Has data issue: false hasContentIssue false
  • English
  • Français

Convection in a long box driven by heating and cooling on the horizontal boundaries

Published online by Cambridge University Press:  26 April 2006

J. J. Sturman ,
G. N. Ivey  and
J. R. Taylor
J. J. Sturman
Affiliation:
Department of Environmental Engineering and Centre for Water Research, The University of Western Australia, Nedlands, Western Australia, 6907, Australia
G. N. Ivey
Affiliation:
Department of Environmental Engineering and Centre for Water Research, The University of Western Australia, Nedlands, Western Australia, 6907, Australia
J. R. Taylor
Affiliation:
Department of Environmental Engineering and Centre for Water Research, The University of Western Australia, Nedlands, Western Australia, 6907, Australia Present address: Australian Defense Force Academy, Northcott Drive, Campbell, ACT 2601, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 310 , 10 March 1996 , pp. 61 - 87
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

Adrian, R. J., Ferreira, R. T. D. S. & Boberg, T. 1986 Turbulent thermal convection in wide horizontal fluid layers. Exps Fluids 4, 121–141.Google Scholar
Armfield, S. & Patterson, J. C. 1991 Direct simulation of wave interactions in unsteady natural convection in a cavity. Intl J. Heat Mass Transfer 34, 929–940.Google Scholar
Badgley, F. J. 1966 Heat budget at the surface of the Arctic Ocean. In Proc. Symp. on Arctic Heat Budget (ed. J. O. Fletcher), pp. 267–277. Rand Corp.
Bejan, A. 1984 Convection Heat Transfer. Wiley
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech. 204, 1–30.Google Scholar
Chou, S.-H., Atlas, D. & Yeh, E.-N. 1986 Turbulence in a convective Marine Atmospheric Layer. J. Atmos. Sci. 43, 547–564.Google Scholar
Coates, M. C., & Patterson, J. C. 1993 Unsteady natural convection in a cavity with a non-uniform absorption of radiation. J. Fluid Mech. 256, 133–161.Google Scholar
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. J. Fluid Mech. 65, 209–229.Google Scholar
Imberger, J. & Patterson, J. C. 1990 Physical limnology. Adv. Appl. Mech. 27, 303–475.Google Scholar
Ivey, G. N. 1984 Experiments on transient, natural convection in a cavity. J. Fluid Mech. 144, 389–401.Google Scholar
Ivey, G. N. & Hamblin, P. F. 1989 Convection near the temperature of maximum density for high Rayleigh number, low aspect ratio rectangular cavities. Trans. ASME C: J. Heat Transfer 111, 100–105.Google Scholar
Killworth, P. D. 1983 Deep convection in the world ocean. Rev. Geophys. Space Phys. 21, 1–26.Google Scholar
Lemkert, C. & Imberger, J. 1993 Energetic bubble plumes in arbitrary stratification. J. Hydraul. Engng ASCE 119, 680–703.Google Scholar
Linden, P. F. & Simpson, J. 1986 Gravity-driven flows in a turbulent fluid. J. Fluid Mech. 172, 481–497.Google Scholar
Malanotte-Rizzoli, P. 1991 The Northern Adriatic Sea as a prototype of convection and water mass formation on the continental shelf. In Deep Convection and Deep Water Formation in the Oceans (ed. P. C. Chu & J. C. Gascard), pp. 229–239. Elsevier.
Maxworthy, T. & Monismith, S. G. 1988 Differential mixing in a stratified fluid. J. Fluid Mech. 189, 571–598.Google Scholar
Mitsumoto, S., Ueda, H. & Ozoe, H. 1983 A laboratory experiment on the dynamics of the land and sea breeze. J. Atmos. Sci. 40, 1228–1240.Google Scholar
Monismith, S., Imberger, J. & Morison, M. L. 1990 Convective motions in the sidearm of a small reservoir. Limnol. Oceanogr. 35, 1676–1702.Google Scholar
Morison, J. H., Mcphee, M. G., Curtin, T. B. & Paulson, C. A. 1992 The oceanography of winter leads. J. Geophys. Res. 97, 11199–11218.Google Scholar
Noh, Y., Fernando, H. J. S. & Ching, C. Y. 1992 Flows induced by the impingement of a two-dimensional thermal on a density interface. J. Phys. Oceanogr. 22, 1207–1219.Google Scholar
Patterson, J. C. & Armfield, S. W. 1990 Transient features of natural convection in a cavity. J. Fluid Mech. 219, 469–497.Google Scholar
Patterson, J. C. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.Google Scholar
Phillips, O. M. 1966 On turbulent convection currents and the circulation of the Red Sea. Deep-Sea Res. 13, 1149–1160.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309–335.Google Scholar
Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill
Siggia, E. D. 1994 High Rayleigh number convection. Ann. Rev. Fluid Mech. 26, 137–168.Google Scholar
Stevens, C. S. & Coates, M. J. 1994 A maximised cross-correlation technique for resolving velocity fields in laboratory experiments. J. Hydraul. Res. 32, 195–211.Google Scholar
Sturman, J. J., Ivey, G. N. & Taylor, J. R. 1992 Convection in a long rectangular box driven by heated and cooled segments of the horizontal boundaries. Proc. 11th Australasian Fluid Mechanics Conference, vol. ii, pp. 1005–1008.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exps. Fluids 10, 181–193.Google Scholar