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Heat transport by parallel-roll convection in a rectangular container

Published online by Cambridge University Press:  21 April 2006

R. W. Walden ,
Paul Kolodner ,
A. Passner  and
C. M. Surko
R. W. Walden
Affiliation:
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA
Paul Kolodner
Affiliation:
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA
A. Passner
Affiliation:
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA
C. M. Surko
Affiliation:
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA
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Abstract

Heat-transport measurements are reported for thermal convection in a rectangular box of aspect’ ratio 10 x 5. Results are presented for Rayleigh numbers up to 35Rc, Prandtl numbers between 2 and 20, and wavenumbers between 0.6 and 1.0kc, where Rc and kc are the critical Rayleigh number and wavenumber for the onset of convection in a layer of infinite lateral extent. The measurements are in good agreement with a phenomenological model which combines the calculations of Nusselt number, as a function of Rayleigh number and roll wavenumber for two-dimensional convection in an infinite layer, with a nonlinear amplitude-equation model developed to account for sidewell attenuation. The appearance of bimodal convection increases the heat transport above that expected for simple parallel-roll convection.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 205 - 234
Copyright
© 1987 Cambridge University Press

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References

Ahlers, G., Cross, M. C., Hohenberg, P. C. & Safran, S. 1981 The amplitude equation near the convective threshold: application to time-dependent heating experiments. J. Fluid Mech. 110, 297–334.Google Scholar
Behringer, R. P. & Ahlers, G. 1982 Heat transport and temporal evolution of fluid flow near the Rayleigh-Bénard instability in cylindrical containers. J. Fluid Mech. 125, 219–258.Google Scholar
Brown, S. N. & Stewartson, K. 1977 On thermal convection in a large box. Stud. Appl. Maths 57, 187–204.Google Scholar
Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46, 140–150.Google Scholar
Busse, F. H. 1978 Non-linear properties of thermal convection. Rep. Prog. Phys. 41, 1929–1967.Google Scholar
Catton, I. 1970 Convection in a closed rectangular region: the onset of motion. Trans. ASME C: J. Heat Transfer 92, 186–188.Google Scholar
Catton, I. 1972a The effect of insulating vertical walls on the onset of motion in a fluid heated from below. J. Heat Mass Transfer 15, 665–672.Google Scholar
Catton, I. 1972b Effect of wall conduction on the stability of a fluid in a rectangular region heated from below. Trans. ASME C: J. Heat Transfer 94, 446–452.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Charlson, G. S. & Sani, R. L. 1970 Thermoconvective instability in a bounded cylindrical fluid layer. Intl J. Heat Mass Transfer 13, 1479–1496.Google Scholar
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141–159.Google Scholar
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Cross, M. C. 1980 Derivation of the amplitude equation at the Rayleigh-Bénard instability. Phys. Fluids 23, 1727–1731.Google Scholar
Cross, M. C., Daniels, P. G., Hohenberg, P. C. & Siggia, E. D. 1980 Effect of distant sidewalls on wave-number selection in Rayleigh-Bénard convection. Phys. Rev. Lett. 45, 898–901.Google Scholar
Cross, M. C., Daniels, P. G., Hohenberg, P. C. & Siggia, E. D. 1983 Phase-winding solutions in a finite container above the convective threshold. J. Fluid Mech. 127, 155–183.Google Scholar
Daniels, P. G. 1977 The effect of distant sidewalls on the transition to finite amplitude Bénard convection. Proc. R. Soc. Lond. A 358, 173–197.Google Scholar
Davies-Jones, R. P. 1970 Thermal convection in an infinite channel with no-slip sidewalls. J. Fluid Mech. 44, 695–704.Google Scholar
Davis, S. H. 1967 Convection in a box: linear theory. J. Fluid Mech. 30, 465–478.Google Scholar
Denny, V. E. & Clever, R. M. 1974 Comparisons of Galerkin and finite difference methods for solving highly nonlinear thermally driven flows. J. Comp. Phys. 16, 271–284.Google Scholar
Frick, H., Busse, F. H. & Clever, R. M. 1983 Steady three-dimensional convection at high Prandtl numbers. J. Fluid Mech. 127, 141–153.Google Scholar
Greenside, H. S. & Coughran, W. M. 1984 Nonlinear pattern formation near the onset of Rayleigh-Bénard convection. Phys. Rev. A 30, 398–428.Google Scholar
Guyon, E. & Rudnick, I. 1968 Size effects in superfluid helium II. I. Experiments in porous systems. J. Phys. Paris 29, 1081–1095.Google Scholar
Kolodner, P., Walden, R. W., Passner, A. & Surko, C. M. 1986 Rayleigh-Bénard convection in an intermediate-aspect-ratio rectangular container. J. Fluid Mech. 163, 195–226.Google Scholar
Krishnamurti, R. 1970a On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow. J. Fluid Mech. 42, 295–307.Google Scholar
Krishnamurti, R. 1970b On the transition to turbulent convection. Part 2. The transition to time-dependent flow. J. Fluid Mech. 42, 309–320.Google Scholar
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Lipps, F. B. & Somerville, R. C. J. 1971 Dynamics of variable wavelength in finite-amplitude Bénard convection. Phys. Fluids 14, 759–765.Google Scholar
Luijkx, J. M. & Platten, J. K. 1981 On the onset of free convection in a rectangular channel. J. Non-Equilibr. Thermodyn. 6, 141–158.Google Scholar
Malkus, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. R. Soc. Lond. A 225, 185–195.Google Scholar
Malkus, W. V. R. 1954b The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225, 196–212.Google Scholar
Motsay, R. W., Anderson, K. E. & Behringer, R. P. 1988 The onset of convection and turbulence in rectangular layers of liquid helium. J. Fluid Mech. (in press).Google Scholar
Newell, A. C. & Whitehead, J. A. 1969 Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279–303.Google Scholar
Plows, W. H. 1968 Some numerical results for two-dimensional steady laminar Bénard convection. Phys. Fluids 11, 1593–1599.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309–335.Google Scholar
Schluter, A., Lortz, D. & Busse, F. H. 1965 On the stability of finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar
Segel, L. A. 1969 Distant side-walls cause slow amplitude modulation of cellular convection. J. Fluid Mech. 38, 203–224.Google Scholar
Stork, K. & Müller, U. 1972 Convection in boxes: experiments. J. Fluid Mech. 54, 599–611.Google Scholar
Threlfall, D. C. 1975 Free convection in low-temperature gaseous helium. J. Fluid Mech. 67, 17–28.Google Scholar
Walden, R. W., Kolodner, P., Passner, A. & Surko, C. M. 1984 Nonchaotic Rayleigh-Bénard convection with four and five incommensurate frequencies. Phys. Rev. Lett. 53, 242–245.Google Scholar
Wesfreid, J., Pomeau, Y., Dubois, M., Normand, C. & Bergé, P. 1978 Critical effects in Rayleigh-Bénard convection. J. Phys. Lett. 39, 725–731.Google Scholar
Whitehead, J. A. & Chan, G. L. 1976 Stability of Rayleigh-Bénard convection rolls and bimodal flow at moderate Prandtl number. Dyn. Atmos. Oceans 1, 33–49.Google Scholar
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat flux transitions of Malkus. Phys. Fluids 10, 1861–1866.Google Scholar
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux. J. Fluid Mech. 54, 351–367.Google Scholar
Zaleski, S., Pomeau, Y. & Pumir, A. 1984 Optimal merging of rolls near a plane boundary. Phys. Rev. A 29, 366–370.Google Scholar