Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-17T23:14:56.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Buoyancy effects in stably stratified horizontal boundary-layer flow

Published online by Cambridge University Press:  26 April 2006

P. G. Daniels  and
R. J. Gargaro
P. G. Daniels
Affiliation:
Department of Mathematics, City University, Northampton Square, London, EC1V OHB, UK
R. J. Gargaro
Affiliation:
Department of Mathematics, City University, Northampton Square, London, EC1V OHB, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes numerical and asymptotic solutions of the steady two-dimensional boundary-layer equations governing buoyant flow on a horizontal, thermally insulated surface. The class of flows considered is one for which there is a uniform external stream at constant temperature but for which conditions upstream lead to a statically stable temperature field within the boundary layer. This has the effect of generating an adverse pressure gradient which, if sufficiently strong, causes the boundary-layer solution to terminate in a singularity. Results are obtained for a range of Prandtl numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 233 - 251
Copyright
© 1993 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

Ackroyd, J. A. D. 1976 Laminar natural convection boundary layers on near-horizontal plates. Proc. R. Soc. Lond. A 352, 249.Google Scholar
Al-Arabi, M. & El-Riedy, M. K. 1976 Natural convection heat transfer from isothermal horizontal plates of different shapes. Intl J. Heat Mass Transfer 19, 1399.Google Scholar
Bandrowski, J. & Rybski, W. 1976 Free convection mass transfer from horizontal plates. Intl J. Heat Mass Transfer 19, 827.Google Scholar
Bejan, A., Al-Homoud, A. A. & Imberger, J. 1981 Experimental study of high Rayleigh number convection in a horizontal cavity with different end temperatures. J. Fluid Mech. 109, 283.Google Scholar
Buckmaster, J. 1970 The behaviour of a laminar compressible boundary layer on a cold wall near a point of zero skin friction. J. Fluid Mech. 44, 237.Google Scholar
Clifton, J. V. & Chapman, A. J. 1969 Natural convection on a finite-size horizontal plate. Intl J. Heat Mass Transfer 12, 1573.Google Scholar
Daniels, P. G. 1992 A singularity in thermal boundary-layer flow on a horizontal surface. J. Fluid Mech. 242, 419.Google Scholar
Daniels, P. G. 1993 High Rayleigh number thermal convection in a shallow laterally heated cavity. Proc. R. Soc. Lond. (to appear.)Google Scholar
Daniels, P. G. & Gargaro, R. J. 1992 Numerical and asymptotic solutions for the thermal wall jet. J. Engng Maths 26, 493.Google Scholar
Faw, R. E. & Dullforce, T. A. 1981 Holographic interferometry measurement of convective heat transfer beneath a heated horizontal plate in air. Intl J. Heat Mass Transfer 24, 859.Google Scholar
Gargaro, R. J. 1991 Thermally driven shallow cavity flows. PhD thesis, City University, London.
Gill, W. N., Zeh, D. W. & Casal, E. del 1965 Free convection on a horizontal plate. Z. Angew Math. Phys. 16, 539.Google Scholar
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625.Google Scholar
Goldstein, R. J. & Lau, K.-S. 1983 Laminar natural convection from a horizontal plate and the influence of plate-edge extensions. J. Fluid Mech. 129, 55.Google Scholar
Goldstein, R. J., Sparrow, E. M. & Jones, D. C. 1973 Natural convection mass transfer adjacent to horizontal plates. Intl J. Heat Mass Transfer 16, 1025.Google Scholar
Goldstein, S. 1948 On laminar boundary layer flow near a position of separation. Q. J. Mech. Appl. Maths 1, 43.Google Scholar
Hunt, R. & Wilks, G. 1980 On the behaviour of the laminar boundary-layer equations of mixed convection near a point of zero skin friction. J. Fluid Mech. 101, 377.Google Scholar
Ivey, G. N. 1984 Experiments on transient natural convection in a cavity. J. Fluid Mech. 144, 389.Google Scholar
Jones, D. R. 1973 Free convection from a semi-infinite flat plate inclined at a small angle to the horizontal. Q. J. Mech. Appl. Maths 26, 77.Google Scholar
Kerr, C. N. 1980 Analog solution of free convection mass transfer from downward-facing horizontal plates. Intl J. Heat Mass Transfer 23, 247.Google Scholar
Merkin, J. 1969 The effect of buoyancy forces on the boundary layer flow over a semi-infinite vertical flat plate in a uniform stream. J. Fluid Mech. 35, 439.Google Scholar
Ostrach, S. 1952 An analysis of laminar free convection flow and heat transfer about a flat plate parallel to the direction of the generating body force. NACA Tech. Note 2635, Washington DC.
Pera, L. & Gebhart, B. 1973 Natural convection boundary layer flow over horizontal and slightly inclined surfaces. Intl J. Heat Mass Transfer 16, 1131.Google Scholar
Pohlhausen, E. 1921 Der warmeaustausch zwichen festen korpern und flussigkeiten mit kleiner reibung und warmeleitung. Z. Angew Math. Mech. 1, 115.Google Scholar
Rotem, Z. & Claassen, L. 1969 Natural convection above unconfined horizontal surfaces. J. Fluid Mech. 39, 173.Google Scholar
Schneider, W. 1979 A similarity solution for combined forced and free convection. Intl J. Heat Mass Transfer 22, 1401.Google Scholar
Schneider, W. & Wasel, M. G. 1985 Breakdown of the boundary-layer approximation for mixed convection above a horizontal plate. Intl J. Heat Mass Transfer 28, 2307.Google Scholar
Simpkins, P. G. & Chen, K. S. 1986 Convection in horizontal cavities. J. Fluid Mech. 166, 21.Google Scholar
Stewartson, K. 1958 On the free convection from a horizontal plate. Z. Angew Math. Phys. 9, 276.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.