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Buoyancy effects in stably stratified horizontal boundary-layer flow

  • P. G. Daniels (a1) and R. J. Gargaro (a1)


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.



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Ackroyd, J. A. D. 1976 Laminar natural convection boundary layers on near-horizontal plates. Proc. R. Soc. Lond. A 352, 249.
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.
Bandrowski, J. & Rybski, W. 1976 Free convection mass transfer from horizontal plates. Intl J. Heat Mass Transfer 19, 827.
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.
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.
Clifton, J. V. & Chapman, A. J. 1969 Natural convection on a finite-size horizontal plate. Intl J. Heat Mass Transfer 12, 1573.
Daniels, P. G. 1992 A singularity in thermal boundary-layer flow on a horizontal surface. J. Fluid Mech. 242, 419.
Daniels, P. G. 1993 High Rayleigh number thermal convection in a shallow laterally heated cavity. Proc. R. Soc. Lond. (to appear.)
Daniels, P. G. & Gargaro, R. J. 1992 Numerical and asymptotic solutions for the thermal wall jet. J. Engng Maths 26, 493.
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.
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.
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625.
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.
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.
Goldstein, S. 1948 On laminar boundary layer flow near a position of separation. Q. J. Mech. Appl. Maths 1, 43.
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.
Ivey, G. N. 1984 Experiments on transient natural convection in a cavity. J. Fluid Mech. 144, 389.
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.
Kerr, C. N. 1980 Analog solution of free convection mass transfer from downward-facing horizontal plates. Intl J. Heat Mass Transfer 23, 247.
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.
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.
Pohlhausen, E. 1921 Der warmeaustausch zwichen festen korpern und flussigkeiten mit kleiner reibung und warmeleitung. Z. Angew Math. Mech. 1, 115.
Rotem, Z. & Claassen, L. 1969 Natural convection above unconfined horizontal surfaces. J. Fluid Mech. 39, 173.
Schneider, W. 1979 A similarity solution for combined forced and free convection. Intl J. Heat Mass Transfer 22, 1401.
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.
Simpkins, P. G. & Chen, K. S. 1986 Convection in horizontal cavities. J. Fluid Mech. 166, 21.
Stewartson, K. 1958 On the free convection from a horizontal plate. Z. Angew Math. Phys. 9, 276.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
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Buoyancy effects in stably stratified horizontal boundary-layer flow

  • P. G. Daniels (a1) and R. J. Gargaro (a1)


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