Scaling of the laminar natural-convection flow in a heated square cavity

Abstract The steady laminar natural-convection flow of air and water in a square heated cavity is calculated for increasingly large Rayleigh number. The flow is calculated by solving both the Navier-Stokes equations and the boundary-layer equations. The results are used to determine the proper scalings of the flow in the different asymptotic flow regions: vertical boundary layers, core region, corner region and horizontal boundary layers. In particular the scalings according to the Navier-Stokes equations agree with the asymptotic model for the core and vertical boundary layers as proposed by Gill [ J. Fluid Mech. 26 , 515–536 (1966)].

[1]  Simon Ostrach,et al.  Natural convection in enclosures , 1988 .

[2]  G. D. Davis.  Natural convection of air in a square cavity: A bench mark numerical solution , 1983 .

[3]  Simon Ostrach.  NATURAL CONVECTION HEAT TRANSFER IN CAVITIES AND CELLS , 1982 .

[4]  P. LeQuéré,et al.  Accurate solutions to the square thermally driven cavity at high Rayleigh number , 1991 .

[5]  W. Graebel.  THE INFLUENCE OF PRANDTL NUMBER ON FREE CONVECTION IN A RECTANGULAR CAVITY , 1981 .

[6]  J. W. Elder,et al.  Laminar free convection in a vertical slot , 1965, Journal of Fluid Mechanics.

[7]  G. Batchelor,et al.  Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures , 1954 .

[8]  A. E. Gill.  The boundary-layer regime for convection in a rectangular cavity , 1966, Journal of Fluid Mechanics.

[9]  P. Simpkins,et al.  Thermal convection in a cavity: the core structure near the horizontal boundaries , 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  S. Ostrach.  An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force , 1953 .

[11]  S. Paolucci,et al.  Transition to chaos in a differentially heated vertical cavity , 1989, Journal of Fluid Mechanics.

[12]  Adrian Bejan,et al.  Note on Gill's solution for free convection in a vertical enclosure , 1979, Journal of Fluid Mechanics.

[13]  S. Ostrach,et al.  NATURAL CONVECTION INSIDE A HORIZONTAL CYLINDER , 1981 .

[14]  W. Tollmien,et al.  Über Flüssigkeitsbewegung bei sehr kleiner Reibung , 1961 .