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Development of Three-Dimensional, Unsteady Natural Convective Flow in a Horizontal Enclosure With a Heated Strip on the Lower Surface and Cooled Top and Side Walls

[+] Author Affiliations
Patrick H. Oosthuizen, Jane T. Paul

Queen’s University, Kingston, Ontario, Canada

Paper No. IMECE2003-42853, pp. 369-376; 8 pages
doi:10.1115/IMECE2003-42853
From:
  • ASME 2003 International Mechanical Engineering Congress and Exposition
  • Heat Transfer, Volume 4
  • Washington, DC, USA, November 15–21, 2003
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 0-7918-3718-1 | eISBN: 0-7918-4663-6, 0-7918-4664-4, 0-7918-4665-2
  • Copyright © 2003 by ASME

abstract

Three dimensional flow in an enclosure with a square vertical cross-section normal to the longitudinal coordinate direction has been numerically studied. This enclosure has a strip on the lower horizontal surface that is heated to a uniform high temperature and the longitudinal vertical side walls and the horizontal top surface of this enclosure are cooled to a uniform low temperature. It has been assumed that the flow is laminar and that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces. The unsteady, three-dimensional governing equations, expressed in dimensionless form, have been numerically solved. The solution has the following parameters: the Rayleigh Number, Ra, the Prandtl number, Pr, the dimensionless longitudinal length of the enclosure relative to the size of the square cross-section, Ay , and the dimensionless width of the heated strip on the lower surface, wH . Results have only been obtained for a Prandtl number of 0.7 and for wH = 1/3. Results have been obtained for values of Ay between 0.5 and 2 for Rayleigh numbers up to 5×105 . In all cases, three-dimensional unsteady flow has been found to exist at the higher Rayleigh numbers. The conditions under which this unsteady flow develops and the effect of Ay on the variation of the mean Nusselt number with Rayleigh number have been investigated. The flow in the enclosure has also been numerically calculated assuming stady twodimensional flow and the heat transfer rates given by this solution has then been compared with the mean heat transfer rates given by the unsteady three-dimensional solution.

Copyright © 2003 by ASME

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