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ISSN Online: 2377-424X

International Heat Transfer Conference 12
August, 18-23, 2002, Grenoble, France

The Development of Three-Dimensional, Unsteady Natural Convection in a Horizontal Enclosure with a Partially Heated Lower Surface and Cooled Vertical Side Walls

Get access (open in a dialog) DOI: 10.1615/IHTC12.1800
6 pages

Resumo

Flow in a rectangular enclosure with a square vertical cross-section normal to the longitudinal coordinate direction and having a strip on the lower horizontal surface which is heated to a uniform high temperature and with the longitudinal vertical side walls cooled to a uniform low temperature has been numerically studied. The square vertical end walls and the upper horizontal surface are adiabatic. 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 solved using a finite-difference procedure. The solution was started with no flow in the enclosure. The solution, in general, 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, Az , 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 Az between 1 and 3 for Rayleigh numbers up to 105 . In all cases, three-dimensional unsteady flow has been found to exist at the higher Rayleigh numbers. The flow in the enclosure has also been numerically calculated assuming steady two-dimensional flow. The heat transfer rate given by the two-dimensional steady state solution has then been compared with the mean transfer rate given by the unsteady three-dimensional solution in order to determine when the results given by the steady two-dimensional solution can be used.