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FREE CONVECTION IN A CUBICAL ENCLOSURE WITH FOUR HEATED SECTIONS ON THE LOWER SURFACE AND ISOTHERMAL SIDE SURFACES

DOI: 10.1615/ICHMT.2008.CHT.550
page 15

Patrick H. Oosthuizen
Department of Mechanical and Materials Engineering, Queen's University, 130 Stuart Street, Kingston, ON, K7L 3N6, Canada

Jane T. Paul
Department of Mechanical and Materials Engineering, Queen's University, Kingston, Ontario, Canada K7L 3N6

Аннотация

The development of unsteady, three-dimensional free convective flow in a cubical enclosure with multiple heated sections on the bottom horizontal surface has been numerically studied. The enclosure considered has square horizontal lower and upper surfaces and square vertical side surfaces. There are four square symmetrically placed isothermal heated sections on the lower surface, the rest of this surface being adiabatic. The vertical side-walls of the enclosure are kept at a uniform low temperature and the top horizontal square surface is adiabatic. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces. The solution has been obtained by numerically solving the unsteady, three-dimensional governing equations written in dimensionless form, the solution being obtained in terms of the vorticity vector and vector potential functions. The dimensionless equations written in this way have been solved using an iterative, semi-implicit finite-difference method. The solution has the following parameters: the Rayleigh number, Ra, the Prandtl number, Pr, the dimensionless size, wH of the square heated sections and the dimensionless distance between the heated sections on the lower surface, wS. Results have only been obtained for a Prandtl number of 0.7. The main emphasis in the present work has been placed on the effect of wS on the results. In order to illustrate this effect results are presented for a single wH value. In a given geometrical situation it was found in all cases that a steady flow exists at low Rayleigh numbers, that an unsteady flow develops at higher Rayleigh numbers and that the flow then again becomes steady at still higher Rayleigh numbers. The conditions under which unsteady flow develops and ceases and the variation of mean Nusselt number have been explored for various values of wS.

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