A Numerical Study of Three-Dimensional Roll Cells within Rigid Boundaries

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Abstract
Three-dimensional natural convection, roll cells within rigid enclosures have been studied with a previously developed numerical technique based on the marker and cell method. Given identical initial conditions, the velocity and temperatures fields are found to be sensitive to the thermal boundary conditions on the side walls and the aspect ratio of the enclosure. Two-dimensional results are also obtained and compared with the corresponding three-dimensional results. The two-dimensional calculations do not agree well with the three dimensional ones, especially for enclosures having aspect ratios less than unity. This indicates that care must be taken in analyzing natural convection problems of this type with two-dimensional methods.

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