Time-dependent nodal integral methods in natural convection near a fluid density maximum

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Time-dependent nodal integral methods were extended to natural convection near a fluid density maximum (inversion layer). An investigation of convection in a rectangular cavity as a function of tilt angle, aspect ratio, and other parameters was performed at low Rayleigh Number (Ra) using the low-order nodal integral methodologies. Bifurcation of the solution into flow and no-flow regimes was examined as a function of Ra and the dimensionless position (R) of the wall temperatures with respect to the extremum temperature. The first critical bifurcation point, Ra*, was shown to be a function of R as well as of angle of tilt and aspect ratio.