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In this paper our most recent research results on natural convection in a closed cylinder, where our interest focuses on pattern structure dependence on aspect ratio and on temperature-dependent viscosity, are summarized. The main results are (a) the experiments on the onset pattern and conditions for pure Rayleigh convection in circular cylinders compare favorably with linearized stability results of Hardin et al. [Int. J. Num. Methods Fluids 10, 79 (1990)], as well as three-dimensional nonlinear calculations made by us; and (b) experiments and nonlinear calculations indicate a variation of the patterns at and near the codimension two points when large temperature differences are introduced, so as to cause a substantial change in viscosity.

The fluid physics of buoyancy-driven (Rayleigh) and interfacial tension-driven (Marangoni) convection is examined for two superimposed layers of fluids. This convection occurs on account of temperature gradients that are imposed perpendicular to the fluid-fluid interface. Interfacial deflections, small as they may be, play an important part in identifying the mechanism that governs the flow, and calculations have been made that indicate whether hot or cold fluid flows towards or away from a crest or a trough. As a result, four possible flow structures or ‘modes’ at the interface have been identified. Two heating styles, heating from below and above, are compared and the behaviour of the fluid physics as a function of total fluid depths, depth ratios and gravity levels is explained. Changes in modes result because of changes in these parameters. We have given plausible physically based arguments that predict the sequential change in modes as these parameters are changed and have ‘verified’ our conjectures with calculations. Flow mechanisms in the case of a solidifying lower phase have also been studied, as this has an application to liquid-encapsulated crystal growth. Where convection is deemed detrimental to crystal homogeneity, we conclude that the liquid-encapsulated method of crystal growth is best conducted under Earth’s gravity.

The Semi-Implicit Method for Pressure-LinkedEquations (SIMPLE) algorithm for heat transfer andfluidflow problems is extended to time-periodic situations. ,l vectorired line group method for solving the system of associated algebraic equations in a rectangular twodimensional compututional domain is developed to speed up the cornf~utations. A multiblock procedure with the line group method is used to solve a piston-tfriven oscillaring heat transfer problem. The numerical results obtained show some interesting new phenomena and agree with analytical results where such comparisons are possible.