Unsteady natural convection in a circular cavity at high Rayleigh and Prandtl numbers with constant and variable viscosity

We consider the unsteady natural convection flow of a high Prandtl number fluid ( O ( Pr ) = 10 3 − 9 × 10 3 ) in a circular cavity. The fluid is initially isothermal and at rest. At t = 0 , the temperature of the wall is suddenly lowered, triggering an unsteady natural convection flow at high Rayleigh numbers, O ( R a ) = 10 9 − 10 10 . Both constant and strongly temperature-dependent variations of viscosity were considered. Boundary layer analyses and two-dimensional numerical simulations of the flow allowed the development of a simple theoretical model to predict the time evolutions of the wall heat transfer rate and the average fluid temperature at different stages of the cooling process. The predictions of the time evolution of relevant quantities, obtained with the theoretical model based on boundary layer analysis, are in a good agreement with the present numerical simulations and experiments reported in the literature.