Combined effects of pressure gradient and buoyancy in the boundary layer of a turbulent convection flow

etc15 Tracking Number 391

The new method for approximating the velocity and temperature of a flow within the boundary layers is developed by applying the combination of the Falkner-Skan approach and perturbation theory. The former enables to include non-zero pressure gradient along a heated horizontal plate where the flow is considered and the latter gives an opportunity to take into account buoyancy effects caused by the temperature difference between the hot plate and the flow above it. It is assumed that buoyancy effects are small. The mathematical model of the developed method includes four ordinary differential equations which are solved numerically. The approach is adapted to Rayleigh-Benard convection considered in a cylindrical cell at aspect ratio one. The results obtained by the mathematical model and by direct numerical simulations of Rayleigh-Benard convection are compared and are presented together with the conclusions made. The simulations were conducted for a closed cylindrical cell of aspect ratio one at the Rayleigh number Ra=3x10^9 and the Prandtl number Pr=0.7 and Pr=7.0.