Simulation numérique de la convection naturelle d'un liquide soumis à des conditions pariétales variables

Abstract

The present work determines numerically and analyses the dynamic and thermal fields resulting from natural convection in vertical cylinders partially filled with a liquid. The finite difference method has been used to solve the equations governing these flows. Two different types of boundary conditions were implemented in the solution of these equations: in the first case, a temperature which varies sinusoidally on all the boundaries of the cylinder was imposed and, in the second case, a sinusoidal heat flux was imposed. In the case of variable wall temperature, it was noticed that the flow becomes more and more complex and passes from a monocellular structure at the beginning of the period to a multicellular structure at the end of the period, provoked by the differences in temperature that appear within the fluid. Also, despite the imposition of the same temperature on all walls, it was observed that the majority of the heat is exchanged through the vertical wall of the cylinder. In the case of variable wall flux, a nearly constant local heat transfer was predicted for all walls but the mean transfer was larger for the transversal wall. The flow is here monocellular and is little perturbed because of the continuous heating. It was also noted the formation of thermal stratification which is not as quickly destroyed as in the case of prescribed variable wall temperature.