ELEMENTARY CONVECTION CELL IN THE HORIZONTAL LAYER OF VISCOUS INCOMPRESSIBLE LIQUID WITH RIGID AND MIXED BOUNDARY CONDITIONS

Abstract

The result of experimental study of convection cells formation of vacuum oil with mixed boundary conditions is presented. The adding small amounts of dispersed phase (aluminum powder) the viscosity and density of the oil didn’t change and under such conditions the boundary conditions for liquid velocity on a rigid boundary can be applied is shown. The experiments demonstrated that exceeding the certain temperature of the container bottom cells of cylindrical shape start to appear in the oil layer with small addition of dispersed phase (oil paint or aluminum powder). The process of appearing of cells finished when the number of cells increases up to the complete filling of oil volume. When amount of the added dispersed phase are small regardless of the its type a rigid boundary conditions can be applied for the lower boundary, i.e. the mixed boundary conditions are present in the layer is shown. The diameter of cells with the mixed boundary conditions varies from 2,65 to 2,83 mm, which is less than the diameter of a cell with free boundary conditions. For a special case there were obtained the analytical solutions of Navier–Stokes equation with rigid boundaries when Rayleigh number is R ≈ 7124.78 and wave number is 7 r k ≈π . The expressions of distribution for perturbed velocity and temperature in cylindrical convection cell were received. This distributions were compared to similar property for free convective cell for the main mode n = 1. It is demonstrated that the diameter of convective cell is inversely related to the value of minimal wave number of the corresponding boundary value problem, i.e. the diameter of a cell with the mixed boundary conditions is less than the diameter of a cell with free boundary conditions, but it’s larger than the diameter of a cell with rigid boundary conditions.