THE HORIZONTAL CONVECTION OF AN INCLINED VISCOUS FLUID FLOW

Abstract

The paper presents the results of a numerical simulation for the viscous fluid flow in a slot with cosinusoidal temperature distribution on the lower plate with the increasing slope of the plates with respect to the horizontal line. The numerical simulation is performed using the Fourier Galerkin method in the x-axis direction and the Chebyshev collocation method in the y-axis direction. The stream function-vorticity formulation of the Navier-Stokes equation in the Oberbeck-Boussinesq approximation is used. The uniform Rayleigh number Ra_uni=250 and the periodic Rayleigh number value of Ra_p=15,30 is employed in the numerical simulation for the fluid with Pr=7 (water). The horizontal convection known as thermal drift is observed at the angle of inclination 0<γ<5° for Ra_p=15 and 0<γ<15° for Ra_p=30. The stream function values are compared with the similar values for different combinations of Ra_uni, Ra_p values. This comparison shows a different behavior of the averaged Nusselt and the friction coefficient number for these situations. The results suggest that the ratio between Ra_uni and Ra_p is very important for the heat and momentum transfer between the plates. In the first two cases we have optimal value of heat transfer when γ=10°, but for Ra_uni=500 and Ra_p=30 the maximal value of Nu,_av is obtained for γ=0°.