Thermal drift in an inclined viscous fluid flow

Abstract

This paper considers viscous fluid flow in a slot between two parallel plates which start inclining with respect to the horizontal line. The lower plate was heated and had non-homogeneous temperature distribution while the upper plate was cooled and with homogeneous temperature distribution. The spatially periodic temperature distribution was gradually applied at the lower plate, after which the plates were slowly inclined in the positive-counterclockwise direction, and the fields of vorticity, stream function, and temperature are presented for different values of the angle of inclination. We used the vorticity-stream function formulation of Navier-Stokes equations, Fourier-Galerkin, and Chebyshev collocation method for numerical simulation of 2-D viscous fluid flow. We carried out numerical simulation using our in-house MATLAB code for subcritical uniform Rayleigh number, Rauni, and periodic Rayleigh number, Rap, on the lower plate. An accurate numerical scheme was developed to capture the full time-dependent behavior here. The interest lied in how the intensities of the vortexes and convection rolls changed as the inclination angle was increased with respect to time. Convection rolls rotating in the clockwise direction expanded and the rolls rotating in the counterclockwise direction shrank and their centers moved closer to the lower wall. Thermal drift appeared between them when the inclination angle started increasing.