Effect of Richardson Number on Unsteady Mixed Convection in a Square Cavity Partially Heated From Below

Abstract

Abstract: The objective of the present study is to analyze the laminar mixed convection in a square cavity with a side length L and moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall and all the other horizontal sides of the cavity are considered adiabatic. The numerical method used is based on a finite difference technique where the spatial partial derivatives and boundary conditions of the phenomenon governing equations are discretized using a high order scheme, and time advance is dealt with by the fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative importance of the natural and forced convection, is chosen as the bifurcation parameter. The effect of the Richardson number on the behavior of the fluid flow and the heat transfer has been analyzed. Although the geometry and boundary conditions concerning the velocity and the temperature are symmetrical relative to the vertical axis passing through the center of the cavity, analysis of the results allowed us to detect the existence of symmetric and asymmetric structures of the flow, completely different, depending on the value of the Richardson number.