Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom

Abstract

A numerical study of transient laminar mixed convection heat transfer characteristics confined within a square (2D) and cubic shape (3D) lid-driven cavity has been carried out. Lateral walls are maintained at a constant cold temperature and move upwards with a constant velocity. A heat source is located at the center of the bottom wall of the cavity and maintained at a constant high temperature. All the remaining parts of the cavity are considered adiabatic. The general conservation equations are discretized according to the Finite Volume method based on the SIMPLER algorithm. Richardson number (Ri) isvaried from 0.1 to 10 and the competition between the natural and forced convection forces can lead the flow to adopt, under certain conditions, intricate behaviours such as loss of symmetry, bifurcations and so on. Obtained results showed that the critical Ri numbers that characterize the transition from the forced convection (two symmetric vortices) to the mixed convection (two asymmetric vortices) happens at Ri = 2.51 and Ri = 4.7 for the 3D and 2d cases, respectively. Then, the second transition from mixed convection to natural convection (four symmetrical vortices) happens at Ri = 6.29 and Ri = 7 for the 3D and 2d cases, respectively. Results indicated also that the heat transfer process was strongly affected by the dominant heat convection regimein which the rate of heat transfer increased in the case of asymmetric branch which is characterized by a dominance of natural convection mode.