Oscillatory heat transfer coefficients in transient natural convection in square cavities

Transient natural convection in a square cavity is studied numerically. Before the onset of heat transfer, the temperature is uniform throughout the cavity. Then the side walls are heated and cooled by +Delta T and -Delta T,respectively. The top and bottom walls are insulated. The problem is formulated by the unsteady 2-D differential equations. In this study, Ra ranged from 10(-1) to 10(10) with Pr fixed at 0.71. The differential equations are solved by a control-volume-based finite difference method. With the unsteady formulation, the results are presented for the transient and steady states. It is found that, at higher Pa, the heat transfer coefficient has an oscillatory behavior as it approaches the steady solution Isotherms are also examined at different times.