Steady and Oscillating Characteristics of Natural Convection in an Enclosure

Abstract

Natural convection in a rectangular enclosure that arises from multiple heat sources at the bottom wall is considered. The top wall is kept at the surrounding temperature while the vertical walls and the rest of the bottom wall excluding the heat sources are assumed to be adiabatic. Based on the above conditions, the mathematical model is formulated in terms of the dimensionless equations. Finite difference method is used to solve the problem. Numerical results reveal that the strength of the stream function significantly increases owing to the increase of the Rayleigh number and the breadth and width of the heat sources. Convection due to multiple heat sources is higher than that for a single heat source, whereas it remains apparently equal for two or more heat sources. It is found from the limit cycle curves that for three heat sources in an enclosure, an increase in the Rayleigh number leads steady-state convection to periodic oscillatory mode. However, when six heat sources are considered in the enclosure, a transition from the steady state to the nonperiodic oscillatory convection occurs owing to the increase of the Rayleigh number.