Dimensionless correlations for natural convection heat transfer from an enclosed horizontal heated plate

Natural convection from a horizontal plate with identically heated top and bottom sides, enclosed in gas- or liquid-filled square cavities cooled at sides, is studied numerically. A computational code based on the SIMPLE-C algorithm for pressure-velocity coupling is used to solve the system of the governing conservation equations of mass, momentum and energy. Simulations are performed using the Rayleigh number based on the plate length, the Prandtl number, the cavity width normalized by the plate length and the distance of the plate from the bottom wall of the enclosure normalized by the cavity width, as controlling parameters. It is found that the heat transfer rate enhances as the Rayleigh number, the Prandtl number and the dimensionless size of the cavity are increased, while it deteriorates as the dimensionless elevation of the plate is increased. Additionally, the heating of the upper side of the plate has an almost imperceptible effect on the heat transfer rate at the lower side of the plate, whereas the amount of heat transferred from the upper side of the plate normally decreases when the lower side of the plate is heated rather than being insulated. Based on the results obtained, suitable dimensionless heat transfer correlations are developed for the entire plate and each heated side.