Free convection heat transfer and fluid flow above horizontal rectangular plates

Results are presented from experimental and theoretical investigations of natural convective heat transfers from horizontal, rectangular, isothermal plates having different aspect ratios. Convective flow structures in water were visualized by injecting dye through openings along the edges of the plate for different values of the aspect ratio and Rayleigh number. Based upon these observations and previous studies of horizontal polygonal surfaces, two models for convective flow structures are proposed. In the first model, the direction of flow of the fluid was assumed to be perpendicular to the edges of the rectangle with the streamlines parallel to each other. In the second model, the flow was assumed to form structures in which the fluid flowed inwards radially from the edges. Solutions of these models are presented in the form of Nusselt-Rayleigh relations with the aspect ratio as a parameter. The theoretical solution was verified using water for rectangular plates having aspect ratios (i.e. length/width)=1 (square), 1.81, 2.52, 3.66, and 4.66.