A NUMERICAL STUDY OF STEADY STATE NATURAL CONVCTIVE HEAT TRANSFER FROM THIN HORIZONTAL RECTANGULAR PLATES OF VARIOUS ASPECT RATIOS

A numerical study of steady natural convective heat transfer from horizontal thin plates having a rectangular shape has been undertaken for various plate aspect ratios. The top and bottom surfaces of the plate were assumed to be isothermal and at same temperature. The heat transfer from the plate was to the surrounding air at ambient conditions. The Boussinesq approximation was adopted, i.e., all fluid properties, except density, were assumed to be constant and the density variation with temperature was obtained using the Boussinesq approximation. A constant Prandtl number was assumed. The results were obtained using the commercial CFD software ANSYS FLUENT. Mean heat transfer rates for the upper and lower surfaces of the plate and averaged over the two surfaces were calculated and expressed in terms of the Nusselt number. The variation of Nusselt number with Rayleigh number was examined. In the initial analysis of the results, the square root of the surface area of the upper or lower surface of the plate was used as the length scale. These results showed significant differences between the variations of Nusselt number with Rayleigh number for the various aspect ratios. Therefore, the results were re-expressed using a length scale equal to 4*Total Surface Area/Total Perimeter. It was found that with this length scale the Nusselt number variations with Rayleigh number for all aspect ratios were much closer to each other and a unique correlation between the Nusselt numbers and Rayleigh numbers based on this length scale was developed.