Fluid flow and heat transfer of natural convection adjacent to upward-facing, rectangular plates of arbitrary aspect ratios

Natural convective flows adjacent to the upward-facing, heated rectangular plates were investigated experimentally. Main concerns were directed to the effects of aspect ratios on the turbulent transition of flows and also on the heat transfer from the plates. For the sake of this, rectangular plates having different width W = 35-500 mm and aspect ratios AR = 1, 2, 3, 5, 8, were fabricated and tested. The experiments began with the visualizations of the flow fields over the plates, then, the measurements of average Nusselt numbers followed. The flow visualizations depicted that the turbulent transition of flows takes place over the plates of AR = 1, 2, 3, 5, 8, when the width-based Rayleigh numbers beyond RaW = 1.5 × 106, 6.5 × 105, 5.0 × 105, 3.5 × 105, 3.0 × 105, respectively. While, when the equivalent diameter of the plate de was adopted, the critical Rayleigh numbers become almost identical as Rade = (1.5-1.7) × 106 regardless of aspect ratios. The average Nusselt numbers based on the plate width NuW were plotted with the Rayleigh numbers RaW. The plots showed gradual decrease with the aspect rations, in particular, in the low Rayleigh number region. The above Nusselt and Rayleigh numbers were next converted to those based on the equivalent diameter. Then, the Nusselt numbers Nude from the plates of different aspect ratios showed identical variations with the Rayleigh numbers Rade. Based on these results, empirical correlations for the laminar and turbulent heat transfer were proposed.