Study of free convection along a heated vertical cylinder using numerical and analytical methods

Abstract

Over the past few decades, there has been numerous and extensive studies conducted on free convection along cylinders. Free convection is commonly studied around cylindrical objects as they are the ones that are normally encountered in real-life engineering applications such as pipes, coils and wires, just to name a few. Some of the surface heating conditions that were employed in these studies were the uniform wall temperature, the variable wall temperature, the constant wall heat flux and the variable wall heat flux. Moreover, these studies mainly employed either numerical or experimental methods for their analysis. Hence, this study conducted by the author focused on the free convection along a heated vertical cylinder, applying both numerical and analytical methods. The surface heating condition used was the variable wall temperature. Following an extensive literature review on convective heat transfer, the free convection along a heated vertical cylinder problem was defined. Following that, a mathematical formulation was conducted for the problem. Next, the velocity profile, temperature profile, skin friction coefficient profile and the heat transfer rate profile graphs were plotted (as ξ,n and Pr values were varied), using the “Maple” software. In general, the skin friction coefficient drops while the heat transfer rate rises as n and Pr was increased. However, an anomaly was observed for the case of n = 2. Following this, a perturbation technique was employed to detemine the analytical solutions. These solutions was applied to determine the skin friction coefficient values and heat transfer rate values. However, these analytical solutions were only applicable for either small (ξ < 1) or very large values of ξ. Nonetheless, it was determined that the analytical solutions obtained had a high degree of accuracy (percentage errors of less than 5% was obtained). This author’s main aim, which was to study the free convection along a heated vertical cylinder using numerical and analytical solutions, was achieved. The insights from these results can serve as a comparison with previous research and can be applied to simulate natural convection heat transfer for other object geometries, orientations and surface heating conditions.