Numerical Study of Natural Convection Around an Isolated Horizontal Cylinder and Determination of Critical Radius Effect With a Variable Heat Transfer Coefficient

Natural convection heat transfer from an insulated horizontal cylinder is studied analytically and numerically. Curved surfaces such as circular cylinder which has a radius smaller than a certain critical size, adding insulation to the surface increases the heat transfer form the surface. This phenomenon occurs if the effects of the increase of the outer surface area on the heat transfer are higher than the decrease by the total thermal resistance of the insulated cylinder. The critical radius is represented as a function of thermal conductivity of the object and convective heat transfer coefficient in the textbooks on heat transfer. This is only valid if both thermal conductivity and convective heat transfer coefficient are constant. In fact, the convective heat transfer coefficient varies with outer diameter of the cylinder while thermal conductivity can be taken as constant. Therefore, a numerical and an analytical study were performed in order to investigate the effects of variable heat transfer coefficient on determining the critical radius. For this aim an isolated horizontal cylinder having different insulation thickness and a constant thermal conductivity was modeled and solved numerically using FLUENT CFD software. Also the same problem was solved analytically and numerical and analytical results were compared. The variation of the total heat transfer from cylinder surface according to insulation thickness is obtained. It is found that the standard critical radius criterion led to significant errors compared to numerical results.