Design charts for radial rectangular fins in terms of performance ratio and maximum effectiveness

A mathematical model for a radial rectangular fin is presented. The fin performance ratio, an indicator to quantify the actual heat flow through a fin relative to a maximum heat flow through a fin. It is dependent on four parameters: the maximum fin effectiveness, the ratio of the coefficient at the fin tip to the coefficient along the side of the fin and the ratios of the fin base radius to the half fin thickness and the fin tip radius to the half fin thickness. The design charts have curves of the performance ratio plotted in terms of the fin aspect ratio against the maximum effectiveness for a particular value of the ratio of the fin radius to the half fin thickness. For low fin tubes, the fin outer radius is fixed as they are designed to replace plain tubes. Hence the charts are for fixed values of the ratio of the fin tip radius to the half fin thickness. For high fin tubes, the fin base radius is fixed and so the charts are for fixed values of the ratio of the base radius to the half fin thickness. Two design charts are provided in this paper. These can be used to rate or design specific radial rectangular fins for a particular heat transfer specification. Examples on how to use the design charts are included.