An analysis was made of the radiant blackbody heat-rejection and weight characteristics of a direct-condensing radiator with a linearly tapered fin between two tubes. Considered in the analysis are such factors as tube armor protection, mutual irradiation occurring between the fin and the adjoining tube surfaces, and fin base thickness and taper angle. Results of the thermal analysis for three fin tapers are presented in terms of a conductance parameter involving a comparison of the radiation capability of a fin with its heat conducting capability, the ratio of fin tip to base thickness, the ratio of tube outside radius to fin length, and the ratio of fin base thickness to fin length. For practical configurations, the effects of fin base thickness and taper angle on total heat transfer are negligible.nThe weight-minimization procedure used in this analysis substantiated the fact that the maximum heat rejection per unit weight occurs at conductance parameters approximately equal to 1 with tapered as well as with constant-thickness fins. For minimum weight, the tapered fin is thicker at the root and is longer than the corresponding minimum-weight constant-thickness fin. The advantages gained by tapered fins are highly dependent on the choice of required armor protection, material, heat-rejection load, and surface temperature. For the illustrative calculations considered, in which a 1-megawatt-system radiator at 1700° R with a 0.90 probability of no punctures in 500 days was prescribed, fin tapering results in a maximum weight saving of 10, per cent for a triangular fin as compared to a constant-thickness fin. A similar result was obtained for a radiator operating at 1160° R for a 30-kilowatt system. The effect of fin tapering on radiator planform area was also investigated. Results indicate that an increase in planform area occurs with increasing fin taper at conditions of maximum heat rejection per unit weight. These conclusions are based on fin and tube heat transfer without consideration of the fluid pressure drop or the header weight contributions that may decrease the indicated advantages of tapering.
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