Convective Heat-Transfer and Flow-Friction Behavior of Small Cylindrical Tubes—Circular and Rectangular Cross Sections

Abstract

Abstract Recent heat-transfer and flow-friction test data (1) for gas flow in small circular and rectangular cylindrical tubes, in the laminar, transition, and low-Reynolds-number turbulent-flow regimes, are examined and compared with earlier results. For circular tubes in laminar flow, the heat-transfer results substantiate very well analytical predictions as summarized by Norris and Streid (2). In turbulent flow, circular-tube heat transfer is correlated by an empirical nondimensional equation of the same form, but with a somewhat lower coefficient than has been commonly employed in the past. The difference is attributable in part to the use of more recent data on air properties in the reduction of test results to a nondimensional form. The transition region for circular tubes is found to extend from about NR ~ 2000 to NR ~ 10,000, and heat-exchanger design in this “dip” region is discussed. Laminar-flow circular-tube friction factors show an entrance length effect, similar to that found for heat transfer, and it is demonstrated that the analysis of Langhaar (3) for flow in a single tube can be employed to predict friction factors with acceptable accuracy for flow through a tube bundle even with the sudden change of flow area at the contracted tube-entrance section. For small circular tubes, as a result of this analysis, recommended design correlations in graphical form are given for the NR range 500 to 50,000. The turbulent-flow heat-transfer and friction performance of rectangular tubes is in close agreement with the characteristics for circular tubes. However, there is a marked difference in the laminar and transition behavior, where the aspect ratio of the rectangular cross-section is demonstrated to have an important influence. It is concluded that considerable additional work, both analytical and experimental, is needed to ascertain laminar and transition flow-friction and heat-transfer characteristics in rectangular tubes.