Heat transfer coefficients of smooth tubes in the turbulent flow regime

Abstract

Several well-known equations are available in literature that can be used to determine the heat transfer coefficients of smooth tubes in the turbulent flow regime. When comparing the results of these equations they vary over a considerable range. Although in many cases it is assumed that the Gnielinski equation is one of the most accurate as it is the most recently developed correlation, the uncertainty of this equation has not be quantified as yet. Many of the equations have been developed using the data that was obtained from experimental testing as far back as 80 years ago. As more accurate instrumentation is available, it should be possible to collect more accurate data during experimental testing. The purpose of this study was threefold: to take accurate heat transfer measurements and to quantify the uncertainties of the Nusselt numbers as a function of Reynolds number; to compare the measured data with existing correlations and to develop an accurate Nusselt number correlation from the data. Experiments were conducted on two smooth circular tubes with a heat transfer length 3.75 m with inner tube diameters of 8.3 mm and 14.2 mm using water over a Reynolds number range of 10 000 to 220 000 and a Prandtl number range of 3.2 to 4. Surface roughness analysis was also performed to ensure the tubes can be considered as smooth tubes. Pressure drop measurements were also taken over tube lengths of 4.1 m as a function of Reynolds number. The experiments were conducted using a tube-in-tube heat exchanger with the hot water in the inner tube and the cold water in the annulus operating in a counter flow configuration. The friction factor values were determined from pressure drop measurements and the heat transfer coefficients were determined from the Wilson Plot method using temperature and mass flow rate measurements. The average uncertainties of the friction factors and Nusselt numbers were both less than 3%. The results were compared to the existing literature and it was found that at lower Reynolds numbers the Nusselt numbers deviated slightly to those of Gnielinski with the results comparing more closely with increasing Reynolds number. The friction factor results correlated well with that of Blasius. A new Nusselt number correlation, which is a function of Reynolds number, Prandtl number and friction factor, was developed. The equation predicted all the measured values within 3%. The equation is, however, limited in not taking into consideration large variations in fluid properties.