انتقال حرارت جریان توسعه یافته و در حال توسعه در لوله های افقی صاف در جریان انتقالی سامان یافته Heat transfer of developing and fully developed flow in smooth horizontal tubes in the transitional flow regime

1. Introduction Design constraints, changes in operating conditions or equipment, corrosion and scaling, can cause heat exchangers to operate in, or close to, the transitional flow regime. In this flow regime, the flow alternates between laminar and turbulent flow and turbulent eddies occur in flashes, known as turbulent bursts. This might cause the pressure drop to increase an order of magnitude. Designers are thus usually advised to avoid this flow regime [1], since the flow is believed to be unstable and chaotic, and little design information is available [2]. According to a recent review paper by Meyer [2], the transitional flow regime has been mainly investigated by Professor Ghajar from Oklahoma State University and his co-workers, and by Professor Meyer from the University of Pretoria and his coworkers. Ghajar and co-workers used local temperature and pressure measurements along a tube length to investigate the effect of different inlet geometries and heating on the heat transfer coefficients and friction factors [3–12]. Although temperature measurements were taken at 31 stations along the test section, their investigations mainly focused on the fully developed flow results at x/D = 192 (station 22). A constant heat flux boundary condition and different mixtures of distilled water and ethylene glycol were used, which resulted in high Prandtl numbers (up to 160). Meyer and Olivier [13–16] used a constant surface temperature boundary condition and water as the test fluid, which resulted in significantly lower Prandtl numbers (approximately 7). Furthermore, the fluid was being cooled and not heated. As they considered the average measurements across a tube length, their data contained both developing (laminar and transitional flow regimes) and fully developed (turbulent flow regime) data. However, the focus was on the effect of inlet geometries and enhanced tubes. Meyer and co-workers also investigated transitional flow in nanofluids [17], micro-channels [18], annular flow [19] and tubes with twisted tape inserts [20]. Similar to Meyer and Olivier [13–16], Bertsche et al. [21] also investigated transitional flow using a constant surface temperature boundary condition (the fluid was also being cooled), using the average measurements along the tube length. As the maximum length-to-diameter ratio of their test section was only 84.7, their data contained developing flow. However, the focus of their study was to compile an experimental database for heat transfer in the transitional flow regime using high Prandtl number fluids, and to compare it with the proposed correlation of Gnielinski [22]. Taler [23] gives a comprehensive overview of the available correlations in the transitional flow regime. The first correlation to predict the overall heat transfer coefficients in the transitional flow regime, was proposed by Hausen in 1959, however, many other studies found that their experimental heat transfer data in the transitional flow regime deviated from this equation [21]. Both Gnielinski [24] and Churchill [25] also developed correlations for developing and fully developed flow in the transitional flow regime. However, Tam and Ghajar [1] concluded that Gnielinski’s and Churchill’s correlations failed to accurately predict mixed convection data, since they did not address the effects of free convection superimposed on the main flow. Heat transfer correlations in the transitional flow regime were also developed by Ghajar and Tam [5], Yu-ting et al. [26] and Lu et al. [27], however, the Prandtl number ranges were limited to the test fluids that were used (mixtures of ethylene glycol and distilled water [5] and molten salt [26,27]).