Single-phase mixed convection of developing and fully developed flow in smooth horizontal tubes in the laminar, transitional, quasi-turbulent and turbulent flow regimes

Abstract

The laminar and turbulent flow regimes have been extensively investigated from as early as 1883, and research has been devoted to the transitional flow regime since the 1990s. However, there are several gaps in the mixed convection literature, especially when the flow is still developing. The purpose of the study was to experimentally investigate the heat transfer and pressure drop characteristics of developing and fully developed flow of low Prandtl number fluids in smooth horizontal tubes for forced and mixed convection conditions.

An experimental set-up was designed and built, and results were validated against literature. Two smooth circular test sections with inner diameters of 4 mm and 11.5 mm were used, and the maximum length-to-diameter ratios were 1 373 and 872 respectively. Heat transfer measurements were taken at Reynolds numbers between 500 and 10 000 at different constant heat fluxes. A total of 648 mass flow rate measurements, 70 301 temperature measurements and 2 536 pressure drop measurements were taken. Water was used as the test fluid and the Prandtl number ranged between 3 and 7.

It was found that a longer thermal entrance length was required for simultaneously hydrodynamically and thermally developing flow. Therefore, a coefficient of at least 0.12 (and not 0.05 as advised in most literature) was suggested. Because free convection effects decreased the thermal entrance length, correlations were also developed to calculate the thermal entrance length for mixed convection conditions. The boundaries between the flow regimes were defined mathematically, and terminology to define transitional flow characteristics was presented. For laminar flow, three different regions (forced convection developing, mixed convection developing and fully developed) were identified in the local heat transfer results and nomenclature and correlations were developed to define and quantify the boundaries of these regions. Correlations were also developed to calculate the local and average laminar Nusselt numbers of mixed convection developing flow. The laminar-turbulent transition along the tube length occurred faster with increasing Reynolds number, and was also influenced by free convection effects. As free convection effects became significant, the effect was first to disrupt the fluctuations inside the test section, leading to a slower laminar-turbulent transition along the tube length compared with forced convection conditions. However, as free convection effects were increased, the fluctuations inside the test section increased and caused the laminar-turbulent transition along the tube length to occur faster.

The Reynolds number at which transition started was found to be independent of axial position for both developing and fully developed flow. However, the end of transition occurred earlier as the flow approached fully developed flow. When the flow was fully developed, the end of transition became independent of axial position. Furthermore, free convection effects affected both the start and end of the transitional flow regime, and caused the Reynolds number range of the transitional flow regime to decrease. Correlations were therefore developed to determine the start and end of the transitional flow regime for developing and fully developed flow in mixed convection conditions. The transitional flow regime across the tube length was divided into three regions. In the first region, the width of the transitional flow regime decreased significantly with axial position as the thermal boundary layer thickness increased, and free convection effects were negligible. In Region 2, the width of the transitional flow regime decreased with axial position, due to the development of the thermal boundary layer, as well as with increasing free convection effects. In the fully developed region (Region 3), the width of the transitional flow regime was independent of axial position, but decreased significantly with increasing free convection effects. At high Grashof numbers, free convection effects even caused the transitional flow regime of fully developed flow to become negligible.

It was found that the boundaries of the different flow regimes were the same for pressure drop and heat transfer, and a relationship between pressure drop and heat transfer existed in all four flow regimes. In the laminar flow regime, this relationship was a function of Grashof number (thus free convection effects), while it was a function of Reynolds number in the other three flow regimes. Correlations to predict the average Nusselt numbers, as well as the friction factors as a function of average Nusselt number, for developing and fully developed flow in all flow regimes were developed.

Finally, flow regime maps were developed to predict the convection flow regime for developing and fully developed flow for a wide range of tube diameters and Prandtl numbers, and these flow regime maps were unique for four reasons. Firstly, they contained contour lines that showed the Nusselt number enhancements due to the free convection effects. Secondly, they were valid for a wide range of tube diameters and Prandtl numbers. Thirdly, the flow regime maps were developed as a function of temperature difference (Grashof number) and heat flux (modified Grashof number). Finally, four of the six flow regime maps were not only valid for fully developed flow, but also for developing flow.