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

Abstract

Highlights• Three laminar regions: Forcedand Mixed Convection Developing and Fully Developed. • Thermal entrance length correlations for forced and mixed convection laminar flow. • Local and average laminar Nusselt number correlations for mixed convection flow. • Influence of free convection on the laminar-turbulent transition. ABSTRACT Correlations to calculate the local and average heat transfer coefficients for single-phase laminar flow through horizontal circular tubes with a constant heat flux boundary condition are usually restricted to fully developed flow, high Prandtl numbers or constant fluid properties. What further complicates the heat transfer characteristics of developing flow, is the local transition from laminar to turbulent flow along the tube length, above the critical Reynolds number. The purpose of this study was to investigate the effects of free convection on the development of the local heat transfer characteristics in smooth horizontal circular tubes heated with a constant heat flux. An experimental set-up was designed, built, and results were validated against literature. Two smooth circular test sections with innerdiameters 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 heat fluxes. A total of 1 046 mass flow rate measurements and 89 459 temperature measurements were taken. Water was used as the test fluid and the Prandtl number ranged between 3 and 7. Three different regions were identified for developing laminar flow and were qualitatively and quantitatively defined. Correlations were developed to determine the thermal entrance lengths, as well as local and average Nusselt numbers for developing and fully developed laminar flow in mixed convection conditions with a constant heat flux boundary condition. In the transitional flow regime, the laminar-turbulent transition along the tube length was divided into four regions, and it was

Computational Study of Flow and Heat Transfer Characteristics of EG-Si3N4 Nanofluid in Laminar Flow in a Pipe in Forced Convection Regime

“…The computationally obtained results converge with decreasing the mesh size in both, the dimensionless radial temperature distribution and the Nusselt number. The analytical solution for the Nusselt number Nu = 4.36 is also correctly evaluated and the computational results for the Nusselt number are in very good agreement with the experimental results in [38] and also the empirical result from [41]. The computed local Nusselt number and the dimensionless radial temperature profile in the pipe cross-section are plotted in Figure 4.…”

“…This is a consequence of the assumption that the effects of the forced heat convection are predominant in comparison to the natural heat convection. This assumption is justified for cases where the flow is constrained to small geometries, such as the one used here (tube with 4 mm inner diameter), whereas the natural heat convection effects become important in larger geometries [38].…”

“…The model is verified for a pure fluid, without nanoparticles, against the known analytical solution [39], the experimental results [38], and the empirical result [41]. In the computational setup, the pipe geometry and fluid (water) properties are the same as in [38], with the Reynolds number of the flow Re = 965, the wall heat flux q = 1000 W/m 2 and the temperature of the fluid at the inlet is T in = 293 K, as listed in Table 1. The fluid in these simulations is Newtonian and the viscous stress tensor is calculated as τ = µ ∇U + (∇U) T , instead of using the Herschel-Bulkley model.…”

Relationship between pressure drop and heat transfer of developing and fully developed flow in smooth horizontal circular tubes in the laminar, transitional, quasi-turbulent and turbulent flow regimes

“…Therefore, this correlation is suited for forced convection conditions, rather than mixed convection conditions. This paper forms part of a bigger study and is complimentary to papers published by Meyer and Everts [1] and Everts and Meyer [34,36]. Meyer and Everts [1] investigated mixed convection laminar flow, as well as the effect of free convection on the laminarturbulent transition along the tube length.…”

“…Another limitation of this approach is that the laminar Nusselt number correlation is for developing forced convection flow and therefore produces a Nusselt number of 4.36 for fully developed flow. In most cases this will not be correct as laminar flow are normally dominated by mixed convection [1], especially when low Prandtl number fluids, such as water, are used. Although this method was tested using the numerical data of Abraham et al [35], Gnielinski [33] mentioned that "no experimental data were found which have allowed checking the Nusselt numbers obtained by the calculation procedure outlined above in the region of linear interpolation, i.e., between 1 000 < Re < 4 000".…”