Development of new correlations for the Nusselt number and the friction factor under turbulent flow of nanofluids in flat tubes

A Computational Fluid Dynamics (CFD) study of heat enhancement in helically grooved tubes was carried out by using a 3-dimensional simulation with the STARCCM+ simulation package software. The k-ε model selected for turbulent flow simulation and the governing equations were solved by using the finite volume method. Geometric models of the current study include 3 rectangular grooved tubes with different groove width (w) and depth (e) which varies from 0.2 mm to 0.6 mm for the same tube length of 2.0m and diameter of 7.1 mm. The simulations were performed in the Reynolds number (Re) range of 4000–10000 with a uniform wall heat flux of 3150 w/m2 applied as a boundary condition on the surface of each tube. The purpose of this research is to investigate the effect of different groove dimensions on the thermal performance and pressure drop of water inside the grooved tubes and clarify the structural nature of the flow in regards to flow swirl and turbulent kinetic energy distributions. It was found that the highest performance belongs to the groove with these dimensions (w = 0.2 mm and e = 0.2 mm) which was considered for further study. Then, for these same groove dimensions four pitch size to tube diameter (p/D) ratios ranging from 1 to 18 were simulated for the same 2.0 m length tube. The results for Nusselt number (Nu) and friction factor (f) showed that by increasing the (p/D) ratio both the Nu numbers and the friction factors (f) values decrease. With a smaller pitch length (p) the turbulence intensity generated by the internal groove was also found to increase. The physical behavior of the turbulent flow and heat transfer characteristics were observed by contour plots which showed an increasing swirl flow and turbulent kinetic energy as p/D decreases. With an increase of the Nu number for smaller p/D ratio, a penalty of a higher pressure drop was obtained. The results were validated with a previous experimental work and the average error between the experimental and CFD Nu numbers and f were 13% and 8% respectively. A higher level of turbulent kinetic energy is observed near the grooves, as compared to the smooth areas of the pipe surface away from the grooves, which are expected to lead to higher levels of heat transfer. The effect of pitch length (p) on the flow pattern were plotted by streamlines along the tubes, by decreasing the pitch size (p/D ratio) an increase in the swirl is noticed as evidenced by the plots of the path lines. Finally, empirical correlations for Nusselt number and friction factor were provided as a function of p/D and Re number. This study indicates that the incorporation of the internal groove, of particular dimensions, can lead to an improvement of performance in heat exchanger devices. A limited variation of the groove dimensions was conducted and it was found that the values of Nu and f do not improve with an increase of (w) nor with that of (e) from 0.2–0.6 mm.

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Friction factor and Nusselt number in flat tubes with rounded edges

International Journal of Heat and Fluid Flow ◽

10.1016/0142-727x(95)00031-k ◽

1995 ◽

Vol 16 (4) ◽

pp. 307-310 ◽

Cited By ~ 5

Author(s):

Marco Spiga ◽

Roberto Dall'Olio

Keyword(s):

Nusselt Number ◽

Friction Factor ◽

Flat Tubes

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Experimental Investigations on Heat Transfer Enhancement in a Horizontal Tube Using Converging and Diverging Conical Strip Inserts

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.592-594.1590 ◽

2014 ◽

Vol 592-594 ◽

pp. 1590-1595 ◽

Cited By ~ 3

Author(s):

Naga Sarada Somanchi ◽

Sri Rama R. Devi ◽

Ravi Gugulothu

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Pressure Drop ◽

Turbulent Flow ◽

Heat Transfer Enhancement ◽

Friction Factor ◽

Working Fluid ◽

Experimental Investigations ◽

Transfer Enhancement ◽

Enhancement Of Heat Transfer

The present work deals with the results of the experimental investigations carried out on augmentation of turbulent flow heat transfer in a horizontal circular tube by means of tube inserts, with air as working fluid. Experiments were carried out initially for the plain tube (without tube inserts). The Nusselt number and friction factor obtained experimentally were validated against those obtained from theoretical correlations. Secondly experimental investigations using three kinds of tube inserts namely Rectangular bar with diverging conical strips, Rectangular bar with converging conical strips, Rectangular bar with alternate converging diverging conical strips were carried out to estimate the enhancement of heat transfer rate for air in the presence of inserts. The Reynolds number ranged from 8000 to 19000. In the presence of inserts, Nusselt number and pressure drop increased, overall enhancement ratio is calculated to determine the optimum geometry of the tube insert. Based on experimental investigations, it is observed that, the enhancement of heat transfer using Rectangular bar with converging and diverging conical strips is more effective compared to other inserts. Key words: Heat transfer, enhancement, turbulent flow, conical strip inserts, friction factor, pressure drop.

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Three-dimensional numerical investigation of turbulent flow and heat transfer inside a horizontal semi-circular cross-sectioned duct

Thermal Science ◽

10.2298/tsci110724065a ◽

2014 ◽

Vol 18 (4) ◽

pp. 1145-1158 ◽

Cited By ~ 3

Author(s):

Kamil Arslan

Keyword(s):

Heat Transfer ◽

Heat Flux ◽

Nusselt Number ◽

Turbulent Flow ◽

Friction Factor ◽

Turbulence Models ◽

Reynolds Numbers ◽

Forced Flow ◽

Flow And Heat Transfer ◽

Darcy Friction Factor

In this study, steady-state turbulent forced flow and heat transfer in a horizontal smooth semi-circular cross-sectioned duct was numerically investigated. The study was carried out in the turbulent flow condition where Reynolds numbers range from 1?104 to 5.5?104. Flow is hydrodynamically and thermally developing (simultaneously developing flow) under uniform surface heat flux with uniform peripheral wall heat flux (H2) boundary condition on the duct?s wall. A commercial CFD program, Ansys Fluent 12.1, with different turbulent models was used to carry out the numerical study. Different suitable turbulence models for fully turbulent flow (k-? Standard, k-? Realizable, k-? RNG, k-? Standard and k-? SST) were used in this study. The results have shown that as the Reynolds number increases Nusselt number increases but Darcy friction factor decreases. Based on the present numerical solutions, new engineering correlations were presented for the average Nusselt number and average Darcy friction factor. The numerical results for different turbulence models were compared with each other and similar experimental investigations carried out in the literature. It is obtained that, k-? Standard, k-? Realizable and k-? RNG turbulence models are the most suitable turbulence models for this investigation. Isovel contours of velocity magnitude and temperature distribution for different Reynolds numbers, turbulence models and axial stations in the duct were presented graphically. Also, local heat transfer coefficient and local Darcy friction factor as function of dimensionless position along the duct were obtained in this investigation.

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Numerical Studies on Thermo-Hydraulic Characteristics of Turbulent Flow in a Tube with a Regularly Spaced Dimple on Twisted Tape

CFD letters ◽

10.37934/cfdl.13.8.2031 ◽

2021 ◽

Vol 13 (8) ◽

pp. 20-31

Author(s):

Birlie Fekadu ◽

Harish H.V ◽

Manjunath. K

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Turbulent Flow ◽

Friction Factor ◽

Thermal Performance ◽

Numerical Study ◽

Constant Heat Flux ◽

Twisted Tape ◽

Performance Factor ◽

Thermal Performance Factor

Heat transfer augmentation is an important concern due to the increase in heat management problems in thermal systems. There are many techniques for enhancement of heat transfer, by active and passive techniques. A commonly used passive technique to enhance heat transfer is by inserting twisted tapes in tubes. This work presents a numerical study on Nusselt number, friction factor, and thermal performance characteristics through a circular pipe built-in with/without dimples on twisted tape. The analysis results for a turbulent flow range of 4500≤Re≤20000 are obtained with a twist ratio of the strip is 3.0. The analysis is carried for full-length tape with constant heat flux. The governing equations are numerically solved by a ﬁnite volume method using the RNG κ–ε model. The simulation results of Nusselt number versus Reynolds number of the plain, plain twisted tape and dimple twisted tape tube with the experimental data give a variation of 4.15%, 3.89%, and 7.65%. The friction factor of the dimple twisted tape tube is 60 to 70% higher than that of the plain twisted tube at different Reynolds numbers. The thermal performance factor of the dimple twisted tape and plain twisted tape tube is 30 to 35% respectively higher than that of the plain tube. Due to thermal performance factor is above unity yields a promising heat transfer enhancement. By the present study, an optimum geometrical parameter can be selected for use in heat exchangers.

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Nusselt number and friction factor correlations for the solar air heater duct furnished with artificial cube shaped roughness elements on the absorber plate

Heat and Mass Transfer ◽

10.1007/s00231-021-03067-0 ◽

2021 ◽

Author(s):

Madhukeshwara Nanjundappa

Keyword(s):

Nusselt Number ◽

Friction Factor ◽

Solar Air Heater ◽

Absorber Plate ◽

Air Heater ◽

Roughness Elements

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Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

Journal of Fluids Engineering ◽

10.1115/1.4002035 ◽

2010 ◽

Vol 132 (7) ◽

Cited By ~ 18

Author(s):

Henrique Stel ◽

Rigoberto E. M. Morales ◽

Admilson T. Franco ◽

Silvio L. M. Junqueira ◽

Raul H. Erthal ◽

...

Keyword(s):

Reynolds Number ◽

Pressure Drop ◽

Turbulent Flow ◽

Friction Factor ◽

Turbulence Models ◽

Reynolds Numbers ◽

Velocity Magnitude ◽

Geometric Configurations ◽

Corrugated Surfaces ◽

Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

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