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Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube with small pipe inserts
International Communications in Heat and Mass Transfer 56 (2014) 1–7
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube with small pipe inserts☆ Tu Wenbin a,b, Tang Yong a,⁎, Zhou Bo a, Lu Longsheng a a b
Key Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes, South China University of Technology, Guangzhou 510640, People's Republic of China Department of Electrical Engineering, Jiangxi University of Science and Technology, Nanchang 330013, People's Republic of China
a r t i c l e
i n f o
Article history: Received 25 October 2013 Receivedin revised form 4 April 2014 Accepted 11 April 2014 Available online 9 May 2014 Keywords: Enhancement Turbulent flow Small pipe inserts Heat transfer
a b s t r a c t Heat transfer performance and pressure drop tests were performed on a circular tube with small pipe inserts. These inserts with different spacer lengths (S = 100, 142.9 and 200 mm) and arc radii (R = 5, 10 and 15 mm) were tested at Reynolds numbers between 4000 and 18,000. Tap water was used as working fluid. The use of pipe inserts allowed for a high heat transfer coefficient with relatively low flow resistance. The Nusselt number and friction factor increase with the decrease in spacer length. Optimal results were obtained for S = 100 mm (R = 10 mm). Heat transfer rates and friction factors were enhanced by 2.09–2.67 and 1.59–1.85 times, respectively, to those in the plain tube. Performance evaluation criterion (PEC) values were approximately 1.79–2.17. The Nusselt number and friction factor increase with the decrease in arc radius. Small pipe inserts with R = 5 mm and S = 100 mm show maximal heat transfer rates of 2.61–3.33 and friction factors of 1.6–1.8 times those of the empty tube. The PEC values were 2.23–2.7. Compared with other inserts, pipe inserts can transfer more heat for the same pumping power for their unique structure. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction The performance of forced convection heat transfer in tubes can be improved through the use of elements such as twisted tape, coiled wire and helical screw-tape [1–3]. The low cost, rapid installation and easy maintenance associated with this augment technique make it attractive compared with other enhancement techniques. Inserted elements typically function as vortex generators by generating swirl flow and modifying velocity distributions. This leads to fluid mixing and the redevelopment of the thermal boundary layers with a resulting enhancement in heat transfer. However, flow resistance is also increased. It is challenging to obtain a high heat transfer rate with low increase in pressure drop. Researchers have designed various inserts to achieve a high heat transfer rate and low increase in pressure drop. Compared with fulllength twisted tapes, multiple short-length twisted tapes can yield a lower pressure drop for the same twist ratio. Saha et al. [4] reported that regularly-spaced twisted tape performed significantly better than full-length twisted tapes at high Reynolds numbers and that the pressure drop decreased by 40%. Ferroni et al. [5] found that multiple short-length twisted tapes yielded pressure drops at least 50% lower ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (W. Tu), [email protected] (Y. Tang).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.04.020 0735-1933/© 2014 Elsevier Ltd. All rights reserved.
than those of most well known full-length tapes. Previous work has adopted techniques such as disrupting the thermal boundary layer and filling of the porous medium to improve heat transfer performance. Murugesan et al. [6] investigated the thermal characteristics of V-cut twisted tape experimentally. The Nusselt number and friction factor for the tube with V-cut twisted tapes were 1.36–2.46 and 2.49–5.82 times, respectively, that of the empty tube. Zhang et al. [7] presented a numerical study on triple and quadruple twisted tapes where an increase of 171% and 182%, respectively, was obtained. However, the friction factors were 4.06 to 7.02 times, respectively, that of the plain tube. Naphon [8] studied the heat transfer characteristics and pressure drop of coil-wire inserts. This insert enhanced the heat transfer significantly, especially in the laminar flow region. Pavel et al. [9] showed that higher heat transfer rates can be achieved by using porous inserts at the expense of a reasonable pressure drop. Helical screw-tape is a modified form of a twisted tape. Unlike twisted tape, which generates swirling flow in two parallel flow directions, helical screw-tape provides a single smooth screw-like direction of motion [10] that greatly reduces flow resistance. Sivashanmugam et al. [11] studied the heat transfer and friction factor characteristics in a circular tube fitted with full-length helical screw elements of different twist ratio and spacer length. The helical screw inserts with spacer were suitable for heat augmentation only in turbulent flow with limited reduction in pumping power. Ibrahim [12] investigated the heat transfer and friction factor in horizontal flat tubes with full length helical screw inserts and found that the Nusselt
2
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
Nomenclature A cp DH d f h k l m• Nu Pr Δp Q Re R Rw Rf S t ΔTm U v ρ μ
surface area of test tube, m2 specific heat of water, J/kg K hydraulic diameter, m tube diameter, m friction factor convective heat transfer coefficient, W/m2 K thermal conductivity, W/m K the length of testing section, m water mass flow rate, kg/s Nusselt number Prandtl number pressure difference, N/m2 mean value of heat transfer rate, W Reynolds number arc radius, mm conduction resistance through the tube wall fouling resistance spacer length, mm temperature, K logarithmic mean temperature difference, K overall heat transfer coefficient, W/m2 K mean velocity in the tube, m/s fluid density, kg/m3 fluid dynamic viscosity N s/m2
Subscripts c cold h hot i inside o outside w wall
number and friction factor decreased with the increase in spacer length and twist ratio for flat tubes. Some researchers realized the difference in flow velocity in different flow regions. They designed a new type of insert, a louvered strip insert, which is small in size in the core flow region where the flow velocity is relatively high and is relatively large in size in the vicinity of the boundary layers. This type of insert resulted in good enhancement and relatively low flow resistance. Fan et al. [13] investigated heat transfer and flow characteristics numerically in a circular tube fitted with louvered strip inserts. Eiamsa-ard et al. [14] investigated heat transfer and friction characteristics in a concentric tube heat exchanger fitted with louvered strips. The increase in the average Nusselt number and friction loss for the inclined forward louvered strip was 284% and 413%. Guo et al. [15] investigated the thermo-hydraulic performance of conical-strip inserts and found that the performance factor was enhanced by 36–61% that of the conical-ring inserts at the Reynolds range of 5000 to 25,000. An increase in shear stress near the boundary layer inevitably results in an increase in the friction factor. However, it could be very different by changing the velocity and temperature field according to the velocity and temperature distribution in the tube. When fluid flows through a tube, the maximum flow velocity exists in the center and the minimum velocity near the wall of the tube. Temperature also has an uneven distribution during heat exchange. Mixing fluids with different temperatures and velocities will result in a significant heat transfer coefficient. Most studies focus on vortex intensity and disregard the distribution of the velocity and temperature field, which may lead to unnecessary disturbances and increase flow resistance. It is possible to devise a structure that distributes the temperature and velocity fields by design. In
this paper, a new type of insert, consisting of small pipes, has been developed. The pipes enable fluid at different temperatures to flow easily and result in a uniform temperature. The geometries of the small pipe inserts are shown in Fig. 1, where some small pipes are mounted on a stainless steel rod and are placed inside the inner test tube. It is expected that a high heat transfer coefficient will be obtained with limited increase in pressure drop. An experiment was performed to investigate the pressure drop and thermal characteristics of the inserts. 2. Experimental setup A schematic diagram of the experimental setup is shown in Fig. 2. It consists of a test section (heat exchanger), cooling water loop and hot water loop. The test section consists of two concentric tubes. Hot water flows through the inner tube and cold water flows through the annulus. The inner and outer tube diameters are 16 and 38 mm, respectively. The inner tube is copper (1300 mm long, 2 mm thick) and the outer tube is Plexiglas (1300 mm long and 5 mm thick). Water is heated in a hot water tank (HH-W600; HengFeng Electronics Manufacturing, Inc., JiangSu Province, China) and its temperature is maintained at 70 °C by a proportional integral derivative controller inside the water tank. The cold water temperature was maintained at ~ 30 °C. Water is pumped through the test section by a pump with flow rate controlled by a control valve. The inlet and outlet water temperatures are measured by four T-type thermocouples (Omeron Inc.). All thermocouples were calibrated before testing with an accuracy of ±0.1 °C. The water flow rate through the test section was measured using a rotameter with an accuracy of ±1%. The pressure in the test tube was measured by a pressure transmitter (P/N:DP1300-DP7E22M4B1N, Senex Inc.) with an accuracy of ± 0.5%. Temperatures and pressures were recorded by using a data logger (Agilent Data Acquisition Unit 34970A). The pipe inserts were copper (2 mm diameter and 0.5 mm thick) with the method of fabrication as shown in Fig. 3(a). A small pipe 20 mm in length was formed into an S-shape. Three such pipes were mounted on a 1000 mm stainless rod. The friction factor can be affected by spacer length [11]. Inserts with different arc radii have different slant angles and could have a significant effect on performance. The effect of slant angle on heat transfer performance is discussed in [14]. Based on these considerations, small pipe inserts with different spacer lengths (S = 100, 149.2 and 200 mm) and arc radii (R = 5, 10 and 15 mm) were tested in this work. The pipe insert geometries are shown in Fig. 3(b) and (c). 3. Data processing Data processing of the measured results is summarized in the following procedures. The heat transfer rate of cold water in the annulus, QC, can be written as: • Q c ¼ mc cp t c;o −t c;i
ð1Þ
• where m c is the cold water mass flow rate, cp is the specific heat of water and tc,i and tc,o are the inlet and outlet cold water temperatures, respectively. The heat transfer from the hot water in the test section, Qh, can be expressed as:
• Q h ¼ mh cp t h;i −t h;o
ð2Þ
where m• h is the mass flow rate of hot water and th,i t and th,o are the inlet and outlet water temperatures, respectively.
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
3
Fig. 1. (a) The scheme illustrating the geometry of the pipe inserts element, and (b) picture of pipe inserts.
The mean value of the heat transfer rate is used as the heat transfer rate of the tube heat exchanger. The mean value of the heat transfer rate, Q, is calculated from: Q¼
Qh þ Qc 2
ð3Þ
The heat transfer rate through the test section is given as: Q ¼ UAi ΔT m
ð4Þ
where ΔTm is the logarithmic mean temperature difference (counter flow was adopted) and can be calculated as: t h;i −t c;o − t h;o −t c;i ! ΔT m ¼ ð5Þ t h;i −t c;o ln t h;o −t c;i
The overall thermal resistance can be expressed as: 1 1 A ¼ þ Rw þ i þ R f ho A0 U hi
ð6Þ
where Rw is the conduction resistance through the tube wall and Rf is the fouling resistance. All tubes are cleaned before the test, and the fouling resistance is neglected. The tube wall resistance, Rw, can be calculated as: Rw ¼
di d ln o 2kw di
ð7Þ
The annulus side heat transfer coefficient, ho, is estimated as: ho DH 0:8 0:4 ¼ 0:023Re Pr k
ð8Þ
where DH is the hydraulic diameter and k is the thermal conductivity.
Fig. 2. Experimental setup. (1) Data acquisition system; (2) pressure transmitter; (3) test section; (4) rotameter; (5) control valve; (6) ball valve; (7) water pump; (8) hot water pump; (9) cooling water tank; (10) hot water tank; (11) heater.
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W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
Fig. 3. (a) The scheme illustrating the fabrication of the pipe inserts element, (b) the shape of pipe with different arc radius, R, and (c) pipe inserts with various spacer lengths, S.
Thus, Nui ¼
hi di k
4. Verification in smooth tube test ð9Þ
The local thermal conductivity of the fluid, k, is calculated from the fluid properties at the local temperature. The friction factor, f, is given by: f ¼
2di Δp ρlv2
ð10Þ
Before testing, the smooth copper tube was tested to validate the experimental setup. Heat transfer and pressure drop data were recorded at the Reynolds number range of 4000–18,000. Data obtained in this work were in good agreement with the standard correlations of the Dittus–Boelter and Gnielinski equation for the Nusselt number and the Blasius and Petukhov equation for the friction factor. Comparisons between experimental and standard correlation data are shown in Figs. 4 and 5. Deviations from this work fall within ±9.5% for the Nusselt number and ±10% for the friction factor. 5. Results and discussion
where v is the mean velocity in the tube. Uncertainties in the Nusselt number, the Reynolds number and the friction factor can be calculated from: δNu ¼ Nu
2 2 2 0:5 δh δk δd þ þ h k d
The performance evaluation criterion (PEC) proposed by Webb [16] was used to evaluate the thermohydraulic performance of the tube fitted with pipe inserts and is expressed as follows:
ð11Þ PEC ¼
δRe ¼ Re
δf ¼ f
2 2 2 2 0:5 δv δρ δd δμ þ þ þ v ρ d μ
2 2 2 2 0:5 δv δρ δd δl δΔp 2 þ þ þ þ v ρ d l Δp
ð12Þ
Nu=Nu0 ð f =f 0 Þ1=3
ð13Þ
in which Nu0 and f0 are calculated from the Dittus–Boelter and Blasius equations. 5.1. Effect of spacer length
ð13Þ
The maximum uncertainties in the Nusselt number, the Reynolds number and the friction factor in this work were 1.72%, 1.2% and 2.24%, respectively.
Fig. 4. Data verification of Nusselt number (Nu) with Reynolds number (Re) for the smooth tube.
In all experiments, the Nusselt number increases with the Reynolds number, while the friction factor decreases with the Reynolds number. Such heat transfer enhancement is attributed to the thin thermal boundary layer at the higher Reynolds number.
Fig. 5. Data verification of friction factor (f) with Reynolds number (Re) for the smooth tube.
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
Fig. 6. Nusselt number (Nu) vs. Reynolds number (Re) for pipe inserts (R = 10 mm) with different spacer lengths.
5
Fig. 8. PEC vs. Reynolds number for pipe inserts (R = 10 mm) with different spacer lengths.
Fig. 6 shows the variation in the Nusselt number with the Reynolds number for pipe inserts (R = 10 mm) with spacer lengths of 100, 142.9 and 200 mm. Pipe inserts have a higher heat transfer performance than smooth tubes. The heat transfer rate increases with the decrease in spacer length. Pipe inserts with a spacer length of 100 mm have the highest heat transfer rate with an enhancement of approximately 2.09–2.67 times that of the smooth tube. Pipe inserts with spacer lengths of 200 mm result in an improvement of 1.83–2.43 times that of the smooth pipe. However, the Nusselt number for S = 200 mm is much closer to that of the other two pipe inserts. This indicates that the spacer length has little influence on heat transfer performance. The friction factor for different spacer lengths is given in Fig. 7. The friction factor increases with the decrease in spacer length. The friction factor for inserts with S = 100 mm is increased 1.59–1.85 times. Data for S = 142.9 mm and S = 200 mm show an increase of 1.37–1.61 and 1.24–1.29 times that of the smooth pipe, respectively. On the whole, the Nusselt number for the pipe inserts (R = 10 mm) with different spacer length is enhanced by 1.8–2.7 times in the Reynolds number range of 4000 to 18,000. The friction factor increases 1.24–1.85 times. A high enhancement can be achieved through temperature field modulation by using pipe inserts. The geometry of small pipe inserts makes it possible for water to flow easily inside and outside the small pipes, and leads to a mixing of water with different temperatures and velocities. This increases the temperature gradient of the thermal boundary layer and causes heat exchange between water regions in the pipe. These factors enhance the heat transfer rate. Moreover, the flow resistance is low,
because the small pipes are too small to generate an intense resistance. Its special structure therefore makes it possible to avoid unnecessary disturbances. The PEC values are shown in Fig. 8 where that for S = 100 mm is the highest at 1.79–2.17. The values for S = 142. 9 mm and S = 200 mm are approximately 1.6–2.12 and 1.7–2.1, respectively. The PEC values decrease with an increase in the Reynolds number. Enhancement is therefore high in the laminar regime and relatively low in the turbulent regime as a result of the temperature difference in the laminar regime being larger than that in the turbulent regime. Interestingly, the plots for S = 142. 9 mm and S = 200 mm cross one other in Figs. 6 and 8. The Nusselt numbers for S = 200 mm and S = 142. 9 mm are close to one other. In the turbulent regime, temperature field modulation cannot affect performance heavily. The longitudinal vortex flow produced by the shape of the pipe inserts therefore dominates performance. However, a spacer length of 142.9 mm seems unfavorable to the development of longitudinal vortex flow. Thus, the heat transfer rate for S = 200 mm is higher than that for S = 142.9 mm in the turbulent regime.
Fig. 7. Friction factor (f) vs. Reynolds number (Re) for pipe inserts (R = 10 mm) with different spacer lengths.
Fig. 9. Nusselt number (Nu) vs. Reynolds number (Re) for pipe inserts (S = 100 mm) with different arc radii, R.
5.2. Effect of pipe shape Fig. 9 shows the variation in the Nusselt number with the Reynolds number for pipe inserts (S = 100 mm) with arc radii of 5, 10 and 15 mm. The pipe shape affects heat transfer performance significantly. Data for R = 5 and 15 mm are approximately 2.61–3.33 and 1.9–2.42
6
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
trend. Pipe inserts of R = 5 mm have a higher heat transfer performance and higher friction factor. Fortunately, the heat transfer rate increases faster than the friction factor. Pipe inserts of R = 5 mm have the highest PEC value of 2.23–2.7 (see Fig. 11). Pipe inserts of R = 10 and 15 mm have a PEC value of 1.79–2.17 and 1.66–2.202, respectively. Pipe inserts of R = 5 mm therefore cause an intense longitudinal vortex flow along the tube which enhances the heat transfer rate. Comparisons between this and previous work are shown in Fig. 12 (a) and (b). The pipe inserts perform better than inserts such as V-cut taps [6], counterclockwise twisted tapes [18] and helical screw-tapes [19], but worse than conical cut-out turbulators with finned inserts [17]. However, the friction factor of the pipe inserts is smallest and the PEC value is the highest (shown in Fig. 12 (b)). Pipe inserts therefore show good thermal performance for their unique structure and are able to modulate the flow field. Fig. 10. Friction factor (f) vs. Reynolds number (Re) for pipe inserts (S = 100 mm) with different arc radii, R.
Fig. 11. PEC vs. Reynolds number for pipe inserts (S = 100 mm) with different arc radii.
times, respectively, that of the smooth tube. The friction factor for R = 5 mm is 1.6–1.8 times that of the smooth tube shown in Fig. 10. The friction factor for R = 15 mm is approximately 1.47–1.73 times that of the smooth tube. The heat transfer performance therefore increases with the decrease in arc radius. Data for the friction factor show a similar
a) Nussselt number for present word and previous work
6. Conclusion The effect of small pipe inserts on heat transfer enhancement, flow resistance and thermal-hydraulic performance at a Reynolds range of 4000–18,000 is described in this paper. Pipe inserts with different spacer lengths (S = 200, 142. 9 and 100 mm) and arc radii (R = 5, 10 and 15 mm) were tested. Water is the working fluid in the experiment. Results from this investigation are summarized as follows: • Tubes fitted with pipe inserts affect the heat transfer coefficient and friction factor. The geometry of the small pipe inserts makes it possible for water to flow easily through the inside and outside of the pipe. This leads to a mixing of water with different temperatures and velocities. Mixing increases the temperature gradient of the thermal boundary layer and causes uniformity in fluid temperature. This enhances heat transfer. • The tube fitted with small pipe inserts can achieve a high heat transfer with a lower increase in friction factor. The friction factor is less than most of those recorded in other literature and is only 1.24–1.87 times that of the smooth tube. • The Nusselt number and friction factor increase with decreasing spacer length. Data for S = 100 mm and R = 10 mm are superior to others. The Nusselt number is approximately 2.09–2.67 times that of the smooth tube. The friction factor is approximately 1.59–1.85 times that caused by the smooth tube alone. The PEC value is approximately 1.79–2.17. • The Nusselt number and friction factor increase with decreasing arc radius. The Nusselt number for S = 100 mm and R = 5 mm is
b) PEC vaules for present word and previous work
Fig. 12. Comparisons with previous work. a) Nusselt number for present and previous work. b) PEC values for present and previous work.
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
2.61–3.33 times that of the smooth tube. The friction factor is approximately 0.044–0.073 times that of the smooth tube and the PEC value is 2.23–2.7. Acknowledgments This work was supported by a major state basic research development program of china (2011CB710703), the National Nature Science Foundation of China (No. 51275180) and the joint funds of NSFCGuangdong of China under Grant No. U0934005. References [1] P.K. Sarma, T. Subramanyam, P.S. Kishore, V. Dharma Rao, Sadik Kakac, A new method to predict convective heat transfer in a tube with twisted tape inserts for turbulent flow, Int. J. Therm. Sci. 41 (2002) 955–960. [2] Sibel Gunes, Veysel Ozceyhan, Orhan Buyukalaca, The experimental investigation of heat transfer and pressure drop in a tube with coiled wire inserts placed separately from the tube wall, Appl. Therm. Eng. 30 (2010) 1719–1725. [3] P. Sivashanmugam, P.K. Nagarajan, Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right and left helical screw-tape inserts, Exp. Thermal Fluid Sci. 32 (2007) 192–197. [4] S.K. Saha, U.N. Gaitonde, A.W. Date, Heat transfer and pressure drop characteristics of laminar flow in a circular tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Sci. 2 (1989) 310–322. [5] P. Ferroni, R.E. Block, N.E. Todreas, A.E. Bergles, Experimental evaluation of pressure drop in round tubes provided with physically separated, multiple, short-length twisted tapes, Exp. Thermal Fluid Sci. 35 (2011) 1357–1369. [6] P. Murugesan, K. Mayilsamy, S. Suresh, P.S.S. Srinivasan, Heat transfer and pressure drop characteristics in a circular tube fitted with and without V-cut twisted tape insert, Int. Commun. Heat Mass Transf. 38 (2011) 329–334. [7] Xiaoyu Zhang, Zhichun Liu, Wei Liu, Numerical studies on heat transfer and flow characteristics for laminar flow in a tube with multiple regularly spaced twisted tapes, Int. J. Therm. Sci. 58 (2012) 157–167.
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[8] Paisarn Naphon, Effect of coil-wire insert on heat transfer enhancement and pressure drop of the horizontal concentric tubes, Int. Commun. Heat Mass Transf. 33 (2006) 753–763. [9] Bogdan I. Pavel, Abdulmajeed A. Mohamad, An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media, Int. J. Heat Mass Transf. 47 (2004) 4939–4952. [10] Xiaoyu Zhang, Zhichun Liu, Wei Liu, Numerical studies on heat transfer and friction factor characteristics of a tube fitted with helical screw-tape without core-rod inserts, Int. J. Heat Mass Transf. 60 (2013) 490–498. [11] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with regularly spaced helical screw-tape inserts, Appl. Therm. Eng. 27 (2007) 1311–1319. [12] E.Z. Ibrahim, Augmentation of laminar flow and heat transfer in flat tubes by means of helical screw-tape inserts, Energy Convers. Manag. 52 (2011) 250–257. [13] A.W. Fan, J.J. Deng, A. Nakayama, W. Liu, Parametric study on turbulent heat transfer and flow characteristics in a circular tube fitted with louvered strip inserts, Int. J. Heat Mass Transf. 55 (2012) 5205–5213. [14] Smith Eiamsa-ard, Somsak Pethkool, Chinaruk Thianpong, Pongjet Promvonge, Turbulent flow heat transfer and pressure loss in a double pipe heat exchanger with louvered strip inserts, Int. Commun. Heat Mass Transf. 35 (2008) 120–129. [15] Jian Guo, Yuexiang Yan, Wei Liu, Fangming Jiang, Aiwu Fan, Effects of upwind area of tube inserts on heat transfer and flow resistance characteristics of turbulent flow, Exp. Thermal Fluid Sci. 48 (2013) 147–155. [16] R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transf. 24 (1981) 715–726. [17] C. Muthusamy, M. Vivar, I. Skryabin, K. Srithar, Effect of conical cut-out turbulators with internal fins in a circular tube on heat transfer and friction factor, Int. Commun. Heat Mass Transf. 44 (2013) 64–68. [18] Smith Eiamsa-ard, Pongjet Promvonge, Performance assessment in a heat exchanger tube with alternate clockwise and counter-clockwise twisted-tape inserts, Int. J. Heat Mass Transf. 53 (2010) 1364–1372. [19] Smith Eiamsa-ard, Pongjet Promvonge, Heat transfer characteristics in a tube fitted with helical screw-tape with/without core-rod inserts, Int. Commun. Heat Mass Transf. 34 (2007) 176–185.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube with small pipe inserts☆ Tu Wenbin a,b, Tang Yong a,⁎, Zhou Bo a, Lu Longsheng a a b
Key Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes, South China University of Technology, Guangzhou 510640, People's Republic of China Department of Electrical Engineering, Jiangxi University of Science and Technology, Nanchang 330013, People's Republic of China
a r t i c l e
i n f o
Article history: Received 25 October 2013 Receivedin revised form 4 April 2014 Accepted 11 April 2014 Available online 9 May 2014 Keywords: Enhancement Turbulent flow Small pipe inserts Heat transfer
a b s t r a c t Heat transfer performance and pressure drop tests were performed on a circular tube with small pipe inserts. These inserts with different spacer lengths (S = 100, 142.9 and 200 mm) and arc radii (R = 5, 10 and 15 mm) were tested at Reynolds numbers between 4000 and 18,000. Tap water was used as working fluid. The use of pipe inserts allowed for a high heat transfer coefficient with relatively low flow resistance. The Nusselt number and friction factor increase with the decrease in spacer length. Optimal results were obtained for S = 100 mm (R = 10 mm). Heat transfer rates and friction factors were enhanced by 2.09–2.67 and 1.59–1.85 times, respectively, to those in the plain tube. Performance evaluation criterion (PEC) values were approximately 1.79–2.17. The Nusselt number and friction factor increase with the decrease in arc radius. Small pipe inserts with R = 5 mm and S = 100 mm show maximal heat transfer rates of 2.61–3.33 and friction factors of 1.6–1.8 times those of the empty tube. The PEC values were 2.23–2.7. Compared with other inserts, pipe inserts can transfer more heat for the same pumping power for their unique structure. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction The performance of forced convection heat transfer in tubes can be improved through the use of elements such as twisted tape, coiled wire and helical screw-tape [1–3]. The low cost, rapid installation and easy maintenance associated with this augment technique make it attractive compared with other enhancement techniques. Inserted elements typically function as vortex generators by generating swirl flow and modifying velocity distributions. This leads to fluid mixing and the redevelopment of the thermal boundary layers with a resulting enhancement in heat transfer. However, flow resistance is also increased. It is challenging to obtain a high heat transfer rate with low increase in pressure drop. Researchers have designed various inserts to achieve a high heat transfer rate and low increase in pressure drop. Compared with fulllength twisted tapes, multiple short-length twisted tapes can yield a lower pressure drop for the same twist ratio. Saha et al. [4] reported that regularly-spaced twisted tape performed significantly better than full-length twisted tapes at high Reynolds numbers and that the pressure drop decreased by 40%. Ferroni et al. [5] found that multiple short-length twisted tapes yielded pressure drops at least 50% lower ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (W. Tu), [email protected] (Y. Tang).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.04.020 0735-1933/© 2014 Elsevier Ltd. All rights reserved.
than those of most well known full-length tapes. Previous work has adopted techniques such as disrupting the thermal boundary layer and filling of the porous medium to improve heat transfer performance. Murugesan et al. [6] investigated the thermal characteristics of V-cut twisted tape experimentally. The Nusselt number and friction factor for the tube with V-cut twisted tapes were 1.36–2.46 and 2.49–5.82 times, respectively, that of the empty tube. Zhang et al. [7] presented a numerical study on triple and quadruple twisted tapes where an increase of 171% and 182%, respectively, was obtained. However, the friction factors were 4.06 to 7.02 times, respectively, that of the plain tube. Naphon [8] studied the heat transfer characteristics and pressure drop of coil-wire inserts. This insert enhanced the heat transfer significantly, especially in the laminar flow region. Pavel et al. [9] showed that higher heat transfer rates can be achieved by using porous inserts at the expense of a reasonable pressure drop. Helical screw-tape is a modified form of a twisted tape. Unlike twisted tape, which generates swirling flow in two parallel flow directions, helical screw-tape provides a single smooth screw-like direction of motion [10] that greatly reduces flow resistance. Sivashanmugam et al. [11] studied the heat transfer and friction factor characteristics in a circular tube fitted with full-length helical screw elements of different twist ratio and spacer length. The helical screw inserts with spacer were suitable for heat augmentation only in turbulent flow with limited reduction in pumping power. Ibrahim [12] investigated the heat transfer and friction factor in horizontal flat tubes with full length helical screw inserts and found that the Nusselt
2
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
Nomenclature A cp DH d f h k l m• Nu Pr Δp Q Re R Rw Rf S t ΔTm U v ρ μ
surface area of test tube, m2 specific heat of water, J/kg K hydraulic diameter, m tube diameter, m friction factor convective heat transfer coefficient, W/m2 K thermal conductivity, W/m K the length of testing section, m water mass flow rate, kg/s Nusselt number Prandtl number pressure difference, N/m2 mean value of heat transfer rate, W Reynolds number arc radius, mm conduction resistance through the tube wall fouling resistance spacer length, mm temperature, K logarithmic mean temperature difference, K overall heat transfer coefficient, W/m2 K mean velocity in the tube, m/s fluid density, kg/m3 fluid dynamic viscosity N s/m2
Subscripts c cold h hot i inside o outside w wall
number and friction factor decreased with the increase in spacer length and twist ratio for flat tubes. Some researchers realized the difference in flow velocity in different flow regions. They designed a new type of insert, a louvered strip insert, which is small in size in the core flow region where the flow velocity is relatively high and is relatively large in size in the vicinity of the boundary layers. This type of insert resulted in good enhancement and relatively low flow resistance. Fan et al. [13] investigated heat transfer and flow characteristics numerically in a circular tube fitted with louvered strip inserts. Eiamsa-ard et al. [14] investigated heat transfer and friction characteristics in a concentric tube heat exchanger fitted with louvered strips. The increase in the average Nusselt number and friction loss for the inclined forward louvered strip was 284% and 413%. Guo et al. [15] investigated the thermo-hydraulic performance of conical-strip inserts and found that the performance factor was enhanced by 36–61% that of the conical-ring inserts at the Reynolds range of 5000 to 25,000. An increase in shear stress near the boundary layer inevitably results in an increase in the friction factor. However, it could be very different by changing the velocity and temperature field according to the velocity and temperature distribution in the tube. When fluid flows through a tube, the maximum flow velocity exists in the center and the minimum velocity near the wall of the tube. Temperature also has an uneven distribution during heat exchange. Mixing fluids with different temperatures and velocities will result in a significant heat transfer coefficient. Most studies focus on vortex intensity and disregard the distribution of the velocity and temperature field, which may lead to unnecessary disturbances and increase flow resistance. It is possible to devise a structure that distributes the temperature and velocity fields by design. In
this paper, a new type of insert, consisting of small pipes, has been developed. The pipes enable fluid at different temperatures to flow easily and result in a uniform temperature. The geometries of the small pipe inserts are shown in Fig. 1, where some small pipes are mounted on a stainless steel rod and are placed inside the inner test tube. It is expected that a high heat transfer coefficient will be obtained with limited increase in pressure drop. An experiment was performed to investigate the pressure drop and thermal characteristics of the inserts. 2. Experimental setup A schematic diagram of the experimental setup is shown in Fig. 2. It consists of a test section (heat exchanger), cooling water loop and hot water loop. The test section consists of two concentric tubes. Hot water flows through the inner tube and cold water flows through the annulus. The inner and outer tube diameters are 16 and 38 mm, respectively. The inner tube is copper (1300 mm long, 2 mm thick) and the outer tube is Plexiglas (1300 mm long and 5 mm thick). Water is heated in a hot water tank (HH-W600; HengFeng Electronics Manufacturing, Inc., JiangSu Province, China) and its temperature is maintained at 70 °C by a proportional integral derivative controller inside the water tank. The cold water temperature was maintained at ~ 30 °C. Water is pumped through the test section by a pump with flow rate controlled by a control valve. The inlet and outlet water temperatures are measured by four T-type thermocouples (Omeron Inc.). All thermocouples were calibrated before testing with an accuracy of ±0.1 °C. The water flow rate through the test section was measured using a rotameter with an accuracy of ±1%. The pressure in the test tube was measured by a pressure transmitter (P/N:DP1300-DP7E22M4B1N, Senex Inc.) with an accuracy of ± 0.5%. Temperatures and pressures were recorded by using a data logger (Agilent Data Acquisition Unit 34970A). The pipe inserts were copper (2 mm diameter and 0.5 mm thick) with the method of fabrication as shown in Fig. 3(a). A small pipe 20 mm in length was formed into an S-shape. Three such pipes were mounted on a 1000 mm stainless rod. The friction factor can be affected by spacer length [11]. Inserts with different arc radii have different slant angles and could have a significant effect on performance. The effect of slant angle on heat transfer performance is discussed in [14]. Based on these considerations, small pipe inserts with different spacer lengths (S = 100, 149.2 and 200 mm) and arc radii (R = 5, 10 and 15 mm) were tested in this work. The pipe insert geometries are shown in Fig. 3(b) and (c). 3. Data processing Data processing of the measured results is summarized in the following procedures. The heat transfer rate of cold water in the annulus, QC, can be written as: • Q c ¼ mc cp t c;o −t c;i
ð1Þ
• where m c is the cold water mass flow rate, cp is the specific heat of water and tc,i and tc,o are the inlet and outlet cold water temperatures, respectively. The heat transfer from the hot water in the test section, Qh, can be expressed as:
• Q h ¼ mh cp t h;i −t h;o
ð2Þ
where m• h is the mass flow rate of hot water and th,i t and th,o are the inlet and outlet water temperatures, respectively.
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
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Fig. 1. (a) The scheme illustrating the geometry of the pipe inserts element, and (b) picture of pipe inserts.
The mean value of the heat transfer rate is used as the heat transfer rate of the tube heat exchanger. The mean value of the heat transfer rate, Q, is calculated from: Q¼
Qh þ Qc 2
ð3Þ
The heat transfer rate through the test section is given as: Q ¼ UAi ΔT m
ð4Þ
where ΔTm is the logarithmic mean temperature difference (counter flow was adopted) and can be calculated as: t h;i −t c;o − t h;o −t c;i ! ΔT m ¼ ð5Þ t h;i −t c;o ln t h;o −t c;i
The overall thermal resistance can be expressed as: 1 1 A ¼ þ Rw þ i þ R f ho A0 U hi
ð6Þ
where Rw is the conduction resistance through the tube wall and Rf is the fouling resistance. All tubes are cleaned before the test, and the fouling resistance is neglected. The tube wall resistance, Rw, can be calculated as: Rw ¼
di d ln o 2kw di
ð7Þ
The annulus side heat transfer coefficient, ho, is estimated as: ho DH 0:8 0:4 ¼ 0:023Re Pr k
ð8Þ
where DH is the hydraulic diameter and k is the thermal conductivity.
Fig. 2. Experimental setup. (1) Data acquisition system; (2) pressure transmitter; (3) test section; (4) rotameter; (5) control valve; (6) ball valve; (7) water pump; (8) hot water pump; (9) cooling water tank; (10) hot water tank; (11) heater.
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W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
Fig. 3. (a) The scheme illustrating the fabrication of the pipe inserts element, (b) the shape of pipe with different arc radius, R, and (c) pipe inserts with various spacer lengths, S.
Thus, Nui ¼
hi di k
4. Verification in smooth tube test ð9Þ
The local thermal conductivity of the fluid, k, is calculated from the fluid properties at the local temperature. The friction factor, f, is given by: f ¼
2di Δp ρlv2
ð10Þ
Before testing, the smooth copper tube was tested to validate the experimental setup. Heat transfer and pressure drop data were recorded at the Reynolds number range of 4000–18,000. Data obtained in this work were in good agreement with the standard correlations of the Dittus–Boelter and Gnielinski equation for the Nusselt number and the Blasius and Petukhov equation for the friction factor. Comparisons between experimental and standard correlation data are shown in Figs. 4 and 5. Deviations from this work fall within ±9.5% for the Nusselt number and ±10% for the friction factor. 5. Results and discussion
where v is the mean velocity in the tube. Uncertainties in the Nusselt number, the Reynolds number and the friction factor can be calculated from: δNu ¼ Nu
2 2 2 0:5 δh δk δd þ þ h k d
The performance evaluation criterion (PEC) proposed by Webb [16] was used to evaluate the thermohydraulic performance of the tube fitted with pipe inserts and is expressed as follows:
ð11Þ PEC ¼
δRe ¼ Re
δf ¼ f
2 2 2 2 0:5 δv δρ δd δμ þ þ þ v ρ d μ
2 2 2 2 0:5 δv δρ δd δl δΔp 2 þ þ þ þ v ρ d l Δp
ð12Þ
Nu=Nu0 ð f =f 0 Þ1=3
ð13Þ
in which Nu0 and f0 are calculated from the Dittus–Boelter and Blasius equations. 5.1. Effect of spacer length
ð13Þ
The maximum uncertainties in the Nusselt number, the Reynolds number and the friction factor in this work were 1.72%, 1.2% and 2.24%, respectively.
Fig. 4. Data verification of Nusselt number (Nu) with Reynolds number (Re) for the smooth tube.
In all experiments, the Nusselt number increases with the Reynolds number, while the friction factor decreases with the Reynolds number. Such heat transfer enhancement is attributed to the thin thermal boundary layer at the higher Reynolds number.
Fig. 5. Data verification of friction factor (f) with Reynolds number (Re) for the smooth tube.
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
Fig. 6. Nusselt number (Nu) vs. Reynolds number (Re) for pipe inserts (R = 10 mm) with different spacer lengths.
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Fig. 8. PEC vs. Reynolds number for pipe inserts (R = 10 mm) with different spacer lengths.
Fig. 6 shows the variation in the Nusselt number with the Reynolds number for pipe inserts (R = 10 mm) with spacer lengths of 100, 142.9 and 200 mm. Pipe inserts have a higher heat transfer performance than smooth tubes. The heat transfer rate increases with the decrease in spacer length. Pipe inserts with a spacer length of 100 mm have the highest heat transfer rate with an enhancement of approximately 2.09–2.67 times that of the smooth tube. Pipe inserts with spacer lengths of 200 mm result in an improvement of 1.83–2.43 times that of the smooth pipe. However, the Nusselt number for S = 200 mm is much closer to that of the other two pipe inserts. This indicates that the spacer length has little influence on heat transfer performance. The friction factor for different spacer lengths is given in Fig. 7. The friction factor increases with the decrease in spacer length. The friction factor for inserts with S = 100 mm is increased 1.59–1.85 times. Data for S = 142.9 mm and S = 200 mm show an increase of 1.37–1.61 and 1.24–1.29 times that of the smooth pipe, respectively. On the whole, the Nusselt number for the pipe inserts (R = 10 mm) with different spacer length is enhanced by 1.8–2.7 times in the Reynolds number range of 4000 to 18,000. The friction factor increases 1.24–1.85 times. A high enhancement can be achieved through temperature field modulation by using pipe inserts. The geometry of small pipe inserts makes it possible for water to flow easily inside and outside the small pipes, and leads to a mixing of water with different temperatures and velocities. This increases the temperature gradient of the thermal boundary layer and causes heat exchange between water regions in the pipe. These factors enhance the heat transfer rate. Moreover, the flow resistance is low,
because the small pipes are too small to generate an intense resistance. Its special structure therefore makes it possible to avoid unnecessary disturbances. The PEC values are shown in Fig. 8 where that for S = 100 mm is the highest at 1.79–2.17. The values for S = 142. 9 mm and S = 200 mm are approximately 1.6–2.12 and 1.7–2.1, respectively. The PEC values decrease with an increase in the Reynolds number. Enhancement is therefore high in the laminar regime and relatively low in the turbulent regime as a result of the temperature difference in the laminar regime being larger than that in the turbulent regime. Interestingly, the plots for S = 142. 9 mm and S = 200 mm cross one other in Figs. 6 and 8. The Nusselt numbers for S = 200 mm and S = 142. 9 mm are close to one other. In the turbulent regime, temperature field modulation cannot affect performance heavily. The longitudinal vortex flow produced by the shape of the pipe inserts therefore dominates performance. However, a spacer length of 142.9 mm seems unfavorable to the development of longitudinal vortex flow. Thus, the heat transfer rate for S = 200 mm is higher than that for S = 142.9 mm in the turbulent regime.
Fig. 7. Friction factor (f) vs. Reynolds number (Re) for pipe inserts (R = 10 mm) with different spacer lengths.
Fig. 9. Nusselt number (Nu) vs. Reynolds number (Re) for pipe inserts (S = 100 mm) with different arc radii, R.
5.2. Effect of pipe shape Fig. 9 shows the variation in the Nusselt number with the Reynolds number for pipe inserts (S = 100 mm) with arc radii of 5, 10 and 15 mm. The pipe shape affects heat transfer performance significantly. Data for R = 5 and 15 mm are approximately 2.61–3.33 and 1.9–2.42
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W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
trend. Pipe inserts of R = 5 mm have a higher heat transfer performance and higher friction factor. Fortunately, the heat transfer rate increases faster than the friction factor. Pipe inserts of R = 5 mm have the highest PEC value of 2.23–2.7 (see Fig. 11). Pipe inserts of R = 10 and 15 mm have a PEC value of 1.79–2.17 and 1.66–2.202, respectively. Pipe inserts of R = 5 mm therefore cause an intense longitudinal vortex flow along the tube which enhances the heat transfer rate. Comparisons between this and previous work are shown in Fig. 12 (a) and (b). The pipe inserts perform better than inserts such as V-cut taps [6], counterclockwise twisted tapes [18] and helical screw-tapes [19], but worse than conical cut-out turbulators with finned inserts [17]. However, the friction factor of the pipe inserts is smallest and the PEC value is the highest (shown in Fig. 12 (b)). Pipe inserts therefore show good thermal performance for their unique structure and are able to modulate the flow field. Fig. 10. Friction factor (f) vs. Reynolds number (Re) for pipe inserts (S = 100 mm) with different arc radii, R.
Fig. 11. PEC vs. Reynolds number for pipe inserts (S = 100 mm) with different arc radii.
times, respectively, that of the smooth tube. The friction factor for R = 5 mm is 1.6–1.8 times that of the smooth tube shown in Fig. 10. The friction factor for R = 15 mm is approximately 1.47–1.73 times that of the smooth tube. The heat transfer performance therefore increases with the decrease in arc radius. Data for the friction factor show a similar
a) Nussselt number for present word and previous work
6. Conclusion The effect of small pipe inserts on heat transfer enhancement, flow resistance and thermal-hydraulic performance at a Reynolds range of 4000–18,000 is described in this paper. Pipe inserts with different spacer lengths (S = 200, 142. 9 and 100 mm) and arc radii (R = 5, 10 and 15 mm) were tested. Water is the working fluid in the experiment. Results from this investigation are summarized as follows: • Tubes fitted with pipe inserts affect the heat transfer coefficient and friction factor. The geometry of the small pipe inserts makes it possible for water to flow easily through the inside and outside of the pipe. This leads to a mixing of water with different temperatures and velocities. Mixing increases the temperature gradient of the thermal boundary layer and causes uniformity in fluid temperature. This enhances heat transfer. • The tube fitted with small pipe inserts can achieve a high heat transfer with a lower increase in friction factor. The friction factor is less than most of those recorded in other literature and is only 1.24–1.87 times that of the smooth tube. • The Nusselt number and friction factor increase with decreasing spacer length. Data for S = 100 mm and R = 10 mm are superior to others. The Nusselt number is approximately 2.09–2.67 times that of the smooth tube. The friction factor is approximately 1.59–1.85 times that caused by the smooth tube alone. The PEC value is approximately 1.79–2.17. • The Nusselt number and friction factor increase with decreasing arc radius. The Nusselt number for S = 100 mm and R = 5 mm is
b) PEC vaules for present word and previous work
Fig. 12. Comparisons with previous work. a) Nusselt number for present and previous work. b) PEC values for present and previous work.
W. Tu et al. / International Communications in Heat and Mass Transfer 56 (2014) 1–7
2.61–3.33 times that of the smooth tube. The friction factor is approximately 0.044–0.073 times that of the smooth tube and the PEC value is 2.23–2.7. Acknowledgments This work was supported by a major state basic research development program of china (2011CB710703), the National Nature Science Foundation of China (No. 51275180) and the joint funds of NSFCGuangdong of China under Grant No. U0934005. References [1] P.K. Sarma, T. Subramanyam, P.S. Kishore, V. Dharma Rao, Sadik Kakac, A new method to predict convective heat transfer in a tube with twisted tape inserts for turbulent flow, Int. J. Therm. Sci. 41 (2002) 955–960. [2] Sibel Gunes, Veysel Ozceyhan, Orhan Buyukalaca, The experimental investigation of heat transfer and pressure drop in a tube with coiled wire inserts placed separately from the tube wall, Appl. Therm. Eng. 30 (2010) 1719–1725. [3] P. Sivashanmugam, P.K. Nagarajan, Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right and left helical screw-tape inserts, Exp. Thermal Fluid Sci. 32 (2007) 192–197. [4] S.K. Saha, U.N. Gaitonde, A.W. Date, Heat transfer and pressure drop characteristics of laminar flow in a circular tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Sci. 2 (1989) 310–322. [5] P. Ferroni, R.E. Block, N.E. Todreas, A.E. Bergles, Experimental evaluation of pressure drop in round tubes provided with physically separated, multiple, short-length twisted tapes, Exp. Thermal Fluid Sci. 35 (2011) 1357–1369. [6] P. Murugesan, K. Mayilsamy, S. Suresh, P.S.S. Srinivasan, Heat transfer and pressure drop characteristics in a circular tube fitted with and without V-cut twisted tape insert, Int. Commun. Heat Mass Transf. 38 (2011) 329–334. [7] Xiaoyu Zhang, Zhichun Liu, Wei Liu, Numerical studies on heat transfer and flow characteristics for laminar flow in a tube with multiple regularly spaced twisted tapes, Int. J. Therm. Sci. 58 (2012) 157–167.
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[8] Paisarn Naphon, Effect of coil-wire insert on heat transfer enhancement and pressure drop of the horizontal concentric tubes, Int. Commun. Heat Mass Transf. 33 (2006) 753–763. [9] Bogdan I. Pavel, Abdulmajeed A. Mohamad, An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media, Int. J. Heat Mass Transf. 47 (2004) 4939–4952. [10] Xiaoyu Zhang, Zhichun Liu, Wei Liu, Numerical studies on heat transfer and friction factor characteristics of a tube fitted with helical screw-tape without core-rod inserts, Int. J. Heat Mass Transf. 60 (2013) 490–498. [11] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with regularly spaced helical screw-tape inserts, Appl. Therm. Eng. 27 (2007) 1311–1319. [12] E.Z. Ibrahim, Augmentation of laminar flow and heat transfer in flat tubes by means of helical screw-tape inserts, Energy Convers. Manag. 52 (2011) 250–257. [13] A.W. Fan, J.J. Deng, A. Nakayama, W. Liu, Parametric study on turbulent heat transfer and flow characteristics in a circular tube fitted with louvered strip inserts, Int. J. Heat Mass Transf. 55 (2012) 5205–5213. [14] Smith Eiamsa-ard, Somsak Pethkool, Chinaruk Thianpong, Pongjet Promvonge, Turbulent flow heat transfer and pressure loss in a double pipe heat exchanger with louvered strip inserts, Int. Commun. Heat Mass Transf. 35 (2008) 120–129. [15] Jian Guo, Yuexiang Yan, Wei Liu, Fangming Jiang, Aiwu Fan, Effects of upwind area of tube inserts on heat transfer and flow resistance characteristics of turbulent flow, Exp. Thermal Fluid Sci. 48 (2013) 147–155. [16] R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transf. 24 (1981) 715–726. [17] C. Muthusamy, M. Vivar, I. Skryabin, K. Srithar, Effect of conical cut-out turbulators with internal fins in a circular tube on heat transfer and friction factor, Int. Commun. Heat Mass Transf. 44 (2013) 64–68. [18] Smith Eiamsa-ard, Pongjet Promvonge, Performance assessment in a heat exchanger tube with alternate clockwise and counter-clockwise twisted-tape inserts, Int. J. Heat Mass Transf. 53 (2010) 1364–1372. [19] Smith Eiamsa-ard, Pongjet Promvonge, Heat transfer characteristics in a tube fitted with helical screw-tape with/without core-rod inserts, Int. Commun. Heat Mass Transf. 34 (2007) 176–185.