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Thermal characteristics in round tube fitted with serrated twisted tape
Applied Thermal Engineering 30 (2010) 1673e1682
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Thermal characteristics in round tube fitted with serrated twisted tape Smith Eiamsa-ard a, *, Pongjet Promvonge b a b
Department of Mechanical Engineering, Faculty of Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand School of Mechanical Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2009 Accepted 22 March 2010 Available online 27 March 2010
The article presents an investigation of the effect of twisted tape with serrated-edge insert on heat transfer and pressure loss behaviors in a constant heat-fluxed tube. In the experiments, the serrated twisted tape (STT) was inserted into the entire test tube with a constant twist ratio in order to generate a continuous swirling airflow. Two geometry parameters of the STT to be considered in the present work are the serration width ratio and the serration depth ratio. The measurements have been conducted for the airflow rate based on Reynolds numbers in the turbulent regime from 4000 to 20,000. The experimental results of the STT inserted tube are compared with those of the plain tube fitted with typical twisted tape (TT). The results show that the heat transfer rate in terms of Nusselt number, Nu increases with the rise in the depth ratio but decreases with raising the width ratio. The heat transfer rate is up to 72.2% and 27% relative to the plain tube and the TT inserted tube, respectively. The use of the STT leads to higher heat transfer rate and friction factor than that of the TT for all cases. The thermal performance factor of the STT tube under constant pumping power is evaluated and found to be above unity indicating that using the STT tube is advantageous over the TT tube or the plain tube. In addition, the empirical correlations developed by relating the serration width ratio, serration depth ratio and Reynolds number are determined. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Friction factor Serrated twisted tape Typical twisted tape Swirl flow
1. Introduction Twisted tapes have been used extensively as a swirl generator to enhance convection heat transfer rate in finding the way to reduce the weight, size and cost of heat exchanger systems in several industrial applications such as chemical engineering process, heat recovery process, air conditioning and refrigeration systems, chemical reactors, power plant, and nuclear reactor, etc. Tubes with twisted tape insert are also an important group of the continuous swirling flow device that generates twin swirling flow motion over the whole tube length of flow at constant heat transfer coefficient (h) and friction factor (f). There are many devices used for producing swirl flow in the tube such as helical vanes, helical grooved tube, helical screw-tape, axial-radial guide vanes and snail entry [1,2] while the twisted tape is one of the most popular group because of low cost, low maintenance, low pressure loss and ease of construction. All of swirling flow devices have been used to generate the tangential velocity, thin the boundary layer [3], enhance the tangential and radial turbulent fluctuation [4], and therefore cause the increase in heat transfer rate and friction loss inside tubes [1e4].
* Corresponding author. Tel./fax: þ66 2 9883666x241. E-mail address: [email protected] (S. Eiamsa-ard). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.03.026
In the past investigations, the heat transfer enhancement by twisted tape insert has been considered on both experimental and numerical works. Saha et al. [5] studied the heat transfer and pressure loss behaviors in a tube fitted with regularly-spaced twisted tape elements. Ray and Date [6] predicted the heat transfer in a square sectioned duct fitted with twisted tape in both laminar and turbulent flows. The heat transfer behaviors were predicted under axially and peripherally constant wall heat flux conditions. Chang et al. [7] conducted an experimental work on the flow friction and heat transfer characteristics in a tube fitted with twisted serrated-tape modified from the TT by attaching ribs repeatedly on two sides of the tape surface to provide additional turbulence intensities. They found that the plain tube fitted with serrated twisted tape provides heat transfer higher than the plain tube without tape inserts. Influences of using the broken twisted tape at various twist ratios on the heat transfer and friction factor were also reported by Chang et al. [8]. They reported that the heat transfer coefficients, mean Fanning friction factor, and thermal performance factors in the tube fitted with the broken twisted tape were, respectively, augmented to 1.28e2.4, 2e4.7 and 0.99e1.8 times over the tube fitted with the TT. Recently, Rahimi et al. [9] examined the heat transfer, friction factor and thermal hydraulic performance in a round tube fitted
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Nomenclature A Cp d D f h I k l L M Nu P DP Pr Q Re t T T~ U
heat transfer surface area, m2 specific heat of fluid, J kg1 K1 serration depth, m inner diameter of test tube, m friction factor heat transfer coefficient, W m2 K1 current, A thermal conductivity of fluid, W m1 K1 length of twisted tape, m length of test section, m mass flow rate, kg s1 Nusselt number ¼ hD/k pressure, Pa pressure drop, Pa Prandtl number ¼ mCp/k heat transfer rate, W Reynolds number ¼ rUD/m thickness of test tube, m temperature, K mean temperature, K average velocity, m s1
with the classic and the modified twisted tape inserts. They found that the jagged twisted tape provides the maximum heat transfer enhancement than other tapes. Bharadwaj et al. [10] investigated the heat transfer and pressure drop in a spirally grooved tube with the TT insert for laminar to fully turbulent regions. The effects of the direction of twist (clockwise and anticlockwise) on the thermo-hydraulic characteristics were also reported. Sharma et al. [11] reported the heat transfer coefficient and friction factor for flow in a round tube with the TT inserts in the transition range of flow with Al2O3 nanofluid for different twist ratios. Krishna et al. [12] experimentally studied the heat transfer characteristics of a tube fitted with straight full twist insert with different spacer distances. Akhavan-Behabadi et al. [13] reported the influence of the twisted tape on heat transfer and pressure drop characteristics in horizontal evaporators for the flow using R-134a. Jaisankar et al. [14e17] conducted an experiment on heat transfer and friction factor characteristics in a thermosyphon solar water heater system with full-length twist, twist fitted with rod and spacer fitted at the trailing edge, helical twisted tapes and spacer at the trailing edge of left-right twisted tapes, respectively. Eiamsa-ard et al. [18] investigated the heat transfer and pressure loss behaviors in a double pipe heat exchanger fitted with regularly-spaced twisted tape elements at several space ratios. Effect of the combined conical-ring turbulator and twisted tape on the heat transfer, friction factor and thermal performance factor characteristics were also studied by Promvonge and Eiamsa-ard [19]. Influence of the tube equipped with the short-length twisted tape on the mean Nusselt number, friction factor and thermal performance factor characteristics for several tape length ratios was examined by Eiamsa-ard et al. [20]. Again, Eiamsa-ard et al. [21e23] reported the effect of the dual twisted tape elements in tandem, twin twisted tape with counter/co-swirling flow and delta-winglet twisted tape on the heat transfer enhancement, friction factor and thermal performance factor. They found that all tape arrangements provide better heat transfer rate than those of the typical twisted tape while the friction factors are also increasing. Eiamsa-ard and Promvonge [2,24] also studied the
V V_ w W y
voltage, volt volume flow rate, m3 s1 serration width, m tape width, m pitch length of twisted tape (180 rotation), m
Greek letters d tape thickness, m r density, kg m3 m dynamic viscosity, kg s1 m1 h thermal performance factor Subscripts a air b bulk conv convection i inlet o outlet s swirl flow generator p plain tube pp pumping power w wall
effect of helical tape with/without core-rod and regularly-spaced helical tape swirl generators on the heat transfer and pressure drop characteristics in a heat exchanger tube while the effects of the helical screw-tape with alternate axis (left and right tapes) and regularly-spaced helical screw-tape on the heat transfer enhancement and thermal performance in laminar and turbulent regions were also reported by Sivashanmugam and Suresh [25e28] and Sivashanmugam and Nagarajan [29]. One way for enhancing heat transfer in a tube is by using a twisted tape having serrate edges in order to increase mixing or turbulence intensity and breaking down the boundary layer apart from using continuous swirling flow in the tube. In the heat transfer enhancement process, twisted tape inserts can be well applied to thermal systems since the twisted tape can help to promote higher heat transfer rate because of better mixing of strong swirling flow and long residence time in the tube. The aim of the present work is to investigate the heat transfer rate (Nu) and friction factor (f) characteristics of continuous swirl flow through a round tube fitted with serrated twisted tape (STT) using the air as the test fluid. A comparison is carried out on both the friction factor and heat transfer between a tube with/without the TT and one with the STT under similar test conditions. The experiments are conducted in the turbulent flow region under uniform heat flux conditions while the STT was inserted over the test tube length at a constant twist ratio (y/W ¼ 4.0). Two geometry parameters of the STT are taken into account: (1) the serration width ratio (w/W ¼ 0.1, 0.2 and 0.3) and (2) the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3). In addition, the thermal performance factor (h) of the tube with the STT is examined under constant pumping power conditions. All of the experiments are carried out at the same entrance conditions with the Reynolds number (Re) based on the inside tube diameter in a range of 4000e20,000. It should be noted that the twisted tape in the current work was modified by forming the serrate-edge of the tape to generate turbulence intensity near the edge region which is totally different from the serrated twisted tape of Chang et al. [7] that was modified by forming ribs on the tape surface to promote the turbulence across the surface.
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2. Experimental set-up
2.2. Experimental procedure
2.1. Test section and twisted tape
In the apparatus setting above, the inlet air at room bulk temperature from a centrifugal blower was directed through an orifice flow meter and passed to the heat transfer test section. The pressure drop of the test tube was measured with an inclined Utube manometer. Manometric fluid was used in an inclined U-tube manometer with specific gravity (SG.) of 0.826 to ensure reasonably accurate measurement of the low pressure drop encountered at low Reynolds numbers. The volumetric airflow rates from the blower were adjusted by varying motor speed through the inverter and measured by the orifice meter situated upstream of the test tube. The inner and outer temperatures of the bulk air were measured at certain points with a data logger in conjunction with the RTD PT 100 type temperature sensors. Fifteen thermocouples were tapped on the local wall of the test tube and the thermocouples were placed round the tube to measure the circumferential temperature variation, which was found to be negligible. The mean local wall temperature was determined by means of calculations based on the reading of Chromel-constantan thermocouples. In each test run, it is necessary to record the data of temperature, volumetric flow rate and pressure drop of the bulk air at steady state conditions in which the inlet air temperature was maintained at 25 C. The Reynolds number of the bulk air was varied from 4000 to 20,000. The local wall temperature (Tw), inlet and outlet air temperatures, the pressure drop across the test section and airflow rate were measured and recorded to evaluate and analyze the heat transfer rate of the heated tube.
A general arrangement of experimental apparatus is shown in Fig. 1. The loop consisted of: (1) an existing 7.5 kW high speed blower, (2) three phase inverter, (3) orifice meter to measure the volumetric airflow rate, (4) inclined/U-tube manometer to measure the pressure loss, (5) the heating test section, (6) variac transformer, (7) amp meter, (8) volt meter, (9) data logger and (10) personal computer. The inside and outside diameters of the copper test tube having a length of L ¼ 1250 mm, and 1.5 mm thickness (t), are 47 mm and 50 mm, respectively. The test tube was heated by continually winding flexible electrical wires providing a uniform heat flux boundary condition. The electrical output power was controlled by a variac transformer to obtain a constant heat flux along the entire length of the test section and by keeping the current less than 3 A. The outer surface of the test tube was well insulated to minimize convective heat loss to surroundings, and necessary precautions were taken to prevent leakages from the system. The characteristic geometries of all tape are illustrated in Fig. 2 (aec). Each of the twisted tape made of aluminium was 1250 mm long, 0.8 mm thick and inserted into the test tube having a uniform heat flux condition. The test tube fitted with TT is presented in Fig. 2 (a) and the modified tape or the STT is also found in Fig. 2(bec). The geometrical dimensions of the STT were y is the pitch length of 180 twist, d is the tape thickness, W is the tape width and D is the inner tube diameter; the severity of the twist is usually referred to as a dimensionless twist ratio, y/W. In each test run, the STT was inserted into the whole length of the test tube with a constant twist ratio, y/W ¼ 4.0. The tape edge was cut to be serrate shape (V-cut) with two geometry parameters: (1) the serration width ratio (w/ W ¼ 0.1, 0.2 and 0.3) and (2) the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3). The details of the test condition and twisted tape geometries are summarized in Table 1.
2.3. Experimental uncertainty To obtain the uncertainties of measurements the reduced data were determined. The uncertainty in the data calculation was based on Ref. [30]. The maximum uncertainties of non-dimensional parameters are 5% for Reynolds number, 10% for Nusselt number and 15% for friction. The uncertainty in the axial velocity
Fig. 1. Experimental set-up.
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Fig. 2. Test tube fitted with typical twisted tape (TT) or twisted tape with serrated-edge (STT): (a) TT, (b) STT at various serration width ratios, w/W, and (c) STT at various serration depth ratios, d/W.
Table 1 Test condition and dimension of the tape geometries.
Parameter study (a) Reynolds number, (Re) (b) Tape width, (W) (c) Twist ratio, (y/W) (d) Tape thickness, (d) (e) Serration depth ratio (d/W) (f) Serration width ratio (w/W)
Typical twisted tape
Serrated twisted tape (STT)
4000e20,000 46 mm 4.0 1.5 mm e e
Similar conditions Similar conditions Similar conditions Similar conditions 0.1, 0.2 and 0.3 0.1, 0.2 and 0.3
measurement was estimated to be less than 7%, and pressure has a corresponding estimated uncertainty of 5%, whereas the uncertainty in temperature measurement at the tube wall is about 0.5%. 3. Data reduction In the present work, the air was used as the working fluid and flowed through a uniform heat flux and insulation tube. The steady state of the heat transfer rate was assumed to be equal to the heat loss from the test section which can be expressed as:
S. Eiamsa-ard, P. Promvonge / Applied Thermal Engineering 30 (2010) 1673e1682
Qa ¼ Qconv
(1)
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a
where
Qa ¼ MCp;a ðTo Ti Þ ¼ VI
(2)
In the experiments, the heat supplied by electrical winding in the test tube was found around 3e5% higher than the heat absorbed by the fluid for thermal equilibrium test due to convection and radiation heat losses from the test section to surroundings. Thus, only the heat transfer rate absorbed by the fluid was taken for internal convective heat transfer coefficient calculation. The convection heat transfer from the test section can be written by:
Qconv ¼ hA T~ w Tb
(3)
whereas,
Tb ¼ ðTo þ Ti Þ=2
(4)
and
_ p;a ðTo Ti Þ=A T~ w Tb h ¼ mC hm ¼
h=15
Nu ¼ hD=k
(7)
The Reynolds number, Re is given by
Re ¼ rUD=m
(8)
Friction factor, f can be written as:
DP rU22
f ¼ L
p
¼
f Re3
0.15 0.1
0
4000
8000
12000 16000 20000 24000
Reynolds number Fig. 3. Validation of the plain tube: (a) Nusselt number (Nu) and (b) friction factor (f).
4. Results and discussion
s
1=3 Rep ¼ Res fs =fp
(10)
The thermal performance criteria, h of the test tube fitted with the STT is defined as the ratio of the heat transfer coefficient for the inserted tube (hs) to that of the plain tube (hp) at the same level of pumping power and can be expressed as follows [31]:
h¼
Blasius equation
0.2
0
and the relationship between friction and Reynolds number can be expressed as:
0.25
(9)
V_ DP p ¼ V_ DP s
f Re3
Manglik and Bergles equation TT Plain tube Petukhov equation
0.05
in which U is mean velocity of the tube. All of thermo-physical properties of the air were determined at the overall bulk air temperature (Tb) from equation (4). For a constant pumping power,
0.3
(6)
where h is the local heat transfer coefficient and evaluated at the outer wall surface of the copper tube. The average wall temperature was calculated from 15 points of local wall temperatures, lined between the inlet and the exit of the test pipe. The average Nusselt number, Nu is estimated as follows:
D
b
Friction factor
X
(5)
1=3 hs f =fp ¼ Nu=Nup hp pp
(11)
The experimental heat transfer and friction factor result in a uniform heat flux tube with/without STT swirl generators are depicted in Figs. 3e7, respectively. Effects of the STT at different serration width (w/W ¼ 1.0, 2.0 and 3.0) and depth ratios (d/ W ¼ 1.0, 2.0 and 3.0) covering a wide variation of the flow rates corresponding to the range of 4000 < Re < 20,000, on the heat transfer, flow friction and thermal performance factor behaviors are also reported. As mentioned earlier, the Nusselt number and the Reynolds number were calculated on the basis of the plain tube diameter; this allows direct comparison with the equivalent plain tube performance. The data are reported in the form of Nusselt numbers (Nu) or friction factor (f) versus Reynolds numbers (Re). Moreover, analyzing the thermal performance of these heat transfer promoters with respect to their heat transfer enhancement efficiencies at the same pumping power level is examined.
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Fig. 4. Effect of the serration width ratio (w/W) on heat transfer rate.
4.1. Validation test
Fig. 6. Effect of serration depth ratio (d/W) on heat transfer rate.
Nu ¼ 0:023Re0:8 Pr0:4 for
For the experimental results, the heat transfer rate and the friction factor of the fully developed turbulent flow in a circular plain tube are first reported and confirmed with the previous correlations [32]. Fig. 3 presents a validation for the heat transfer (Nu) and the friction factor (f) results that calculated from the heat transfer coefficient (h) or the pressure drop (DP) data using equations (7) and (9). The experiment of the plain tube was performed for heating condition and its results was compared with those from DittuseBoelter, and Gnielinski correlations for heat transfer and compared with Blasius or Petukhov correlation for friction factor. Nusselt number correlations: Empirical correlation of DittuseBoelter:
Re > 10; 000
Empirical correlation of Gnielinski:
Nu ¼
ðf =8ÞðRe 1000ÞPr for 3000 < Re < 500; 000 1 þ 12:7ðf =8Þ0:5 Pr0:33 1
Friction factor correlations: Empirical correlation of Blasius:
f ¼ 0:316Re0:25 f ¼ 0:184Re0:2
for for
Re 20; 000 Re 20; 000
0.3 STT, w/W = 0.1 STT, w/W = 0.2 STT, w/W = 0.3 TT Plain tube
0.25
Friction factor
0.2
0.15
0.1
0.05
0 0
4000
8000
12000
16000
20000
24000
Reynolds number Fig. 5. Effect of the serration width ratio (w/W) on friction factor.
(12)
Fig. 7. Effect of serration depth ratio (d/W) on friction factor.
(13)
(14) (15)
S. Eiamsa-ard, P. Promvonge / Applied Thermal Engineering 30 (2010) 1673e1682
Empirical correlation of Petukhov:
f ¼ ð0:790ln Re 1:64Þ2
for
3000 Re 500; 000
(16)
In the figures, the heat transfer rate (Nu) and the friction factor (f) are plotted as a function of Reynolds number (Re). It is apparent that the results of the present plain tube are in excellent agreement with the previous correlations for both heat transfer and friction factor. They are within 5% deviation with DittuseBoelter correlation and around 12% with Blasius equation as can be seen in Fig. 3(aeb), respectively. With the help of experimental data of the plain tube, the following empirical Nusselt number (Nu) and friction factor (f) relationships are derived for axial flow of the plain tube which is correlated as follows: Nu ¼ 0.018 Re0.814Pr0.4
(17)
f ¼ 0.786 Re0.33
(18)
Fig. 3(aeb) also shows the verification of using the twisted tape of the present work with the correlation of Manglik and Bergles [33]. It is seen that the present heat transfer and friction factor results are in good agreement with the previous work and show slightly lower values. 4.2. Effect of serration width ratio 4.2.1. Heat transfer The relationships between heat transfer (Nu) and Reynolds numbers (Re) of the tube fitted with (1) TT and (2) STT at the width ratios, w/W ¼ 0.1, 0.2 and 0.3 for d/W ¼ 0.1 are demonstrated in Fig. 4. The Reynolds number (Re) based on the inner diameter of the inlet test tube varies from 4000 to 20,000. In the figure, it is worth noting that the trend of increasing heat transfer rate (Nu) with Reynolds number for the STT is similar to that for the plain tube or the TT insert. The heat transfer enhancement of the tube with STT is found to be better than that the plain tube with/without TT. The use of the STT provides (1) strong mixing or turbulence flow near the serratededge leading to destruction of thermal boundary layer and (2) swirling flow creating better flow mixing between the fluid at the core and the tube wall. Both flow phenomena promote an increase in the tangential and radial turbulent fluctuation or the turbulence intensity, thinning the boundary layer [3], and therefore cause the rise in heat transfer rate inside a tube. It is interesting to note that the smaller width ratio (w/W ¼ 0.1) yields higher heat transfer rate than the larger ones (w/W ¼ 0.2 and 0.3). This is likely from the higher turbulence intensity near the serrate-edge and better mixing between fluid and heating wall surface. Under the present experimental conditions, the mean heat transfer rate for tube fitted with STT is found to be about 42.2%, 36.7% and 32.7% above the plain tube for w/W ¼ 0.1, 0.2 and 0.3, respectively. In addition, the turbulence and the swirling flow generated by the STT cause the boundary layer disruption near the tape edge leading to heat transfer enhancement than those obtained from the TT around 11.3%, 7% and 4% at width ratios, w/W ¼ 1.0, 2.0 and 3.0, respectively. 4.2.2. Friction factor Effect of using the tube fitted with STT at several serration width ratio (w/W ¼ 0.1, 0.2 and 0.3) on friction factor characteristic is showed in Fig. 5. In the figure, the friction factors are in the similar trend for both the plain tube with/without twisted tape inserts. The tube fitted with STT provides higher friction factor value than the plain tube with/without TT. It is seen that the friction factor is increased for both tubes fitted with STT and TT. The friction factor
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for the STT is up to 179% higher than the plain tube alone. This is because of the flow blockage from using the STT and friction loss from the increased surface area. It is also observed that the use of the STT gives higher friction factor than that of the TT due to higher turbulence fluctuation of the fluid in the tape edge region acted by the serrated-edge. Besides, the presence of the STT reduces flow areas, resulting in high turbulence intensity. This leads to the substantial pressure loss action of the fluid (hot air) between the serrate-edged surface and the inner tube wall higher than the TT case. The mean friction factors of the STT at w/W ¼ 0.1, 0.2 and 0.3, respectively, are found to be about 17.5%, 10.2%, 5.5% higher than those of the TT. It is visible that the friction factor of the STT reduces with the increase in the width ratio (w/W). In addition, the friction factor of the STT with w/W ¼ 0.1 is about 11.4% and 4.5% higher than those with w/W ¼ 0.2 and 0.3, respectively. 4.3. Effect of serration depth ratio 4.3.1. Heat transfer Effect of the serration depth ratio (d/W) on the heat transfer rate in the plain tube fitted with STT is presented in Fig. 6. With the values obtained from experimental data, the changes in heat transfer rate (Nu) with Reynolds numbers are also presented. It is found that higher heat transfer rate (Nu) can be obtained by the tube fitted with STT of all depth ratios (d/W). It is obvious that the heat transfer rates increase with the increase in Reynolds number. The turbulence intensity of the swirl flow depends on the shape of the STT for different serration depth ratios (d/W ¼ 0.1, 0.2 and 0.3) at a constant w/W ¼ 0.1. With this, an increase in the heat transfer rate is obtained up to 72.2% in comparison with the plain tube. The mean increase in the heat transfer rate from using the STT is at 42.2%, 47.2% and 52% for d/W ¼ 0.1, 0.2 and 0.3, respectively. It can be observed that the heat transfer rates (Nu) tend to increase considerably with the rise in the depth ratio value. In all cases, the tube with STT insert provides higher values of heat transfer rate (Nu) than the tube with/without TT. It seems that the STT not only produce more turbulence than the TT but also increase the fluid mixing near the tape edge regime. Heat transfer augmentation in this study is a consequence of formation of the swirl flow mixing with using the STT in the test tube and the increase of the turbulence near the wall. This is because the increase of the near-wall velocity produces larger temperature gradients and higher heat transfer rate. The boundary layer along the tube wall would be thinner with the increase of radial swirl and pressure. Therefore, heat could be transferred easily through the flow. 4.3.2. Friction factor Friction factor results for the tube fitted with STT and TT in turbulent flow under uniform heat flux conditions are depicted in Fig. 7. The figure presents the variation of friction factor versus Reynolds number for the tube with STT inserts at different serration depth ratios, d/W ¼ 0.1, 0.2 and 0.3 in which the friction factor of the plain tube is also plotted for comparison. It is seen that the friction factor for the tube with STT insert is higher than that for the tube with/without TT of all ranges studied. It can be attributed to higher turbulence intensity or swirl flow at the near tube wall than the tube with/without TT. The friction factor increases with increasing the depth ratio (d/W) for a given Reynolds number and reaches a maximum at the highest depth ratio, d/W ¼ 0.3. This is likely from discontinuing the development of the boundary layer near the tube wall during course of flow through the tube with STT especially for the highest serration depth ratio (d/W ¼ 0.3). Moreover, the friction factor of the STT with d/W ¼ 0.1, 0.2 and 0.3 is, respectively, at 148.6%, 194.7% and 233% higher than the plain tube while at 17.5%, 39.3%, 57.5% above that of the TT.
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Heat transfer and friction factor correlations for the tube with STT inserts were obtained experimentally that it can be written in terms of Reynolds number (Re), Prandtl number (Pr), serration width ratio (w/W) and depth ratio (d/W) as below:
Nu=Nup ¼ 3:877Re0:103 Pr0:4 ð1 þ ðw=WÞÞ0:13 ð1 þ ðd=WÞÞ0:67 (19) f =fp ¼ 3:63Re0:057 ð1 þ ðw=WÞÞ0:53 ð1 þ ðd=WÞÞ1:86
(20)
The fitted values of heat transfer rate (Nu) by equations (19) and friction factor by equation (20) are compared with the experimental values, and are shown in Figs. 8 and 9, respectively. The fitted values agree well with experimental data within 5%, and 10%, respectively, for heat transfer (Nu) and friction factor (f). 4.4. Thermal performance In performance evaluation, the thermal performance factor under constant pumping power condition is taken into account by using equations (11). The influences of the STT insert on the thermal performance factor (h) are depicted in Figs. 10 and 11. Fig. 10 presents the variation of Reynolds number (Re) and the thermal performance factor (h) at constant pumping power for STT inserts at different serration width ratio (w/W ¼ 0.1, 0.2 and 0.3). For a net energy gain, the value of the thermal performance factor must be greater than unity. It is visible that at lower Reynolds number (Re), the increase in the thermal performance factor is comparatively higher, but at higher Re, it is smaller. For a given Reynolds number the thermal performance factor tends to increase with decreasing width ratio (w/W). This can be attributed to stronger turbulence/ swirl flow generated by the STT primarily responsible for thermal performance factor with the highest of 1.17 for the smallest width ratio, w/W ¼ 1.0. The experimental results show that the thermal performance factor vary between 0.98 and 1.17, 0.97 and 1.12, and 0.96 and 1.09 for the width ratio, w/W ¼ 1.0, 2.0 and 3.0, respectively. The effect of the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3) on the thermal performance factor is presented in Fig. 11. In general,
the thermal performance factor for the STT is found to be 5.5%, 3.5% and 2.6% higher than that for the TT. It is apparent that the thermal performance factor (h) increases with the reduction of the depth ratios (d/W), apart from decreasing Reynolds numbers. The thermal performance factor are varied between 0.96 and 1.17, 0.96 and 1.13, and 0.96 and 1.10, for d/W ¼ 0.1, 0.2 and 0.3, respectively. In addition, the STT with d/W ¼ 0.3 and 0.2 shows the reduction of thermal performance factor of about 2.93% and 2.11%, respectively, in comparison with one with d/W ¼ 0.1. Under the constant pumping power condition, the thermal performance factor of the STT is found to be better than that of the TT for all the ratios investigated. The thermal performance factor shows the increase trend with the reduction of the depth ratio (d/ W) and width ratio (w/W), which is generally low at high Reynolds numbers for all tapes studied. Regarding to maximum thermal
Fig. 8. Prediction of Nusselt number versus experimental result.
Fig. 10. Effect of the serration width ratio (w/W) on thermal performance factor.
Fig. 9. Prediction of friction factor versus experimental result.
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Fig. 11. Effect of the serration depth ratio (d/W) on thermal performance factor.
performance factor, the smaller depth ratios (d/W ¼ 0.1) and width ratio (w/W ¼ 0.1) is the optimum value for using the STT. The comparison of thermal performance factors in tubes equipped with the present STT and other tape inserts in previous work is shown in Fig. 12. The jagged, notched, perforated tapes with y/ W ¼ 2.94 of Rahimi et al. [9] and the serrated twisted tapes with y/ W ¼ 4 of Chang et al. [7] correlation were chosen for comparison. The thermal performance factor was evaluated at a constant pumping power. The general trend found for all tapes is that the thermal performance factor increases with decreasing Reynolds number. Comparatively, the present STT gives slightly lower thermal performance factor than the jagged tape of Rahimi et al. [9], due to the lower flow disturbance near the tube wall. On the other hand, the present STT offers higher performance factor than the serrated-tape of Chang et al. [7], since the present STT generates considerably lower pressure loss, influencing by the form of the tape. In addition, the present STT also provides higher thermal performance factor than the perforated and notched tapes, as the STT possesses more effective heat transfer enhancement. In general, the thermal performance of the modified twisted tapes is better than that of the TT and is around 1.1e1.4 depending on the twisted tape types.
5. Conclusions In this paper, a round tube fitted with the STT has been investigated experimentally. Effect of the serration width ratio (w/ W ¼ 0.1, 0.2 and 0.3) and the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3) on the heat transfer, flow friction and thermal performance factor characteristics are also reported. The experiments have been conducted in the turbulent flow regime under uniform heat flux conditions while the STT at a constant twist ratio (y/ w ¼ 4.0) was inserted into the test tube. The following conclusions can be drawn: 1. The experimental result shows that the mean heat transfer rate (Nu) of the tube fitted with the STT increases at about 72.2% in comparison with the plain tube. The increase in heat transfer rate with increasing the depth ratio (d/W ¼ 0.1, 0.2 and 0.3) and decreasing the serration width ratio (w/W). For the STT with the highest d/W ¼ 0.3 and the lowest w/W ¼ 0.1, the increase in heat transfer rate is in a range of 42e72.2% in comparison with
Fig. 12. Comparison of thermal performance of the present STT with previous work.
the plain tube alone, for the Reynolds number ranging from 4000 to 20,000. 2. The STT provides higher turbulence flow near the serrate-edge tape and the tube wall leading to higher friction factor of about 2.5, 2.3 and 2.2 times, for w/W ¼ 0.1, 0.2 and 0.3, and of some 2.5, 2.9 and 3.3 times for d/W ¼ 0.1, 0.2 and 0.3, respectively, over the plain tube. In addition, the larger spacing of serration width or smaller serration depth, yields smaller pressure loss than the higher one. 3. The thermal performance factor (h) of the STT shows the decreasing trend with the increase in Reynolds number (Re) for all tape inserts. The lower serration width ratio (w/W ¼ 0.1) provides higher thermal performance factor than the larger one (w/W ¼ 0.2 and 0.3) and also the lower serration depth ratio (d/W ¼ 0.1) gives higher value. The maximum enhancement efficiencies (h) for the STT and TT appear at the lower Reynolds number. The peaks of thermal performance factor for the STT with d/W ¼ 0.1, 0.2 and 0.3, are found to be 1.17, 1.13, and 1.10, while those with w/W ¼ 0.1, 0.2 and 0.3, are 1.17, 1.12, and 1.09, respectively for the range of parameters investigated.
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4. In general, the STT gives higher heat transfer rate than the TT around 4e27% while yields higher friction factor than the TT at about 5e68%. In addition, the thermal performance factor of all STT is better than that of the TT in a range of 2e12%. 5. It is found that both heat transfer rate (Nu) and friction factor (f) are significantly affected by the tape geometry parameters and fluid flow (d/W, w/W, Re, and Pr). The empirical correlations have been developed with relating to the serration width ratio (w/W), the serration depth ratio (d/W) and Reynolds number (Re), and the correlations are also fitted well with the majority of the data within 5% and 10% for the present correlations of heat transfer and friction factor, respectively. Acknowledgements The author would like to acknowledge the Thailand Research Fund (TRF) for the financial support of this research. References [1] Aydın Durmus, Ayla Durmus, M. Esen, Investigation of heat transfer and pressure drop in a concentric heat exchanger with snail entrance. Appl. Therm. Eng 22 (2002) 321e332. [2] S. Eiamsa-ard, P. Promvonge, Enhancement of heat transfer in a tube with regularly-spaced helical tape swirl generators. Solar Energy 78 (4) (2005) 483e494. [3] K.S. Yajnik, M.V. Subbaiah, Experiments on swirling turbulent flows: part I e similarity in swirling flows. J. Fluid Mech 60 (1973) 665e687. [4] O. Kitoh, Experimental study of turbulent swirling flow in a straight pipe. J. Fluid Mech 225 (1991) 445e479. [5] S.K. Saha, A. Dutta, S.K. Dhal, Friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly spaced twisted-tape elements. Int. J. Heat Mass Transfer 44 (22) (2001) 4211e4223. [6] S. Ray, A.W. Date, Friction and heat transfer characteristics of flow through square duct with twisted tape insert. Int. J. Heat Mass Transfer 46 (5) (2003) 889e902. [7] S.W. Chang, Y.J. Jan, J.S. Liou, Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape. Int. J. Therm. Sci. 46 (5) (2007) 506e518. [8] S.W. Chang, T.L. Yang, J.S. Liou, Heat transfer and pressure drop in tube with broken twisted tape insert. Exp. Therm. Fluid Sci. 32 (2) (2007) 489e501. [9] M. Rahimi, S.R. Shabanian, A.A. Alsairafi, Experimental, CFD studies on heat transfer and friction factor characteristics of a tube equipped with modified twisted tape inserts. Chem. Eng. Process. 48 (3) (2009) 762e770. [10] P. Bharadwaj, A.D. Khondge, A.W. Date, Heat transfer and pressure drop in a spirally grooved tube with twisted tape insert. Int. J. Heat Mass Transfer 52 (7e8) (2009) 1938e1944. [11] K.V. Sharma, L. Syam Sundar, P.K. Sarma, Estimation of heat transfer coefficient and friction factor in the transition flow with low volume concentration of Al2O3 nanofluid flowing in a circular tube and with twisted tape insert. Int. Commun. Heat Mass Transfer 36 (5) (2009) 503e507. [12] S.R. Krishna, G. Pathipaka, P. Sivashanmugam, Heat transfer and pressure drop studies in a circular tube fitted with straight full twist. Exp. Therm. Fluid Sci. 33 (3) (2009) 431e438. [13] M.A. Akhavan-Behabadi, Ravi Kumar, A. Mohammadpour, M. Jamali-Asthiani, Effect of twisted tape insert on heat transfer and pressure drop in horizontal evaporators for the flow of R-134a. Int. J. Refrig 32 (5) (2009) 922e930.
[14] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of twisted tapes. Appl. Therm. Eng. 29 (5e6) (2009) 1224e1231. [15] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Experimental studies on heat transfer and friction factor characteristics of forced circulation solar water heater system fitted with helical twisted tapes. Solar Energy 83 (11) (2009) 1943e1952. [16] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Studies on heat transfer and friction factor characteristics of thermosyphon solar water heating system with helical twisted tapes. Energy 34 (9) (2009) 1054e1064. [17] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, S. Suresh, Experimental investigation of heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of lefteright twisted tapes. Energy Convers and Manag 50 (10) (2009) 2638e2649. [18] S. Eiamsa-ard, C. Thianpong, P. Promvonge, Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements. Int. Commun. Heat Mass Transfer 33 (10) (2006) 1225e1233. [19] P. Promvonge, S. Eiamsa-ard, Heat transfer behaviors in a tube with combined conical-ring and twisted-tape insert. Int. Commun. Heat Mass Transfer 34 (7) (2007) 849e859. [20] S. Eiamsa-ard, C. Thianpong, P. Eiamsa-ard, P. Promvonge, Convective heat transfer in a circular tube with short-length twisted tape insert. Int. Commun. Heat Mass Transfer 36 (3) (2009) 365e371. [21] S. Eiamsa-ard, C. Thianpong, P. Eiamsa-ard, P. Promvonge, Thermal characteristics in a heat exchanger tube fitted with dual twisted tape elements in tandem. Int. Commun. Heat Mass Transfer 37 (1) (2010) 39e46. [22] S. Eiamsa-ard, C. Thianpong, P. Eiamsa-ard, Turbulent heat transfer enhancement by counter/co-swirling flow in a tube fitted with twin twisted tapes. Exp. Therm. Fluid Sci. 34 (1) (2010) 53e62. [23] S. Eiamsa-ard, K. Wongcharee, P. Eiamsa-ard, C. Thianpong, Heat transfer enhancement in a tube using delta-winglet twisted tape inserts. Appl. Therm. Eng. 30 (4) (2010) 310e318. [24] S. Eiamsa-ard, P. Promvonge, Heat transfer characteristics in a tube fitted with helical screw-tape with/without core-rod inserts. Int. Commun. Heat Mass Transfer 34 (2) (2007) 176e185. [25] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with helical screw-tape inserts. Chem. Eng. Process.: Process Intensification 46 (12) (2007) 1292e1298. [26] 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 (8e9) (2007) 1311e1319. [27] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with helical screw-tape inserts. Appl. Therm. Eng. 26 (16) (2006) 1990e1997. [28] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with regularly spaced helical screw-tape inserts. Exp. Therm. Fluid Sci. 31 (4) (2007) 301e308. [29] 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. Therm. Fluid Sci. 32 (1) (2007) 192e197. [30] ANSI/ASME, Measurement Uncertainty, PTC 19, 1e1985. Part I. 1986. [31] K. Yakut, B. Sahin, S. Canbazoglu, Performance and flow-induced vibration characteristics for conical-ring turbulators. Appl. Energy 79 (2004) 65e76. [32] F.P. Incropera, P.D. Witt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer. John-Wiley & Sons, 2006. [33] R.K. Manglik, A.E. Bergles, Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes: Part II: Transition and turbulent flows. Trans. ASME J. Heat Transfer 115 (41) (1993) 890e896.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Thermal characteristics in round tube fitted with serrated twisted tape Smith Eiamsa-ard a, *, Pongjet Promvonge b a b
Department of Mechanical Engineering, Faculty of Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand School of Mechanical Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2009 Accepted 22 March 2010 Available online 27 March 2010
The article presents an investigation of the effect of twisted tape with serrated-edge insert on heat transfer and pressure loss behaviors in a constant heat-fluxed tube. In the experiments, the serrated twisted tape (STT) was inserted into the entire test tube with a constant twist ratio in order to generate a continuous swirling airflow. Two geometry parameters of the STT to be considered in the present work are the serration width ratio and the serration depth ratio. The measurements have been conducted for the airflow rate based on Reynolds numbers in the turbulent regime from 4000 to 20,000. The experimental results of the STT inserted tube are compared with those of the plain tube fitted with typical twisted tape (TT). The results show that the heat transfer rate in terms of Nusselt number, Nu increases with the rise in the depth ratio but decreases with raising the width ratio. The heat transfer rate is up to 72.2% and 27% relative to the plain tube and the TT inserted tube, respectively. The use of the STT leads to higher heat transfer rate and friction factor than that of the TT for all cases. The thermal performance factor of the STT tube under constant pumping power is evaluated and found to be above unity indicating that using the STT tube is advantageous over the TT tube or the plain tube. In addition, the empirical correlations developed by relating the serration width ratio, serration depth ratio and Reynolds number are determined. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Friction factor Serrated twisted tape Typical twisted tape Swirl flow
1. Introduction Twisted tapes have been used extensively as a swirl generator to enhance convection heat transfer rate in finding the way to reduce the weight, size and cost of heat exchanger systems in several industrial applications such as chemical engineering process, heat recovery process, air conditioning and refrigeration systems, chemical reactors, power plant, and nuclear reactor, etc. Tubes with twisted tape insert are also an important group of the continuous swirling flow device that generates twin swirling flow motion over the whole tube length of flow at constant heat transfer coefficient (h) and friction factor (f). There are many devices used for producing swirl flow in the tube such as helical vanes, helical grooved tube, helical screw-tape, axial-radial guide vanes and snail entry [1,2] while the twisted tape is one of the most popular group because of low cost, low maintenance, low pressure loss and ease of construction. All of swirling flow devices have been used to generate the tangential velocity, thin the boundary layer [3], enhance the tangential and radial turbulent fluctuation [4], and therefore cause the increase in heat transfer rate and friction loss inside tubes [1e4].
* Corresponding author. Tel./fax: þ66 2 9883666x241. E-mail address: [email protected] (S. Eiamsa-ard). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.03.026
In the past investigations, the heat transfer enhancement by twisted tape insert has been considered on both experimental and numerical works. Saha et al. [5] studied the heat transfer and pressure loss behaviors in a tube fitted with regularly-spaced twisted tape elements. Ray and Date [6] predicted the heat transfer in a square sectioned duct fitted with twisted tape in both laminar and turbulent flows. The heat transfer behaviors were predicted under axially and peripherally constant wall heat flux conditions. Chang et al. [7] conducted an experimental work on the flow friction and heat transfer characteristics in a tube fitted with twisted serrated-tape modified from the TT by attaching ribs repeatedly on two sides of the tape surface to provide additional turbulence intensities. They found that the plain tube fitted with serrated twisted tape provides heat transfer higher than the plain tube without tape inserts. Influences of using the broken twisted tape at various twist ratios on the heat transfer and friction factor were also reported by Chang et al. [8]. They reported that the heat transfer coefficients, mean Fanning friction factor, and thermal performance factors in the tube fitted with the broken twisted tape were, respectively, augmented to 1.28e2.4, 2e4.7 and 0.99e1.8 times over the tube fitted with the TT. Recently, Rahimi et al. [9] examined the heat transfer, friction factor and thermal hydraulic performance in a round tube fitted
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Nomenclature A Cp d D f h I k l L M Nu P DP Pr Q Re t T T~ U
heat transfer surface area, m2 specific heat of fluid, J kg1 K1 serration depth, m inner diameter of test tube, m friction factor heat transfer coefficient, W m2 K1 current, A thermal conductivity of fluid, W m1 K1 length of twisted tape, m length of test section, m mass flow rate, kg s1 Nusselt number ¼ hD/k pressure, Pa pressure drop, Pa Prandtl number ¼ mCp/k heat transfer rate, W Reynolds number ¼ rUD/m thickness of test tube, m temperature, K mean temperature, K average velocity, m s1
with the classic and the modified twisted tape inserts. They found that the jagged twisted tape provides the maximum heat transfer enhancement than other tapes. Bharadwaj et al. [10] investigated the heat transfer and pressure drop in a spirally grooved tube with the TT insert for laminar to fully turbulent regions. The effects of the direction of twist (clockwise and anticlockwise) on the thermo-hydraulic characteristics were also reported. Sharma et al. [11] reported the heat transfer coefficient and friction factor for flow in a round tube with the TT inserts in the transition range of flow with Al2O3 nanofluid for different twist ratios. Krishna et al. [12] experimentally studied the heat transfer characteristics of a tube fitted with straight full twist insert with different spacer distances. Akhavan-Behabadi et al. [13] reported the influence of the twisted tape on heat transfer and pressure drop characteristics in horizontal evaporators for the flow using R-134a. Jaisankar et al. [14e17] conducted an experiment on heat transfer and friction factor characteristics in a thermosyphon solar water heater system with full-length twist, twist fitted with rod and spacer fitted at the trailing edge, helical twisted tapes and spacer at the trailing edge of left-right twisted tapes, respectively. Eiamsa-ard et al. [18] investigated the heat transfer and pressure loss behaviors in a double pipe heat exchanger fitted with regularly-spaced twisted tape elements at several space ratios. Effect of the combined conical-ring turbulator and twisted tape on the heat transfer, friction factor and thermal performance factor characteristics were also studied by Promvonge and Eiamsa-ard [19]. Influence of the tube equipped with the short-length twisted tape on the mean Nusselt number, friction factor and thermal performance factor characteristics for several tape length ratios was examined by Eiamsa-ard et al. [20]. Again, Eiamsa-ard et al. [21e23] reported the effect of the dual twisted tape elements in tandem, twin twisted tape with counter/co-swirling flow and delta-winglet twisted tape on the heat transfer enhancement, friction factor and thermal performance factor. They found that all tape arrangements provide better heat transfer rate than those of the typical twisted tape while the friction factors are also increasing. Eiamsa-ard and Promvonge [2,24] also studied the
V V_ w W y
voltage, volt volume flow rate, m3 s1 serration width, m tape width, m pitch length of twisted tape (180 rotation), m
Greek letters d tape thickness, m r density, kg m3 m dynamic viscosity, kg s1 m1 h thermal performance factor Subscripts a air b bulk conv convection i inlet o outlet s swirl flow generator p plain tube pp pumping power w wall
effect of helical tape with/without core-rod and regularly-spaced helical tape swirl generators on the heat transfer and pressure drop characteristics in a heat exchanger tube while the effects of the helical screw-tape with alternate axis (left and right tapes) and regularly-spaced helical screw-tape on the heat transfer enhancement and thermal performance in laminar and turbulent regions were also reported by Sivashanmugam and Suresh [25e28] and Sivashanmugam and Nagarajan [29]. One way for enhancing heat transfer in a tube is by using a twisted tape having serrate edges in order to increase mixing or turbulence intensity and breaking down the boundary layer apart from using continuous swirling flow in the tube. In the heat transfer enhancement process, twisted tape inserts can be well applied to thermal systems since the twisted tape can help to promote higher heat transfer rate because of better mixing of strong swirling flow and long residence time in the tube. The aim of the present work is to investigate the heat transfer rate (Nu) and friction factor (f) characteristics of continuous swirl flow through a round tube fitted with serrated twisted tape (STT) using the air as the test fluid. A comparison is carried out on both the friction factor and heat transfer between a tube with/without the TT and one with the STT under similar test conditions. The experiments are conducted in the turbulent flow region under uniform heat flux conditions while the STT was inserted over the test tube length at a constant twist ratio (y/W ¼ 4.0). Two geometry parameters of the STT are taken into account: (1) the serration width ratio (w/W ¼ 0.1, 0.2 and 0.3) and (2) the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3). In addition, the thermal performance factor (h) of the tube with the STT is examined under constant pumping power conditions. All of the experiments are carried out at the same entrance conditions with the Reynolds number (Re) based on the inside tube diameter in a range of 4000e20,000. It should be noted that the twisted tape in the current work was modified by forming the serrate-edge of the tape to generate turbulence intensity near the edge region which is totally different from the serrated twisted tape of Chang et al. [7] that was modified by forming ribs on the tape surface to promote the turbulence across the surface.
S. Eiamsa-ard, P. Promvonge / Applied Thermal Engineering 30 (2010) 1673e1682
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2. Experimental set-up
2.2. Experimental procedure
2.1. Test section and twisted tape
In the apparatus setting above, the inlet air at room bulk temperature from a centrifugal blower was directed through an orifice flow meter and passed to the heat transfer test section. The pressure drop of the test tube was measured with an inclined Utube manometer. Manometric fluid was used in an inclined U-tube manometer with specific gravity (SG.) of 0.826 to ensure reasonably accurate measurement of the low pressure drop encountered at low Reynolds numbers. The volumetric airflow rates from the blower were adjusted by varying motor speed through the inverter and measured by the orifice meter situated upstream of the test tube. The inner and outer temperatures of the bulk air were measured at certain points with a data logger in conjunction with the RTD PT 100 type temperature sensors. Fifteen thermocouples were tapped on the local wall of the test tube and the thermocouples were placed round the tube to measure the circumferential temperature variation, which was found to be negligible. The mean local wall temperature was determined by means of calculations based on the reading of Chromel-constantan thermocouples. In each test run, it is necessary to record the data of temperature, volumetric flow rate and pressure drop of the bulk air at steady state conditions in which the inlet air temperature was maintained at 25 C. The Reynolds number of the bulk air was varied from 4000 to 20,000. The local wall temperature (Tw), inlet and outlet air temperatures, the pressure drop across the test section and airflow rate were measured and recorded to evaluate and analyze the heat transfer rate of the heated tube.
A general arrangement of experimental apparatus is shown in Fig. 1. The loop consisted of: (1) an existing 7.5 kW high speed blower, (2) three phase inverter, (3) orifice meter to measure the volumetric airflow rate, (4) inclined/U-tube manometer to measure the pressure loss, (5) the heating test section, (6) variac transformer, (7) amp meter, (8) volt meter, (9) data logger and (10) personal computer. The inside and outside diameters of the copper test tube having a length of L ¼ 1250 mm, and 1.5 mm thickness (t), are 47 mm and 50 mm, respectively. The test tube was heated by continually winding flexible electrical wires providing a uniform heat flux boundary condition. The electrical output power was controlled by a variac transformer to obtain a constant heat flux along the entire length of the test section and by keeping the current less than 3 A. The outer surface of the test tube was well insulated to minimize convective heat loss to surroundings, and necessary precautions were taken to prevent leakages from the system. The characteristic geometries of all tape are illustrated in Fig. 2 (aec). Each of the twisted tape made of aluminium was 1250 mm long, 0.8 mm thick and inserted into the test tube having a uniform heat flux condition. The test tube fitted with TT is presented in Fig. 2 (a) and the modified tape or the STT is also found in Fig. 2(bec). The geometrical dimensions of the STT were y is the pitch length of 180 twist, d is the tape thickness, W is the tape width and D is the inner tube diameter; the severity of the twist is usually referred to as a dimensionless twist ratio, y/W. In each test run, the STT was inserted into the whole length of the test tube with a constant twist ratio, y/W ¼ 4.0. The tape edge was cut to be serrate shape (V-cut) with two geometry parameters: (1) the serration width ratio (w/ W ¼ 0.1, 0.2 and 0.3) and (2) the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3). The details of the test condition and twisted tape geometries are summarized in Table 1.
2.3. Experimental uncertainty To obtain the uncertainties of measurements the reduced data were determined. The uncertainty in the data calculation was based on Ref. [30]. The maximum uncertainties of non-dimensional parameters are 5% for Reynolds number, 10% for Nusselt number and 15% for friction. The uncertainty in the axial velocity
Fig. 1. Experimental set-up.
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Fig. 2. Test tube fitted with typical twisted tape (TT) or twisted tape with serrated-edge (STT): (a) TT, (b) STT at various serration width ratios, w/W, and (c) STT at various serration depth ratios, d/W.
Table 1 Test condition and dimension of the tape geometries.
Parameter study (a) Reynolds number, (Re) (b) Tape width, (W) (c) Twist ratio, (y/W) (d) Tape thickness, (d) (e) Serration depth ratio (d/W) (f) Serration width ratio (w/W)
Typical twisted tape
Serrated twisted tape (STT)
4000e20,000 46 mm 4.0 1.5 mm e e
Similar conditions Similar conditions Similar conditions Similar conditions 0.1, 0.2 and 0.3 0.1, 0.2 and 0.3
measurement was estimated to be less than 7%, and pressure has a corresponding estimated uncertainty of 5%, whereas the uncertainty in temperature measurement at the tube wall is about 0.5%. 3. Data reduction In the present work, the air was used as the working fluid and flowed through a uniform heat flux and insulation tube. The steady state of the heat transfer rate was assumed to be equal to the heat loss from the test section which can be expressed as:
S. Eiamsa-ard, P. Promvonge / Applied Thermal Engineering 30 (2010) 1673e1682
Qa ¼ Qconv
(1)
1677
a
where
Qa ¼ MCp;a ðTo Ti Þ ¼ VI
(2)
In the experiments, the heat supplied by electrical winding in the test tube was found around 3e5% higher than the heat absorbed by the fluid for thermal equilibrium test due to convection and radiation heat losses from the test section to surroundings. Thus, only the heat transfer rate absorbed by the fluid was taken for internal convective heat transfer coefficient calculation. The convection heat transfer from the test section can be written by:
Qconv ¼ hA T~ w Tb
(3)
whereas,
Tb ¼ ðTo þ Ti Þ=2
(4)
and
_ p;a ðTo Ti Þ=A T~ w Tb h ¼ mC hm ¼
h=15
Nu ¼ hD=k
(7)
The Reynolds number, Re is given by
Re ¼ rUD=m
(8)
Friction factor, f can be written as:
DP rU22
f ¼ L
p
¼
f Re3
0.15 0.1
0
4000
8000
12000 16000 20000 24000
Reynolds number Fig. 3. Validation of the plain tube: (a) Nusselt number (Nu) and (b) friction factor (f).
4. Results and discussion
s
1=3 Rep ¼ Res fs =fp
(10)
The thermal performance criteria, h of the test tube fitted with the STT is defined as the ratio of the heat transfer coefficient for the inserted tube (hs) to that of the plain tube (hp) at the same level of pumping power and can be expressed as follows [31]:
h¼
Blasius equation
0.2
0
and the relationship between friction and Reynolds number can be expressed as:
0.25
(9)
V_ DP p ¼ V_ DP s
f Re3
Manglik and Bergles equation TT Plain tube Petukhov equation
0.05
in which U is mean velocity of the tube. All of thermo-physical properties of the air were determined at the overall bulk air temperature (Tb) from equation (4). For a constant pumping power,
0.3
(6)
where h is the local heat transfer coefficient and evaluated at the outer wall surface of the copper tube. The average wall temperature was calculated from 15 points of local wall temperatures, lined between the inlet and the exit of the test pipe. The average Nusselt number, Nu is estimated as follows:
D
b
Friction factor
X
(5)
1=3 hs f =fp ¼ Nu=Nup hp pp
(11)
The experimental heat transfer and friction factor result in a uniform heat flux tube with/without STT swirl generators are depicted in Figs. 3e7, respectively. Effects of the STT at different serration width (w/W ¼ 1.0, 2.0 and 3.0) and depth ratios (d/ W ¼ 1.0, 2.0 and 3.0) covering a wide variation of the flow rates corresponding to the range of 4000 < Re < 20,000, on the heat transfer, flow friction and thermal performance factor behaviors are also reported. As mentioned earlier, the Nusselt number and the Reynolds number were calculated on the basis of the plain tube diameter; this allows direct comparison with the equivalent plain tube performance. The data are reported in the form of Nusselt numbers (Nu) or friction factor (f) versus Reynolds numbers (Re). Moreover, analyzing the thermal performance of these heat transfer promoters with respect to their heat transfer enhancement efficiencies at the same pumping power level is examined.
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Fig. 4. Effect of the serration width ratio (w/W) on heat transfer rate.
4.1. Validation test
Fig. 6. Effect of serration depth ratio (d/W) on heat transfer rate.
Nu ¼ 0:023Re0:8 Pr0:4 for
For the experimental results, the heat transfer rate and the friction factor of the fully developed turbulent flow in a circular plain tube are first reported and confirmed with the previous correlations [32]. Fig. 3 presents a validation for the heat transfer (Nu) and the friction factor (f) results that calculated from the heat transfer coefficient (h) or the pressure drop (DP) data using equations (7) and (9). The experiment of the plain tube was performed for heating condition and its results was compared with those from DittuseBoelter, and Gnielinski correlations for heat transfer and compared with Blasius or Petukhov correlation for friction factor. Nusselt number correlations: Empirical correlation of DittuseBoelter:
Re > 10; 000
Empirical correlation of Gnielinski:
Nu ¼
ðf =8ÞðRe 1000ÞPr for 3000 < Re < 500; 000 1 þ 12:7ðf =8Þ0:5 Pr0:33 1
Friction factor correlations: Empirical correlation of Blasius:
f ¼ 0:316Re0:25 f ¼ 0:184Re0:2
for for
Re 20; 000 Re 20; 000
0.3 STT, w/W = 0.1 STT, w/W = 0.2 STT, w/W = 0.3 TT Plain tube
0.25
Friction factor
0.2
0.15
0.1
0.05
0 0
4000
8000
12000
16000
20000
24000
Reynolds number Fig. 5. Effect of the serration width ratio (w/W) on friction factor.
(12)
Fig. 7. Effect of serration depth ratio (d/W) on friction factor.
(13)
(14) (15)
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Empirical correlation of Petukhov:
f ¼ ð0:790ln Re 1:64Þ2
for
3000 Re 500; 000
(16)
In the figures, the heat transfer rate (Nu) and the friction factor (f) are plotted as a function of Reynolds number (Re). It is apparent that the results of the present plain tube are in excellent agreement with the previous correlations for both heat transfer and friction factor. They are within 5% deviation with DittuseBoelter correlation and around 12% with Blasius equation as can be seen in Fig. 3(aeb), respectively. With the help of experimental data of the plain tube, the following empirical Nusselt number (Nu) and friction factor (f) relationships are derived for axial flow of the plain tube which is correlated as follows: Nu ¼ 0.018 Re0.814Pr0.4
(17)
f ¼ 0.786 Re0.33
(18)
Fig. 3(aeb) also shows the verification of using the twisted tape of the present work with the correlation of Manglik and Bergles [33]. It is seen that the present heat transfer and friction factor results are in good agreement with the previous work and show slightly lower values. 4.2. Effect of serration width ratio 4.2.1. Heat transfer The relationships between heat transfer (Nu) and Reynolds numbers (Re) of the tube fitted with (1) TT and (2) STT at the width ratios, w/W ¼ 0.1, 0.2 and 0.3 for d/W ¼ 0.1 are demonstrated in Fig. 4. The Reynolds number (Re) based on the inner diameter of the inlet test tube varies from 4000 to 20,000. In the figure, it is worth noting that the trend of increasing heat transfer rate (Nu) with Reynolds number for the STT is similar to that for the plain tube or the TT insert. The heat transfer enhancement of the tube with STT is found to be better than that the plain tube with/without TT. The use of the STT provides (1) strong mixing or turbulence flow near the serratededge leading to destruction of thermal boundary layer and (2) swirling flow creating better flow mixing between the fluid at the core and the tube wall. Both flow phenomena promote an increase in the tangential and radial turbulent fluctuation or the turbulence intensity, thinning the boundary layer [3], and therefore cause the rise in heat transfer rate inside a tube. It is interesting to note that the smaller width ratio (w/W ¼ 0.1) yields higher heat transfer rate than the larger ones (w/W ¼ 0.2 and 0.3). This is likely from the higher turbulence intensity near the serrate-edge and better mixing between fluid and heating wall surface. Under the present experimental conditions, the mean heat transfer rate for tube fitted with STT is found to be about 42.2%, 36.7% and 32.7% above the plain tube for w/W ¼ 0.1, 0.2 and 0.3, respectively. In addition, the turbulence and the swirling flow generated by the STT cause the boundary layer disruption near the tape edge leading to heat transfer enhancement than those obtained from the TT around 11.3%, 7% and 4% at width ratios, w/W ¼ 1.0, 2.0 and 3.0, respectively. 4.2.2. Friction factor Effect of using the tube fitted with STT at several serration width ratio (w/W ¼ 0.1, 0.2 and 0.3) on friction factor characteristic is showed in Fig. 5. In the figure, the friction factors are in the similar trend for both the plain tube with/without twisted tape inserts. The tube fitted with STT provides higher friction factor value than the plain tube with/without TT. It is seen that the friction factor is increased for both tubes fitted with STT and TT. The friction factor
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for the STT is up to 179% higher than the plain tube alone. This is because of the flow blockage from using the STT and friction loss from the increased surface area. It is also observed that the use of the STT gives higher friction factor than that of the TT due to higher turbulence fluctuation of the fluid in the tape edge region acted by the serrated-edge. Besides, the presence of the STT reduces flow areas, resulting in high turbulence intensity. This leads to the substantial pressure loss action of the fluid (hot air) between the serrate-edged surface and the inner tube wall higher than the TT case. The mean friction factors of the STT at w/W ¼ 0.1, 0.2 and 0.3, respectively, are found to be about 17.5%, 10.2%, 5.5% higher than those of the TT. It is visible that the friction factor of the STT reduces with the increase in the width ratio (w/W). In addition, the friction factor of the STT with w/W ¼ 0.1 is about 11.4% and 4.5% higher than those with w/W ¼ 0.2 and 0.3, respectively. 4.3. Effect of serration depth ratio 4.3.1. Heat transfer Effect of the serration depth ratio (d/W) on the heat transfer rate in the plain tube fitted with STT is presented in Fig. 6. With the values obtained from experimental data, the changes in heat transfer rate (Nu) with Reynolds numbers are also presented. It is found that higher heat transfer rate (Nu) can be obtained by the tube fitted with STT of all depth ratios (d/W). It is obvious that the heat transfer rates increase with the increase in Reynolds number. The turbulence intensity of the swirl flow depends on the shape of the STT for different serration depth ratios (d/W ¼ 0.1, 0.2 and 0.3) at a constant w/W ¼ 0.1. With this, an increase in the heat transfer rate is obtained up to 72.2% in comparison with the plain tube. The mean increase in the heat transfer rate from using the STT is at 42.2%, 47.2% and 52% for d/W ¼ 0.1, 0.2 and 0.3, respectively. It can be observed that the heat transfer rates (Nu) tend to increase considerably with the rise in the depth ratio value. In all cases, the tube with STT insert provides higher values of heat transfer rate (Nu) than the tube with/without TT. It seems that the STT not only produce more turbulence than the TT but also increase the fluid mixing near the tape edge regime. Heat transfer augmentation in this study is a consequence of formation of the swirl flow mixing with using the STT in the test tube and the increase of the turbulence near the wall. This is because the increase of the near-wall velocity produces larger temperature gradients and higher heat transfer rate. The boundary layer along the tube wall would be thinner with the increase of radial swirl and pressure. Therefore, heat could be transferred easily through the flow. 4.3.2. Friction factor Friction factor results for the tube fitted with STT and TT in turbulent flow under uniform heat flux conditions are depicted in Fig. 7. The figure presents the variation of friction factor versus Reynolds number for the tube with STT inserts at different serration depth ratios, d/W ¼ 0.1, 0.2 and 0.3 in which the friction factor of the plain tube is also plotted for comparison. It is seen that the friction factor for the tube with STT insert is higher than that for the tube with/without TT of all ranges studied. It can be attributed to higher turbulence intensity or swirl flow at the near tube wall than the tube with/without TT. The friction factor increases with increasing the depth ratio (d/W) for a given Reynolds number and reaches a maximum at the highest depth ratio, d/W ¼ 0.3. This is likely from discontinuing the development of the boundary layer near the tube wall during course of flow through the tube with STT especially for the highest serration depth ratio (d/W ¼ 0.3). Moreover, the friction factor of the STT with d/W ¼ 0.1, 0.2 and 0.3 is, respectively, at 148.6%, 194.7% and 233% higher than the plain tube while at 17.5%, 39.3%, 57.5% above that of the TT.
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Heat transfer and friction factor correlations for the tube with STT inserts were obtained experimentally that it can be written in terms of Reynolds number (Re), Prandtl number (Pr), serration width ratio (w/W) and depth ratio (d/W) as below:
Nu=Nup ¼ 3:877Re0:103 Pr0:4 ð1 þ ðw=WÞÞ0:13 ð1 þ ðd=WÞÞ0:67 (19) f =fp ¼ 3:63Re0:057 ð1 þ ðw=WÞÞ0:53 ð1 þ ðd=WÞÞ1:86
(20)
The fitted values of heat transfer rate (Nu) by equations (19) and friction factor by equation (20) are compared with the experimental values, and are shown in Figs. 8 and 9, respectively. The fitted values agree well with experimental data within 5%, and 10%, respectively, for heat transfer (Nu) and friction factor (f). 4.4. Thermal performance In performance evaluation, the thermal performance factor under constant pumping power condition is taken into account by using equations (11). The influences of the STT insert on the thermal performance factor (h) are depicted in Figs. 10 and 11. Fig. 10 presents the variation of Reynolds number (Re) and the thermal performance factor (h) at constant pumping power for STT inserts at different serration width ratio (w/W ¼ 0.1, 0.2 and 0.3). For a net energy gain, the value of the thermal performance factor must be greater than unity. It is visible that at lower Reynolds number (Re), the increase in the thermal performance factor is comparatively higher, but at higher Re, it is smaller. For a given Reynolds number the thermal performance factor tends to increase with decreasing width ratio (w/W). This can be attributed to stronger turbulence/ swirl flow generated by the STT primarily responsible for thermal performance factor with the highest of 1.17 for the smallest width ratio, w/W ¼ 1.0. The experimental results show that the thermal performance factor vary between 0.98 and 1.17, 0.97 and 1.12, and 0.96 and 1.09 for the width ratio, w/W ¼ 1.0, 2.0 and 3.0, respectively. The effect of the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3) on the thermal performance factor is presented in Fig. 11. In general,
the thermal performance factor for the STT is found to be 5.5%, 3.5% and 2.6% higher than that for the TT. It is apparent that the thermal performance factor (h) increases with the reduction of the depth ratios (d/W), apart from decreasing Reynolds numbers. The thermal performance factor are varied between 0.96 and 1.17, 0.96 and 1.13, and 0.96 and 1.10, for d/W ¼ 0.1, 0.2 and 0.3, respectively. In addition, the STT with d/W ¼ 0.3 and 0.2 shows the reduction of thermal performance factor of about 2.93% and 2.11%, respectively, in comparison with one with d/W ¼ 0.1. Under the constant pumping power condition, the thermal performance factor of the STT is found to be better than that of the TT for all the ratios investigated. The thermal performance factor shows the increase trend with the reduction of the depth ratio (d/ W) and width ratio (w/W), which is generally low at high Reynolds numbers for all tapes studied. Regarding to maximum thermal
Fig. 8. Prediction of Nusselt number versus experimental result.
Fig. 10. Effect of the serration width ratio (w/W) on thermal performance factor.
Fig. 9. Prediction of friction factor versus experimental result.
S. Eiamsa-ard, P. Promvonge / Applied Thermal Engineering 30 (2010) 1673e1682
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Fig. 11. Effect of the serration depth ratio (d/W) on thermal performance factor.
performance factor, the smaller depth ratios (d/W ¼ 0.1) and width ratio (w/W ¼ 0.1) is the optimum value for using the STT. The comparison of thermal performance factors in tubes equipped with the present STT and other tape inserts in previous work is shown in Fig. 12. The jagged, notched, perforated tapes with y/ W ¼ 2.94 of Rahimi et al. [9] and the serrated twisted tapes with y/ W ¼ 4 of Chang et al. [7] correlation were chosen for comparison. The thermal performance factor was evaluated at a constant pumping power. The general trend found for all tapes is that the thermal performance factor increases with decreasing Reynolds number. Comparatively, the present STT gives slightly lower thermal performance factor than the jagged tape of Rahimi et al. [9], due to the lower flow disturbance near the tube wall. On the other hand, the present STT offers higher performance factor than the serrated-tape of Chang et al. [7], since the present STT generates considerably lower pressure loss, influencing by the form of the tape. In addition, the present STT also provides higher thermal performance factor than the perforated and notched tapes, as the STT possesses more effective heat transfer enhancement. In general, the thermal performance of the modified twisted tapes is better than that of the TT and is around 1.1e1.4 depending on the twisted tape types.
5. Conclusions In this paper, a round tube fitted with the STT has been investigated experimentally. Effect of the serration width ratio (w/ W ¼ 0.1, 0.2 and 0.3) and the serration depth ratio (d/W ¼ 0.1, 0.2 and 0.3) on the heat transfer, flow friction and thermal performance factor characteristics are also reported. The experiments have been conducted in the turbulent flow regime under uniform heat flux conditions while the STT at a constant twist ratio (y/ w ¼ 4.0) was inserted into the test tube. The following conclusions can be drawn: 1. The experimental result shows that the mean heat transfer rate (Nu) of the tube fitted with the STT increases at about 72.2% in comparison with the plain tube. The increase in heat transfer rate with increasing the depth ratio (d/W ¼ 0.1, 0.2 and 0.3) and decreasing the serration width ratio (w/W). For the STT with the highest d/W ¼ 0.3 and the lowest w/W ¼ 0.1, the increase in heat transfer rate is in a range of 42e72.2% in comparison with
Fig. 12. Comparison of thermal performance of the present STT with previous work.
the plain tube alone, for the Reynolds number ranging from 4000 to 20,000. 2. The STT provides higher turbulence flow near the serrate-edge tape and the tube wall leading to higher friction factor of about 2.5, 2.3 and 2.2 times, for w/W ¼ 0.1, 0.2 and 0.3, and of some 2.5, 2.9 and 3.3 times for d/W ¼ 0.1, 0.2 and 0.3, respectively, over the plain tube. In addition, the larger spacing of serration width or smaller serration depth, yields smaller pressure loss than the higher one. 3. The thermal performance factor (h) of the STT shows the decreasing trend with the increase in Reynolds number (Re) for all tape inserts. The lower serration width ratio (w/W ¼ 0.1) provides higher thermal performance factor than the larger one (w/W ¼ 0.2 and 0.3) and also the lower serration depth ratio (d/W ¼ 0.1) gives higher value. The maximum enhancement efficiencies (h) for the STT and TT appear at the lower Reynolds number. The peaks of thermal performance factor for the STT with d/W ¼ 0.1, 0.2 and 0.3, are found to be 1.17, 1.13, and 1.10, while those with w/W ¼ 0.1, 0.2 and 0.3, are 1.17, 1.12, and 1.09, respectively for the range of parameters investigated.
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4. In general, the STT gives higher heat transfer rate than the TT around 4e27% while yields higher friction factor than the TT at about 5e68%. In addition, the thermal performance factor of all STT is better than that of the TT in a range of 2e12%. 5. It is found that both heat transfer rate (Nu) and friction factor (f) are significantly affected by the tape geometry parameters and fluid flow (d/W, w/W, Re, and Pr). The empirical correlations have been developed with relating to the serration width ratio (w/W), the serration depth ratio (d/W) and Reynolds number (Re), and the correlations are also fitted well with the majority of the data within 5% and 10% for the present correlations of heat transfer and friction factor, respectively. Acknowledgements The author would like to acknowledge the Thailand Research Fund (TRF) for the financial support of this research. References [1] Aydın Durmus, Ayla Durmus, M. Esen, Investigation of heat transfer and pressure drop in a concentric heat exchanger with snail entrance. Appl. Therm. Eng 22 (2002) 321e332. [2] S. Eiamsa-ard, P. Promvonge, Enhancement of heat transfer in a tube with regularly-spaced helical tape swirl generators. Solar Energy 78 (4) (2005) 483e494. [3] K.S. Yajnik, M.V. Subbaiah, Experiments on swirling turbulent flows: part I e similarity in swirling flows. J. Fluid Mech 60 (1973) 665e687. [4] O. Kitoh, Experimental study of turbulent swirling flow in a straight pipe. J. Fluid Mech 225 (1991) 445e479. [5] S.K. Saha, A. Dutta, S.K. Dhal, Friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly spaced twisted-tape elements. Int. J. Heat Mass Transfer 44 (22) (2001) 4211e4223. [6] S. Ray, A.W. Date, Friction and heat transfer characteristics of flow through square duct with twisted tape insert. Int. J. Heat Mass Transfer 46 (5) (2003) 889e902. [7] S.W. Chang, Y.J. Jan, J.S. Liou, Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape. Int. J. Therm. Sci. 46 (5) (2007) 506e518. [8] S.W. Chang, T.L. Yang, J.S. Liou, Heat transfer and pressure drop in tube with broken twisted tape insert. Exp. Therm. Fluid Sci. 32 (2) (2007) 489e501. [9] M. Rahimi, S.R. Shabanian, A.A. Alsairafi, Experimental, CFD studies on heat transfer and friction factor characteristics of a tube equipped with modified twisted tape inserts. Chem. Eng. Process. 48 (3) (2009) 762e770. [10] P. Bharadwaj, A.D. Khondge, A.W. Date, Heat transfer and pressure drop in a spirally grooved tube with twisted tape insert. Int. J. Heat Mass Transfer 52 (7e8) (2009) 1938e1944. [11] K.V. Sharma, L. Syam Sundar, P.K. Sarma, Estimation of heat transfer coefficient and friction factor in the transition flow with low volume concentration of Al2O3 nanofluid flowing in a circular tube and with twisted tape insert. Int. Commun. Heat Mass Transfer 36 (5) (2009) 503e507. [12] S.R. Krishna, G. Pathipaka, P. Sivashanmugam, Heat transfer and pressure drop studies in a circular tube fitted with straight full twist. Exp. Therm. Fluid Sci. 33 (3) (2009) 431e438. [13] M.A. Akhavan-Behabadi, Ravi Kumar, A. Mohammadpour, M. Jamali-Asthiani, Effect of twisted tape insert on heat transfer and pressure drop in horizontal evaporators for the flow of R-134a. Int. J. Refrig 32 (5) (2009) 922e930.
[14] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of twisted tapes. Appl. Therm. Eng. 29 (5e6) (2009) 1224e1231. [15] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Experimental studies on heat transfer and friction factor characteristics of forced circulation solar water heater system fitted with helical twisted tapes. Solar Energy 83 (11) (2009) 1943e1952. [16] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, Studies on heat transfer and friction factor characteristics of thermosyphon solar water heating system with helical twisted tapes. Energy 34 (9) (2009) 1054e1064. [17] S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, S. Suresh, Experimental investigation of heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of lefteright twisted tapes. Energy Convers and Manag 50 (10) (2009) 2638e2649. [18] S. Eiamsa-ard, C. Thianpong, P. Promvonge, Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements. Int. Commun. Heat Mass Transfer 33 (10) (2006) 1225e1233. [19] P. Promvonge, S. Eiamsa-ard, Heat transfer behaviors in a tube with combined conical-ring and twisted-tape insert. Int. Commun. Heat Mass Transfer 34 (7) (2007) 849e859. [20] S. Eiamsa-ard, C. Thianpong, P. Eiamsa-ard, P. Promvonge, Convective heat transfer in a circular tube with short-length twisted tape insert. Int. Commun. Heat Mass Transfer 36 (3) (2009) 365e371. [21] S. Eiamsa-ard, C. Thianpong, P. Eiamsa-ard, P. Promvonge, Thermal characteristics in a heat exchanger tube fitted with dual twisted tape elements in tandem. Int. Commun. Heat Mass Transfer 37 (1) (2010) 39e46. [22] S. Eiamsa-ard, C. Thianpong, P. Eiamsa-ard, Turbulent heat transfer enhancement by counter/co-swirling flow in a tube fitted with twin twisted tapes. Exp. Therm. Fluid Sci. 34 (1) (2010) 53e62. [23] S. Eiamsa-ard, K. Wongcharee, P. Eiamsa-ard, C. Thianpong, Heat transfer enhancement in a tube using delta-winglet twisted tape inserts. Appl. Therm. Eng. 30 (4) (2010) 310e318. [24] S. Eiamsa-ard, P. Promvonge, Heat transfer characteristics in a tube fitted with helical screw-tape with/without core-rod inserts. Int. Commun. Heat Mass Transfer 34 (2) (2007) 176e185. [25] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with helical screw-tape inserts. Chem. Eng. Process.: Process Intensification 46 (12) (2007) 1292e1298. [26] 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 (8e9) (2007) 1311e1319. [27] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with helical screw-tape inserts. Appl. Therm. Eng. 26 (16) (2006) 1990e1997. [28] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with regularly spaced helical screw-tape inserts. Exp. Therm. Fluid Sci. 31 (4) (2007) 301e308. [29] 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. Therm. Fluid Sci. 32 (1) (2007) 192e197. [30] ANSI/ASME, Measurement Uncertainty, PTC 19, 1e1985. Part I. 1986. [31] K. Yakut, B. Sahin, S. Canbazoglu, Performance and flow-induced vibration characteristics for conical-ring turbulators. Appl. Energy 79 (2004) 65e76. [32] F.P. Incropera, P.D. Witt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer. John-Wiley & Sons, 2006. [33] R.K. Manglik, A.E. Bergles, Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes: Part II: Transition and turbulent flows. Trans. ASME J. Heat Transfer 115 (41) (1993) 890e896.