Pressure drop and heat transfer comparison for both microfin tube and twisted-tape inserts in laminar flow

Experimental Thermal and Fluid Science 18 (1999) 323±333

Pressure drop and heat transfer comparison for both micro®n tube and twisted-tape inserts in laminar ¯ow S. Al-Fahed a, L.M. Chamra a

b,*

, W. Chakroun

a

Center of Research for Experimental Thermal Sciences, Mechanical and Industrial Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait b Mississippi State University, Department of Mechanical Engineering, Mississippi State, MS 39762-5925, USA Received 31 January 1997; received in revised form 1 May 1997; accepted 27 May 1998

Abstract Experiments were carried out to compare pressure drop and heat transfer coecients for a plain, micro®n, and twisted-tape insert-tubes. The twisted-tape experiments include three di€erent twist ratios each with two di€erent widths. The data were taken at Reynolds numbers well in the laminar region. The heat transfer data were obtained in a single shell-and-tube heat exchanger where steam is used as a heat source to obtain a uniform wall temperature and the working ¯uid in the tube is oil. The twist ratio and the width of the tape seem to have a large e€ect on the performance of the twisted-tape insert. The results demonstrate that as the twist ratio decreases, the twisted-tape will give better heat transfer enhancement. The loose-®t (W ˆ 10:8 mm) is recommended to be used in the design of heat exchanger where low twist ratios (Y ˆ 5:4, and Y ˆ 3:6) and high pressure drop situations are expected since it is easier to install and remove for cleaning purposes. Other than these situations, the tight-®t tape gives a better performance over the loose-®t tape. For the micro®n tube tested in this paper, the data shows a small increase in both heat transfer and pressure drop. This type of micro®n tube is not recommended to be used in laminar ¯ow conditions. Ó 1999 Elsevier Science Inc. All rights reserved. Keywords: Micro®n tube; Twisted-tape inserts; Heat transfer; Pressure drop

1. Introduction Many studies were conducted previously to analyse heat transfer and pressure drop of both twisted-tapeinserts and ®nned tubes. Most of the early work was concerned with the e€ect of twisted-tape on turbulent ¯ow conditions [1±3]. Du Plessis [4] conducted a numerical and experimental heat transfer study, respectively, for laminar isothermal boundary layer condition with twisted-tape-insert. Hong and Bergles [5] correlated heat transfer and pressure drop data for twisted-tapeinsert for uniform wall temperature conditions using distilled water and ethylene glycol as the working ¯uids. Manglik and Bergles [6,7] also reported experimental data for twisted-tape. Their pressure drop data indicated that the friction factor depends primarily on the Reynolds number and swirl parameter (Sw ˆ Re2 =Y ). The increase in the swirl ¯ow gives a resultant increase in the *

Corresponding author. Tel.: +1 601 325 3260; Fax: +1 601 325 7223.

friction factor. In addition, Manglik and Bergles [7] correlated the heat transfer e€ect of twisted tape for free and forced convection. Bandypadhyay et al. [8] carried out heat transfer experiments on twisted-tape-insert in mixed convection. Chakroun and Al-Fahed [9] studied the e€ect of twisted-tape width on both heat transfer and pressure drop for fully developed laminar ¯ow. Micro®n tubes are routinely used to provide enhancement for tube-side refrigerant condensation and evaporation. However, the potential for using micro®n tubes for single-phase ¯ow has been gaining momentum. This tube, illustrated in Fig. 1(a), has triangular crosssection ®ns 0.2±0.35 mm high at helix angles between 8 and 30 (measured from the tube center line). Brognaux et al. [10] reported heat transfer and friction characteristics for single-phase ¯ow in single-grooved and crossgrooved micro®n tubes. Their results showed that the micro®n tubes provided heat transfer enhancement as high as 1.8 times that of the plain tubes. Most of data reported by Brognaux et al. were taken for turbulent ¯ow. Data for laminar ¯ow will be reported here for the complete understanding of the micro®n tubes.

0894-1777/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 9 8 ) 1 0 0 3 7 - 7

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Fig. 1. Schematic drawings of both micro®n and twisted-tape insert.

The present work investigates both micro®n and twisted-tape enhancement techniques from both heat transfer and pressure drop point of views. The work also investigates the e€ect of the twisted-tape width on the enhancement of heat transfer by comparing the results of two di€erent twisted-tape widths. The two twistedtape widths considered in this study give width ratios (twisted-tape width to the inside diameter ratio) of 0.95 and 0.77. The 0.95 width ratio is considered to be the tight-®t, where as the 0.77 width ratio is considered to be the loose-®t. The work will investigate the conditions where the loose-®t twisted-tape can be used since it is easier for installing and cleaning over the tight-®t one.

A comparison is carried out on both pressure drop, and heat transfer for plain tube, micro®n tube, and tube with twisted-tape-inserts. The twisted-tape-insert experiments include three di€erent twist-ratios each with two di€erent tape widths. The experiments are conducted in the laminar ¯ow region and at uniform wall temperature conditions. The objective of the work is to investigate the use of twisted-tape-insert and the micro®n tube in the design of shell-and-tube heat exchangers, as well as to analyze their thermal performance in order to reduce the operating cost. The thermal improvement results in an increase in the pumping power caused by the increase of pressure drop.

S. Al-Fahed et al. / Experimental Thermal and Fluid Science 18 (1999) 323±333

2. Experimental procedure The experimental work is conducted to reach a more general and practical look at the e€ect of micro®n and twisted-tape-insert tubes for both heat transfer and friction factor coecients. Data are collected for fully developed laminar ¯ow under a uniform wall temperature conditions. The test ¯uid used in the experiment is a high viscosity oil which gives values of Reynolds number well in the laminar region. Steam is used as the heating medium to achieve a uniform wall condition. The twisted-tape-insert arrangements composed of three di€erent twist ratios in which Y is equal to 3.6, 5.4 and 7.1 (Y ˆ H =Di , where H is the wave length of the twisted-tape, Di is the internal diameter of the tube); each of two di€erent widths. The one with width W ˆ 13:2 mm is considered to be the tight-®t and the one with W ˆ 10:8 mm is the loose-®t. The schematic drawings of both micro®n and twisted-tape-insert are shown in Fig. 1. The micro®n has 60 ®ns along the internal periphery. The height of the ®n is 0.2 mm, while the helix angle with respect to the tube axis range is 15 . On the other hand, the twisted-tape inserts are made out of copper material of three di€erent twist ratios each having two widths W ˆ 13:2 (tight-®t) and W ˆ 10:8 mm (loose-®t). The experimental set-up for the pressure drop measurements is shown in Fig. 2. A brief description of the apparatus is given below. A more detailed discussion about the facility can be found in Ref. [9]. The apparatus consists of a closed loop through which the oil is circulated continuously by means of a gear pump. The oil used in the test section is Shell Tellus R5 which has a high-viscosity in order to maintain values of Reynolds numbers well in the laminar region. The properties of the oil used in the experiment are given by: m ˆ …9:617 ÿ 0:1045 T†10ÿ6 ; q ˆ 879:2 ÿ 0:615 T;

m2 =s;

…1†

kg=m3 ;

Cp ˆ 1:79693 ‡ 0:004424 T;

…2† kJ=kg K;

k ˆ 1:335  10ÿ4 ‡ 0:23410  10ÿ8 T;

…3† KW=…m K†: …4†

325

The oil is drawn from the reservoir and delivered by way of a Rotameter to the perspex settling chamber. A parabolic bell mouth is located at the entrance of the ¯ow chamber to eliminate the entrance e€ects. A copper tube is used in the test section with an outside diameter of 15.9 mm and an inside diameter of 14.0 mm. The total length of the tube is 4.4 m; however, the test section for both micro®n and twisted-tape-insert tubes is 2 m long. The tube is adjusted on its support to be straight and horizontal. Pressures are measured with a digital transducer with a range from 0 to 3 bars. The pressure drop across each test section is determined directly from the pressure taps that are situated at the inlet and outlet of each test section. The friction factor is calculated by Dp …Di ÿ L†: …5† qV 2 =2 The heat transfer test facility is shown in Fig. 3. The rig consists of three sections of single tube-in-tube heat exchangers, two of which consist of smooth copper tubes with an inside diameter of 14.0 mm and a wall thickness of 1.05 mm. The third test section consists of the micro®n tube described before. Each test section has a nominal length of 1m, preceded by a calming length of 2 m to eliminate any entrance e€ects. Saturated steam is introduced into the annulus and is used as an isothermal heat source. The whole system is insulated by wrapping insulation tape around all the exposed portions of the system. Each tube geometry was tested separately. This was done by closing the valves at the inlet and the outlet of the other two sections while collecting data for the speci®ed tube. Inlet and outlet ¯uid bulk temperatures were determined by using the mixing cup technique. Both wall and test ¯uid temperatures were measured using copper constantan thermocouples with 273 K reference junction. The wall temperature is obtained by taking the average of 15 thermocouples installed in ®ve axial locations along the wall of the tube. At each location three thermocouples were installed 120 apart around the circumference of the tube (Fig. 4). Each thermocouples is soldered in a groove inside the wall. The groove which was ®led in the outer wall of the tube has a depth of 0.5 mm. After soldering, an insulating f ˆ

Fig. 2. Schematic diagram of the pressure drop test facility.

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Fig. 3. Schematic diagram of the heat transfer test facility.

high temperature silicon is applied on top of the soldered thermocouples to protect them from direct exposure to the steam in the annulus. The average working temperatures range from 31 C to 34 C for the inlet temperature, 38±46 C for the outlet temperature and about 104 C for the average wall temperature. To maintain steady state conditions for each test run, a waiting period of about 15 min was considered before collecting data. Steady state conditions were reached when no temperature changes were detected. The average inside heat transfer coecient and the mean Nusselt number are calculated as follows: _ p …To ÿ Ti †; Q ˆ mC

…6†

Q ˆ hi Ai …Tw ÿ Tb †; where To ‡ Ti ; Tb ˆ 2 hence hi and Nusselt number are calculated by hi ˆ

_ p …Tw ÿ Ti † mC ; Ai …Tw ÿ Tb †

…7† …8†

…9†

hi D i : …10† k All ¯uid properties are evaluated at the mean bulk temperature, Tb .

Nm ˆ

Fig. 4. Schematic diagram showing the location of the thermocouples along the wall of the tube.

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327

3. Uncertainty analysis

4. Plain tube quali®cation

The uncertainty in the experimentally determined friction factor and Nusselt number were estimated based on the procedures of Coleman and Steele [11] and ANSI/ASME standard [12]. The uncertainty U in the measured value of either Nusselt number or friction factor is expressed as follows.

The plain-tube data serves as a quali®cation for the facility and the procedure used over the range of Reynolds number anticipated. Pressure drop and heat transfer data were collected and the results were compared to known correlations. Fig. 5 presents a comparison for the friction factor results calculated from the pressure drop data using Eq. (5) with the analytical solution of the laminar ¯ow in plain tube. The data show an excellent agreement with the 64/Re equation. Heat transfer data are plotted as Graetz number versus Nu …lb =lw †ÿ0:14 in Fig. 6. The plain-tube data are found to be in good agreement with the Seider±Tate correlation:  0:14 lb 1=3 Nm ˆ 2:02 Gz ; …16† lw where _ p mC : …17† Gz ˆ kL This equation is valid over the range of parameters 4 < Gz < 10; 000 and 0:0044 < …lb =lw † < 9:75 and is based on the mean bulk temperature. The values of Reynolds numbers and Graetz numbers for the present experimental work range from 230±2300 and 300±4500, respectively.

U ˆ …Eb2 ‡ Ep2 †1=2 ;

…11†

where Eb is the bias error and Ep is the precision limit error in the measured value. The expressions used in the determination of the friction factor and Nusselt number are given in Eqs. (5) and (10), respectively, These expressions can be expressed in the form Num ˆ Num …m1 ; m2 ; m3 ;


; mm † and

…12†

…13† f ˆ f …m1 ; m2 ; m3 ;


; mm †; where m is the number of variables involved in each equation. The expression for Eb and Ep are, respectively, given as follows: 2 m  X oNum 2 epi ; …14† Ep ˆ ori iˆ1 Eb2

ˆ

m  X oNum iˆ1

ebi

  oNum oNum 0 0 eb1 eb2 ‡


; …15† or1 or2 where epi is the precision limit error in the variable ri , ebi is the bias limit error in the variable ri , and e0bi e0bj are the correlated bias error for variable ri and rj . Similar equation can be used for the friction factor where the Nusselt number …Num † is substituted by the friction factor …f † in Eqs. (14) and (15). A computer program was prepared to determine the uncertainties in the measured variables using Eq. (11). To estimate the uncertainty for each Nusselt number and friction factor, the partial derivatives in Eqs. (14) and (15) were calculated numerically using a central di€erence method. Only the bias errors of temperature readings are correlated with each other since the same thermocouple wires were used to measure all the temperatures. The overall uncertainty ranges from 8% to 13% for the friction factor and 5% to 10% for Nusselt number, depending upon the ¯ow conditions. For the FLR and HTR de®ned later, their uncertainties are almost negligible since most of the uncertainties in the variable are found to be bias. Chakroun et al. [13] have found that when the results are reported as ratios of two quantities obtained from the same data reduction equation, the uncertainty in the ratio will be mostly due to precision. In the reported data, it was found that the uncertainties are mostly bias errors. Therefore, the values of FLR and HTR can be reported with a good degree of accuracy. ‡2



ori

2

5. Pressure drop and heat transfer results The comparison is carried out on plain, micro®n, and twisted-tape-insert tube with three twist ratios of 3.6, 5.4, and 7.1; each having two tape-widths of 13.2 and 10.8 mm. Both tight-®t and loose-®t twisted tapes were investigated. The 13.2 mm-width twisted tape is inserted

Fig. 5. Friction factor data and correlation for the plain tube.

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S. Al-Fahed et al. / Experimental Thermal and Fluid Science 18 (1999) 323±333

Fig. 6. Heat transfer data and Sieder±Tate correlation for the plain tube.

with a tight-®t since the width is close to the inside diameter of the tube. The 10.8 mm-width twisted tape is a loose-®t and the tape is held straight throughout the experiments. The loose-®t was investigated since it is easier to install and clean, therefore it is desired to be used in heat exchangers. All the eight di€erent geometries were investigated by comparing both pressure drop and heat transfer results in order to optimize the arrangement that will increase heat transfer without too much increase in pressure drop. Pressure drop results are illustrated in Figs. 7 and 9. Fig. 7 presents the friction factor data versus Reynolds number. The ®gure compares the results of each twistedtape ratio for both tight-®t and loose-®t tapes. The plain and the micro®n tube data are plotted with the data of each twist-ratio for easy comparison. The ®gure shows almost no increase in friction factor data for the micro®n over that of the plain data. However, the twistedtapes show substantial increase of friction over that of plain and micro®n tubes data. For Y equal to 3.6 the tight-®t twisted-tape data shows an increase over the loose-®t data except at low Reynolds numbers. The crossing point is around Reynolds number equal to 1050, below which the trend is switched and the loose-®t data is higher than that of the tight-®t data. The same trend is observed for Y equal to 5.4 except that the crossing point shifted further to an approximate value of Reynolds number equal to 1200. For Y equal to 7.1, the loose-®t tape exhibit higher friction factor than the tight-®t twisted-tape. Manglik and Bergles [7] have correlated friction factor as a function of Reynolds number and a swirl parameter, Sw . The swirl parameter describes the intensity of the secondary motion induced by the twisted tape. The correlation for the friction factor for laminar swirl ¯ow is given by

Fig. 7. Comparison of friction factor data for micro®n, twisted-tape insert, and plain tube for laminar ¯ow.

 …f Re†sw ˆ 15:767

p ‡ 2 ÿ 2d=Di p ÿ ÿ4d=Di

2

ÿ
1=6 1‡10ÿ6 Sw2:55 :

…18† Fig. 8 shows the experimental data and the correlation given by Eq. (18). The ®gure shows that the correlation predicts the friction data within 15%. The experimental data were curve-®tted to allow comparison of the friction factor with respect to plain tube at the same Reynolds number. The comparison is done with the introduction of the Friction Loss Ratio (FLR). The Friction Loss Ratio (FLR) is de®ned as the friction factor of a particular case over that of the plain tube. Since most of the uncertainties in the results are bias or systematic errors, the FLR values can be compared with each other with a high degree of con®dence [13] FLR ˆ

fgiven;case : fplain;case

…19†

Fig. 9 shows the FLR variation with the Reynolds number for three di€erent twist ratio. The ®gure shows clearly that the FLR of the micro®n tube is approximately one, indicating that the pressure drop for the micro®n is not di€erent from that of the plain tube. It is not surprising that the results for the micro®n tube used in this experiment are close to the plain tube data, since the ®ns height used here are small (the ®ns height are in

S. Al-Fahed et al. / Experimental Thermal and Fluid Science 18 (1999) 323±333

329

Fig. 8. Comparison of micro®n and twisted-tape insert in terms of Friction Loss Ratio (de®ned in Eq. (19)) versus Reynolds number.

the order of 0.2 mm). The height of the ®ns are small compared to the boundary layer thickness and all the ®ns are embedded inside the viscous layer, therefore no e€ect of the ®ns are seen when compared to the plain data. These ®ndings will be discussed in greater detail in the heat transfer results. Marner and Bergles [14] reported a substantial increase in friction factor for an internally ®nned tube compared to a plain one in the laminar region, however the ®n height used in their study was 2.08 mm. FLR values for the twisted-tape-insert vary from 2 to 8 depending upon the ¯ow conditions and the geometry of the twisted tape. For Y equal to 3.6 the ®gure illustrates an increasing trend for both the tight-®t tape and the loose-®t one. The loose-®t tape has higher values than that of the tight-®t at low Reynolds number, but at high Reynolds numbers the FLR of the loose-®t take lower values than that of the tight-®t. A similar trend is seen in the data of Y equal to 5.4. The FLR values of both the tight-®t and the loose-®t tapes ranges from 2.3 to 6.6 and from 3.5 to 6, respectively. For Y equal to 7.1 the FLR values are all higher for the loose-®t tape than the tight-®t one. The FLR values vary from 2 to 5.4 and from 3 to 6 for both the tight-®t and loose-®t tapes, respectively. Two competing physical e€ects caused the friction factor for both the tight-®t tape and the loose-®t tape to behave in this manner. The swirl ¯ow and the helical motion inside the tube cause an increase in friction factor. The swirling e€ect is increased by decreasing the wavelength of the twisted-tape. When the width of the twisted-tape decreases, some of the ¯uid is forced to ¯ow between the tape and the tube causing an increase in the edge velocity which therefore changes the ¯ow behavior. This behavior will be more clari®ed and better understood in the following results of heat transfer. Heat transfer results are presented in Figs. 10 and 12. Fig. 10 presents Num …lb =lw †ÿ0:14 versus Graetz number

Fig. 9. Comparison of the friction experimental data with the correlation of Manglik and Bergles [7].

for all eight cases: plain tube, micro®n tube and the six twisted-tape-insert geometries. All cases were tested for a range of Graetz numbers from 300 to 4000. The ®gure shows an increase in the heat transfer results for both micro®n and twisted-tape-insert over that of the plain tube data. The heat transfer data for the micro®n tube shows a relatively small increase over the plain data. The increase is in the order of 4% which is within the uncertainty limit of the data. The e€ect of twisted-tapeinsert is more pronounced and the increase in heat transfer can reach about four times that of a plain tube. The data for the tight-®t tape for Y equal to 3.6, 5.4, and 7.1 show an increase of 225%, 157%, 114%, respectively, over the plain data; however, the loose-®t data show an increase of 166%, 125%, and 130%, respectively. These values are calculated at Graetz number of 3800. The data for the tight-®t and the loose-®t tapes depend on the value of the twist ratio. The trend in the heat transfer data is similar to that of the friction factor. For Y ˆ 3:6 the heat transfer data for the tight-®t show an increase over the loose-®t data at high Graetz number. Similar behavior is seen for Y equal to 5.4 where again the data for the tight-®t W ˆ 13:2 mm are higher than that of the loose-®t W ˆ 10:8. However, the data for the twist ratio of 7.1 behave di€erently, and the heat transfer data for the loose-®t increase over that of the tight-®t. The

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S. Al-Fahed et al. / Experimental Thermal and Fluid Science 18 (1999) 323±333

Fig. 10. Comparison of heat transfer for micro®n, twisted-tape insert, and plain tube versus Graetz number.

change in trend for W ˆ 13:2 and W ˆ 10:8 at Y ˆ 7:1 is due to the presence of two physical conditions. For this twist ratio, the increase in heat transfer due to the helical motion becomes less e€ective; however the increase that is due to the squeezed velocity between the tube wall and the twisted-tape becomes more pronounced resulting in a change in trend. The heat transfer data for all twisted tapes were correlated as suggested by Manglik and Bergles [7] to the swirl parameter by the following equation: Num ˆ 0:318

S0:569 w

 Pr

0:3

lb lw

ÿ0:14 :

…20†

Fig. 11 shows that the Manglik and Bergles equation correlate the heat transfer data within 10%. The same heat transfer results are curve-®tted and plotted in Fig. 12. The heat transfer results are plotted in terms of Heat Transfer Ratio (HTR) versus Reynolds number. The Heat Transfer Ratio is de®ned as HTR   ÿ0:14  Num llwb given;case ˆ :  ÿ0:14  Num llwb

…21†

plain;case

Fig. 12 is a composite plot where it shows the HTR values for all geometries. The HTR values for the tight®t of Y ˆ 3.6 are higher than those of the loose-®t. At high Reynolds number the HTR value for the tight-®t is about 3.2 compared to 2.7 for the loose-®t. For Y ˆ 5.4 a similar trend is seen where all the HTR values for the tight-®t are higher than those of the loose-®t. The HTR for the tight-®t takes a value of 2.6 compared to 2.2 for

Fig. 11. Comparison of micro®n and twisted-tape inserts in terms of Heat Transfer Ratio (de®ned in Eq. (21)) versus Reynolds number.

the loose-®t at high Reynolds number. For Y ˆ 7.1 the loose-®t data show an increase in HTR values over that of the tight-®t case. The increase in the HTR value for the loose-®t over the tight-®t reach 0.5 at high Reynolds number demonstrating that loose-®t performs better in transferring heat compared to the tight-®t tape. The HTR values at this twist ratio for both the loose-®t and the tight-®t are 2.5 and 2, receptively at a Reynolds number of 2300. The HTR values for the micro®n tube is approximately one, which shows that the increase in heat transfer for the micro®n tube is negligible compared to the plain data. The data, when plotted as HTR versus Reynolds number, can be compared with a high degree of accuracy since most of the error in the measurements are bias or systematic. Two competing physical e€ects cause the heat transfer data for the tight-®t and the loose-®t to depend highly on the twist ratio. The swirl ¯ow and the helical motion inside the tube tend to increase the heat transfer. Also when the width of the twisted-tape decreases, part of the ¯ow will be squeezed with high velocity between the tape and the tube surface and that also increases the heat transfer. Fig. 13 presents the Heat Transfer Ratio versus the Friction Loss Ratio. The ®gure gives a clear picture of the behavior of the twisted-tape and the micro®n tubes from both pressure drop and heat transfer point of views. When the Heat Transfer Ratio is plotted versus Reynolds number, no information on the pressure loss is given. So the information is not too useful unless it is related to the drop in pressure. In this plot, the net result is displayed where both heat transfer and pressure drop are plotted against each other. Fig. 11 presents the relation between the heat transfer data and the pressure drop data within the tested range of Reynolds number. So by measuring the pressure drop of one of these cases,

S. Al-Fahed et al. / Experimental Thermal and Fluid Science 18 (1999) 323±333

Fig. 12. Comparison of the heat transfer experimental data with the correlation of Manglik and Bergles [7].

the heat transfer results can be extracted from this ®gure. The ®gure demonstrates that the tight-®t cases for Y ˆ 3.6 and Y ˆ 5.4 are performing better, in general, than in the loose-®t. When the friction factor is about three times that of plain tube (FLR ˆ 3) for Y ˆ 3.6, the heat transfer for the tight-®t and the loose-®t will be 1.8 and 1.2 times that of a plain tube. Towards higher values of pressure drop, the two curves for Y ˆ 3.6 and Y ˆ 5.4 are closer to each other indicating that both the loose-®t and the tight-®t are behaving similarly. This result is very useful since the loose-®t is more desired to be used than the tight-®t in heat exchangers. The loose-®t is easier to install and clean in a heat exchanger than the tight-®t one. The behavior is di€erent for Y ˆ 7.1. Even though the HTR for the loose-®t are higher than the tight-®t when plotted versus Reynolds number but also the Friction Loss Ratios are higher. The net results shown in this ®gure, indicate that the tight-®t is performing better than the loose-®t at higher pressure drop values. The HTR for the tight-®t and the loose-®t are 1.85 and 2.05, respectively at the FLR of 7. So the results of the HTR versus Reynolds number alone is somewhat misleading and no de®nite conclusion on the performance of the twisted-tape can be obtained. The ®gure also indicates that as the twisted-tape ratio decreases, the performance of the tape increases. The plot

331

Fig. 13. Heat Transfer Ratio versus Friction Loss Ratio for the micro®n and all cases of the twisted-tape insert.

for the micro®n indicates that at higher values of pressure drop the HTR remains constant. All the data in Fig. 11 are correlated as HTR versus FLR for the range of Reynolds number tested in this work. All correlations have a general form of HTR ˆ X0 ‡ X1 FLR ‡ X2 FLR2 ;

…22†

where X0 , X1 , and X2 for each case are given in Table 1. The coecient of determination is also given in Table 1 for each case.

6. Conclusion An experimental work has been performed to compare both heat transfer and pressure drop results for plain, micro®n, and twisted-tape-insert tubes. The twisted-tape-inserts include three twist ratios and two di€erent widths. The e€ect of width from both heat transfer and pressure drop point of views is also discussed. The data were collected for Reynolds number in the laminar region. Oil is used as the working ¯uid and steam is used as the heating source to obtain a uniform wall temperature.

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Table 1 Constants to be used in the correlation between the HTR and the FLR described in Eq. (22) Case description Y ˆ 3.6, W ˆ 13.2 Y ˆ 3.6, W ˆ 10.8 Y ˆ 5.4, W ˆ 13.2 Y ˆ 5.4, W ˆ 10.8 Y ˆ 7.1, W ˆ 13.2 Y ˆ 7.1, W ˆ 10.8 Micro®n

mm mm mm mm mm mm

X0

X1

X2

r2

1.426 0.0435 1.24 )0.329 1.2797 1.4815 )7.71

0.136 0.4836 0.17 0.664 0.1143 0.0592 13.24

8.49 ´ 10ÿ3 )0.0139 4.6 ´ 10ÿ4 )0.0416 0.0 0.0 )4.957

0.997 0.995 0.99 0.993 0.982 0.975 0.963

The heat transfer data indicate that the twisted-tapeinserts is an e€ective method for increasing heat transfer. The heat transfer increases with increasing the twist ratio. The e€ect of width is directly related to the twist ratio used. For twist ratios of 3.6 and 5.4, the tight-®t tape gives higher values for the heat transfer than the loose-®t. For Y ˆ 7.1, the loose-®t geometry gives a higher value of heat transfer than the tight-®t one. Similar behavior is seen for the pressure drop data where the tight-®t tape for both Y ˆ 3.6 and 5.4 twist ratios are higher than the loose-®t data. For twist ratio of 7.1, the behavior is di€erent, where the loose-®t pressure drop data are higher. For the micro®n tube tested in this paper, the data shows a small increase in both heat transfer and pressure drop coecients over the plain values. This type of micro®n is not recommended to be used for laminar ¯ow conditions. The Heat Transfer Ratio and the Friction Loss Ratio are plotted against each other to quantify the increase in heat transfer compared to the drop in pressure. The HTR and the FLR are de®ned as the heat transfer and the friction factor for a given case normalized by the values of the plain case. For Y ˆ 3.6 and 5.4, the results demonstrate that for lower pressure drop values, the tight-®t gives higher increase in heat transfer than the loose-®t. However at higher pressure drop, the heat transfer for both the tight-®t and the loose-®t are nearly the same. The behavior is di€erent for Y ˆ 7.1 where the loose-®t gives consistently higher heat transfer values at lower range of pressure drop and lower heat transfer values at higher range of pressure drop. So the loose-®t is recommended to be used with a low twist ratio in the design of heat exchangers when high pressure drop is expected. The loose-®t is more desirable to be used since it is easier for cleansing and installing. However, if pressure drop is a concern in a fairly clean tube-side stream, signi®cant improvement in the heat transfer coecient can be obtained using the tight-®t tapes. Notation Ac Ai Cp

2

axial cross sectional area, m area based on the inside diameter, m2 speci®c heat, J/(kg K)

Di Do Eb Ep f Gz H e hi k L m Num Pr Q Re wr To Ti TW U V W Y a d Dp l m q

inside diameter, m outside diameter, m bias error precision error friction factor, Eq. (1), dimensionless Graetz number (ˆ mCp =kL), dimensionless twist wave length, m Micro®n height, m inside heat transfer coecient, W/(m2 K) thermal conductivity of the ¯uid, W/(m K) length of the test section, m mass ¯ow rate, kg/s mean Nusselt number (ˆ hi Di =k), dimensionless Prandtl number (ˆ lCp =k), dimensionless heat gained by the oil, W. Reynolds number (ˆ qVD=l), dimensionless wall thickness of the Micro®n tube, m outlet oil bulk temperature, K inlet oil bulk temperature, K average wall temperature, K Uncertainty average velocity, m/s width of twisted-tape, m twist ratio, H/D, dimensionless Micro®n helix angle with respect to the tube axis, degrees thickness of twisted-tape, m pressure drop, N/m2 dynamic viscosity, kg/(m s) kinematic viscosity, m2 /s ¯uid density, kg/m3

Subscripts b bulk ¯uid w tube wall

References [1] R. Royds, Heat Transmission by Radiation Conduction and Convection, 1st ed., Constable, London, 1921, pp. 191±201. [2] R. Koch, Diuckverlust and Warmeubergang bei veiwirbelter Stromung, VDI-Forschungsheft 469, Series B, vol. 24, 1958, pp. 1±44.

S. Al-Fahed et al. / Experimental Thermal and Fluid Science 18 (1999) 323±333 [3] R.F. Lopina, A.E. Bergles, Heat transfer and pressure drop in tape generated swirl ¯ow of single-phase water, Journal of Heat Transfer 91 (1969) 434±442. [4] J.P. Du Plessis, Laminar ¯ow and heat transfer in a smooth tube with a twisted-tape insert, Ph.D Thesis, Department of Mechanical Engineering, University of Stellubosch, South Africa, 1982. [5] S.W. Hong, A.E. Bergles, Augmentation of laminar ¯ow heat transfer in tubes by means of twisted-tape insert, International Journal of Heat Transfer 13 (1975) 76-HT-QQ. [6] R.M. Manglik, A.E. Bergles, A correlation for laminar ¯ow enhanced heat transfer in uniform wall temperature circular tubes with twisted-tape inserts, Advances in Heat Transfer-1987, HTDvol. 1987, ASME, New York, pp. 19±25. [7] R.M. Manglik, A.E. Bergles, Heat transfer and pressure drop correlation for twisted-tape insert in isorthermal tubes: part I ± laminar ¯ows, Journal of Heat Transfer 115 (1993) 881±889. [8] P.S. Bandyopadhyay, U.N. Gaitonde, S.P. Sukhatme, In¯uence of free convection on heat transfer during laminar ¯ow in tubes with twisted-tapes, Experimental Thermal aud Fluid Science 4 (1991) 577±586.

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[9] W.M. Chakroun, S. Al-Fahed, The e€ect of twisted-tape width on heat transfer and pressure drop for fully developed laminar ¯ow, Journal of Engineering for Gas Turbines and Power 118 (1996) 584±589. [10] L.J. Brognaux, R.L. Webb, L.M. Chamra, B.Y. Chung, Singlephase heat transfer in micro-®n tubes, International Journal of Heat and Mass Transfer 40 (18) (1997) 4345±4357. [11] H.W. Coleman, W.G. Steele, Experimental and Uncertainty Analysis for Engineers, Wiley, New York, 1989. [12] ANSI/ASME, Measurement Uncertainity, Report PTC 19.11985, 1986. [13] W.M. Chakroun, R.P. Taylor, H.W. Coleman, W.G. Steele, Bias Error Reduction in Experimental Results by Presentation as a Ratio to a Baseline Experiment-A Heat Transfer Case Study, paper AIAA 93-0922, presented at the 31st Aerospace Sciences Meeting, Redo, NV, 1993. [14] W.J. Marner, A.E. Bergles, Augmentation of highly viscous laminar heat transfer inside tubes with constant wall temperature, Experimental Thermal and Fluid Science 2 (1989) 252±267.