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Water-to-water heat transfer in tube–tube heat exchanger: Experimental and analytical study
Applied Thermal Engineering 25 (2005) 2715–2729 www.elsevier.com/locate/apthermeng
Water-to-water heat transfer in tube–tube heat exchanger: Experimental and analytical study Milind V. Rane *, Madhukar S. Tandale Mechanical Engineering Department, Heat Pump Laboratory, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India Received 28 July 2004; accepted 5 January 2005
Abstract Tube–tube heat exchanger (TTHE) is a low cost, vented double wall heat exchanger which increases reliability by avoiding mixing of fluids exchanging heat. It can be potentially used for heat recovery from engine cooling circuit, oil cooling, desuperheating in refrigeration and air conditioning, dairy, and pharmaceutical industry, chemical industry, refinery, etc. These tube–tube heat exchangers are successfully demonstrated for superheat recovery water heating applications, condenser and evaporator in heat pumps, lube oil cooler for shipboard gas turbines, milk chilling and pasteurizing application. This paper presents an experimental study on various layouts of TTHE for water-to-water heat transfer. The theoretical and experimental results on this type of heat exchanger configuration could not be located in literature. Overall heat transfer coefficient and pumping power were experimentally determined for a fixed tube length and surface area of serpentine layouts with different number of bends and results are compared with straight tube TTHE. In the case investigated, serpentine layout TTHE with seven bends has shown optimum performance, with overall heat transfer coefficient 17% higher than straight tube TTHE. Two out of five serpentine layout TTHE have shown poor heat transfer performance than straight tube TTHE. The experimental results also indicate that there is a definite optimum for a number of bends in serpentine layout TTHE. An analytical model for prediction of thermo-hydraulic performance of straight layout has been developed and validated experimentally. 2005 Published by Elsevier Ltd.
*
Corresponding author: Tel.: +91 22 2576 7514; fax: +91 22 2572 4544. E-mail address: [email protected] (M.V. Rane).
1359-4311/$ - see front matter 2005 Published by Elsevier Ltd. doi:10.1016/j.applthermaleng.2005.01.007
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Keywords: Double wall heat exchanger; Serpentine layout; Straight tube; Analytical model
1. Introduction A tube–tube heat exchanger (TTHE) is a double wall tubular heat exchanger wherein two or more tubes are placed side-by-side and bonded thermally using thermal bonding material (TBM) for effective transfer of heat. Use of bends and straight lengths in tube–tube heat exchanger results in significant enhancement in heat transfer due to secondary flows induced in the bends. The secondary flows induced in bend leads to heat transfer enhancement in bend as well as in straight length downstream of bend without significant increase in pressure drop [1,2]. Dean was first to point out that the occurrence of a secondary flow at right angles to the main flow is due to centrifugal force [4]. The distorted flow condition by the induced secondary flow persists at a downstream distance of more than 50dtÆi for single-phase and 70dtÆi for two-phase [5]. Chen et al. [6] proposed empirical correlation for U-type wavy tubes with small diameter and short separation between consecutive bends (l/dtÆi = 1.93–7). Their correlation shows good agreements with the experimental data. However, extrapolations of correlation with wider operating range needs further examination to check their applicability. Recently, Chen et al. [5] have proposed a new correlation for friction factor applicable for wider separation between the consecutive bends (l/dtÆi = 0–30) but valid for limited range of Re (50–10,000). Ohadi et al. [7] have reported their study on effect of bend on pressure drop in a straight section downstream of a 180 bend. They found about 9% higher pressure drop in downstream section due to bend. Multi-stream Hampson heat exchanger with paired tubes reported by Kao [7] is helical coil type for three fluids. The paired tubes are soldered with tin–lead solder having thermal conductivity about 10% of copper, which may not be effective in liquid–liquid heat exchange due to its low thermal conductivity. In many heat transfer augmentation techniques, the augmentation is usually accompanied by significant increase in the pumping power required to overcome increase in pressure drop for the same heat transfer rate. But, in case of TTHE with serpentine layout the secondary flows induced due to bend continue their effect in the downstream portion of a bend [1,2]. Heat transfer enhancement in downstream section is maximum at the leading edge and diminishes along its length. Experimental and theoretical results on single-phase heat transfer on tube–tube heat exchanger configuration could not be located in literature. This paper experimentally investigates the thermo-hydraulic performance of serpentine layout TTHE with different number of bends (3, 6, 7, 8 and 9) in water-to-water heat transfer. Also, an experimental comparison of thermohydraulic performance of serpentine layout TTHE modules with straight tube TTHE is done. An analytical model for prediction of thermo-hydraulic performance of straight tube TTHE is developed and validated. In this type of heat exchanger, there is a wide choice of configurations to select depending on application like liquid–liquid, gas–liquid, two-phase etc. Fig. 1 shows different configurations of TTHE. Configuration 1–1 is preferred for high thermal conductivity tube material, 2–1 for gas–liquid application and configuration n–n for low thermal conductivity tube material. In some of the applications different diameter tubes are paired together allowing greater flexibility
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Nomenclature A heat transfer surface area, m2 BV ball valve C Cold/heat capacity, J/K d diameter of tube, m dp pressure drop, N/m2 dbend diameter of bend, m FS full scale f friction factor, dimensionless H Hot h heat transfer coefficient, W/m2 K k thermal conductivity, W/m K l length of tube, m length of tube sector acting as a fin, m lfin lpm liters per minute lst.section length of straight section of serpentine tube, m LMTD log mean temperature difference, degree m mass flow rate, kg/s NTU number of transfer units Nu Nusselt number, dimensionless PICCV pressure independent characterized control valve Pr Prandtl number, dimensionless Q heat transfer rate, W Re Reynolds number, dimensionless R, Rth thermal resistance, K/W r fouling resistance, m2 K/W t temperature, C TBM thermal bonding material U overall heat transfer coefficient, W/m2 K w thickness, m gap between adjacent tubes, m wg wpp.tot total pumping power, W Subscripts av average bend tube bend c cold f fouling h hot i inside o outside
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min max N pt t tbm Greek e gfs /
minimum maximum number of variables per tube tube thermal bonding material symbols effectiveness, dimensionless fin surface efficiency, dimensionless semi-fill angle subtended by thermal bonding material at tube centre, degree
H
C
TBM
(a)
H
H
C
TBM
(b)
H
C
C
H
H
C
TBM
(c)
Fig. 1. Sectional view of three TTHE configurations. (a) 1–1 TTHE, (b) 2–1 TTHE and (c) n–n TTHE.
in optimising the heat exchanger with respect to heat transfer coefficient and pressure drop. The configuration 2–1 shown in Fig. 1(b) is used in TTHE for recovery of superheat from a 60 TR chiller for one of the hotels in Mumbai [3].
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Some of the features of TTHE giving advantages over tube-in-tube and shell-and-tube heat exchangers are: (a) Possibility of using different material for tubes carrying fluids in order to reduce the cost. Reduction in material used by having two tubes used side-by-side, instead of one inside the other as the case in tube-in-tube heat exchangers. (b) For a particular design pressure, outer tube wall thickness is high which increases weight and hence cost of heat exchanger. In TTHE, tubes are placed side-by-side. Hence, diameter of tube replacing the outer tube is small. This reduces the thickness, weight and cost of the tubes. This along with reduced cost of headers leads to cheaper and reliable design in spite of small additional weight and cost due to TBM. (c) An ability of TTHE to handle fluids with fibrous materials, partial or complete extraction or introduction of fluids at intermediate temperature, increase or decrease the capacity of heat exchanger by increasing or decreasing number of tube sets, good accessibility of all tubes for ease of repair, in case of leakage.
2. Experimental setup Schematic diagram of the experimental setup for conducting water-to-water heat transfer experiments on TTHE modules is shown in Fig. 3. It includes a test section (TTHE module covered with insulation), an electric water heater, valves, pump and instrumentation for measurement. The experimental setup consists of two fluid circuits. The first circuit, as shown in Fig. 3, is closed loop for hot water. Hot water is generated in an electric water heater, which has a capacity of about 9 kW. Flow rate of hot water from water heater is controlled by adjusting valve and temperature of hot water at inlet to the test section is controlled by three-phase Variac. Hot water temperature at inlet and outlet of the test section is measured by K type thermocouples. The second circuit is cooling water circuit as shown in the upper half of the Fig. 3. This is open loop with the digital turbine meter for measuring cooling water flow rate and pressure independent characterized control valve (PICCV) for regulating the flow rate. The water flow rate is adjusted to different values and maintained constant by pressure independent characterized control valve. Thermocouples are placed in cooling water stream to measure temperatures at inlet and outlet of a test section. 2.1. Test section The test section comprising tube–tube heat exchanger module, is shown as a sectional view in Fig. 2(a). Various modules of TTHE are fabricated for test. TTHE modules being tested consist of two copper tubes of 9.525 mm OD, which are brazed all along their lengths with copper filler material. The copper filler, which will be referred in this paper as thermal bonding material (TBM), subtends semi-fill angle /max of 36.7 at the tube centre. The gap between the tubes, wg is measured at different sections along the length to calculate the average gap between the tubes of TTHE module. The simulation results show that for TTHE with copper tubes, a gap of up to
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(a)
(b)
Fig. 2. TTHE module. (a) Cross-sectional view of 1–1 TTHE module; (b) serpentine layout TTHE module with six bends.
1 mm has insignificant effect on heat transfer. However, with lower thermal conductivity TBM, the effect of gap will be considerable. The average gap between the tubes is less than 0.5 mm for all modules tested. This small gap between the tubes allow thermal bonding material to flow to other side of tubes during brazing. Hot water flows through one tube and cooling water through other. All modules during the tests are oriented such that the hot water tube is below the cooling water tube. This eliminates
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Fig. 3. Schematic of experimental setup for water-to-water heat transfer.
the effects, though insignificant, of variants other than number of bends on performance of modules. All modules are insulated thermally from their surroundings during tests by the closed cell foam insulation (thickness 25.4 mm and thermal conductivity 0.046 W/m K). 2.1.1. Straight layout 1–1 TTHE module (one tube for hot water and another tube for cooling water) fabricated using two copper tubes with 9.525 mm OD. These straight tubes are brazed all along their lengths with copper filler. 2.1.2. Serpentine layout A pair of copper tubes with 9.525 mm OD is first bent to a serpentine shape on tube bending machine. The ratio of bend diameter to tube diameter (dbend/dtÆi) is 5.29. These tubes are brazed all along their lengths. Five modules of serpentine layout with 3, 6, 7, 8 and 9 bends are fabricated giving different ratio of length of the straight section to tube diameter (lst.section/dtÆi). Fig. 2(b) shows serpentine layout TTHE with six bends. 2.2. Experimental method The cooling water inlet temperature during the test is 29 ± 0.5 C. The flow rate of water is adjusted by pressure independent characterized control valve and held constant irrespective of tap water pressure. The cooling water flow rate is changed from 3 to 10 lpm in step of about 1 lpm. Flow rate on two sides is kept same in all sets of readings. The temperature of hot water inlet to the test section is adjusted to 85 ± 0.1 C by changing heater input through three-phase Variac.
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2.2.1. Instrumentation Instruments used for measuring various parameters during the experimentation are: (a) Water flow rate is measured using digital turbine meter. Make: GPI turbine meter, Model No. S050 N1/200 , Mid-flow, accuracy: ±2% of reading in the range 3.8–37.9 lpm, range: 1.9–37.9 lpm. (b) Flow rate of cooling water below 3.8 lpm is measured by measuring weight of water using weighing balance with an accuracy of ±1% of reading. Make: PAG Oerlikon AG CH-Dietikon Precisa Balances, Model No. 87113 type 2300-9535/H6200D. The range and resolution of instrument is 0–6.2 kg and 0.1 g respectively. This was done since the accuracy of turbine meter is lower than ±2% for flow rate below 3.8 lpm. (c) The pressure losses are measured by digital differential pressure transducers. Make: HBM, Digibar, range: 0–1.2 bar, resolution: ±0.5% of the measurement, and accuracy: ±2%. The instrument was calibrated using accurate dial gauge having accuracy of 0.1% of FS. (d) The fluid temperatures are measured using K type thermocouples with an accuracy of ±0.3 C. The range and resolution of instrument is 20 to 300 C and 0.1 C, respectively. Thermocouples are calibrated using thermocouple calibrator in Instrumentation Laboratory. The bends in serpentine TTHE modules tested are not perfectly circular in cross-section due to the manufacturing process used. As a result of this, the tube cross-section became elliptical due to flattening. The maximum flattening of the bends of all modules tested is less than 8%. The flattening is calculated by following equation [12] flattening ¼
ðd tmax d tmin Þ 0.5 ðd tmax þ d t. min Þ
ð1Þ
Since 10% flattening results in very small 0.3% reduction in cross-sectional area; 8% flattening in the present case is expected to have insignificant effect on pressure drop.
3. Results and discussion Pressure drop and heat transfer results for the layouts tested in water-to-water heat transfer are shown in Figs. 4 and 5. 3.1. Pressure drop Fig. 4 represents variation in experimental pressure drop with mass flow rate on hot water side for all six modules of TTHE. In serpentine layouts, the pressure drop increases with number of bends. The straight layout TTHE has shown lowest pressure drop amongst all layouts tested, which is as expected.
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Pressure Drop on Hot Water Side, dph (bar)
7 Straight Serpentine (3 bends) Serpentine (6 bends) Serpentine (7 bends) Serpentine (8 bends)
6 5
Serpentine (9 bends)
4 3 2 1 0
2
4
6 8 Flow Rate of Water, mh(kg/min)
10
12
Fig. 4. Variations in pressure drop with mass flow rate of water.
Overall Heat Transfer Coefficient, Ui.h (kW/m2 K)
3.4 Straight Serpentine Serpentine Serpentine Serpentine Serpentine
3.2 3.0 2.8
(3 (6 (7 (8 (9
bends) bends) bends) bends) bends)
2.6 2.4 2.2 2.0 1.8 1.6 1.4
0
4
8
12
16
20
24
Total Pumping Power, Wpp.tot (W)
Fig. 5. Variations in experimental overall heat transfer coefficient with total pumping power.
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3.2. Overall heat transfer coefficient Fig. 5 represents variation of experimentally determined overall heat transfer coefficient with total pumping power for six modules tested. For a fixed pumping power, serpentine layout TTHE with seven bends has shown highest overall heat transfer coefficient. Its maximum value is higher than straight tube TTHE by 17%. When comparison is done amongst serpentine layouts, the overall heat transfer coefficient is highest in serpentine layout with seven bends and lowest with nine bends. For serpentine layout with three bends, the overall heat transfer coefficient is lower than serpentine layout with seven bends in this range of flow rate. Thus, the experimental results indicate that in serpentine layout TTHE, there is a definite optimum for a number of bends for a particular application. In serpentine layout with three and six bends, with dbend/dtÆi of 55.3 and 28.1, respectively, part of the straight sections does not offer enhancement in heat transfer. Effect of secondary flow diminishes long before the fluid enters the subsequent bend. In serpentine layouts with eight and nine bends, with dbend/dtÆi of 20.9 and 15.8, respectively, the secondary flow generated by the previous bend probably persists as the fluid enters in the next bend. Since the secondary flow is reversed in subsequent bends in a serpentine layout, pressure drop increases without commensurate increase in heat transfer. Benefits of the bends are not realized, since number of bends per unit length is large as in the case of eight and nine bends, the secondary flow is first neutralized as it passes the bend and reversed as it comes out. The consecutive bend interactions are so severe that the performance of the serpentine layout is worse than that of a straight tube TTHE. The quantities measured directly include the volume flow rate of water, inlet and outlet temperature of water. The uncertainty in measurement of volume flow rate of water is ±2% of reading (maximum uncertainty: ±0.2 lpm). The uncertainty of temperature measurement is ±0.3 C. According to the uncertainty analysis based on Kline and McClintock method illustrated by Moffat [11], the maximum uncertainties of overall heat transfer coefficient, heat transfer rate, and log mean temperature difference is 3.3%, 3% and 0.76%, respectively.
4. Model development An effectiveness-NTU method is used in the model developed for performance prediction of tube–tube heat exchanger. The present model developed for straight tube–tube heat exchanger incorporates following attributes: (a) Layout: straight. (b) Flow configuration: counter flow or parallel flow. (c) Geometric parameters of tubes: number, diameter, thickness, material on two sides. (d) Thermal bonding of tubes: material and its size (/), gap between the adjacent tubes. Appropriate parameters like length of fin, lfin (part of the tube transferring heat by fin effect), number of tubes on two sides, semi-fill angle / are included in the model to analyse most of the configurations (various configurations with different number of tubes) of tube–tube heat exchan-
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ger. The performance parameters like overall heat transfer coefficient, pressure drop, pumping power, cost, and size of heat exchanger are calculated for straight layout. Input parameters to the model are inlet temperatures and mass flow rates of water. Other input parameters necessary for the analysis are flow arrangement, number of tubes, tube material, tube diameter, tube thickness, thermal bonding material and its size. Following assumptions were made in the model development. (a) Steady state operation. (b) No heat loss to the surroundings. (c) No heat transfer in the direction of flow. (d) Uniform fluid distribution in all tubes in multiple tube tube–tube heat exchanger. (e) One dimensional flow of heat through part of the tube and thermal bonding material. (f) No phase change.
4.1. Heat transfer equations The net heat transfer depends on the waterside heat transfer coefficients, fouling factors, thermal resistance by tube walls, and thermal bonding material. The correlations for heat transfer coefficients and friction factors reported in the literature have been used in the model. Few important equations used in the model are given below. NTU is calculated by NTU ¼
UA C min
ð2Þ
Theoretical relations for effectiveness as a function of NTU and heat capacity ratio are available for different flow arrangements like counter flow or parallel flow. For counter flow, equation for effectiveness is e¼
1 exp½NTU ð1 C ratio Þ 1 C ratio exp½NTU ð1 C ratio Þ
ð3Þ
where, C ratio ¼
C min C max
The maximum possible heat transfer rate is calculated by Qmax ¼ C min ðthi tci Þ
ð4Þ
The actual heat transfer rate in heat exchanger is calculated by equation Q ¼ e C min ðthi tci Þ
ð5Þ
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4.2. Heat transfer coefficient The net heat transfer depends on heat transfer coefficients, fouling factors, thermal resistance by tube walls, and thermal bonding material. Gnielinskis correlation [9] is used for heat transfer coefficient calculation for transition region as well as fully developed turbulent flow for a straight smooth circular tube Nu ¼
f ðRe 2
1000Þ Pr f 0.5 1 þ 12.7 2 ðPr2=3 1Þ
ð6Þ
For 2300 6 Re 6 5 · 106 and 0.5 6 Pr 6 2000. It is modified version of second Petukhov correlation, which agrees with most reliable experimental data to an accuracy of ±5%. 4.3. Friction factor For friction factor in fully developed turbulent flow for a straight smooth circular tube, Prandtl, Karman, Nikuradse (PKN) correlation is classical correlation valid for wide range of Re (4 · 103 6 Re 6 107). The correlation is also used for comparison of recent correlations. h pffiffiffii 1 pffiffiffi ¼ 1.7372 ln Re f 0.3946 ð7Þ f Predictions of this correlation agree with the extensive experimental measurements within ±2 [4]. However, the PKN correlation is not explicit form; Techo, Tickner, James correlation [10] is used for friction factor calculations. 1 Re pffiffiffi ¼ 1.7372 ln ð8Þ 1.964 ln Re 3.8215 f This explicit form of PKN correlation agrees within ±0.1% of PKN correlation for 104 6 Re 6 2.5 · 108.
5. Overall heat transfer coefficient The overall heat transfer coefficient is obtained using following expression 1 1 1 1 1 þ rfh þ Rthh þ Rthtbm þ Rthc þ þ rfc ¼ UA hh Ah gfsh hc Ac gfsc
ð9Þ
RthÆtbm is thermal resistance of thermal bonding material. Thickness of thermal bonding material (measured in the direction of heat transfer) varies from minimum at / = 0 to maximum at the limiting value /max. RthÆh and RthÆc are thermal resistance of portion of tubes in contact with thermal bonding material on hot water and cooling water side, respectively. Similarly, rfÆh and rfÆc are fouling resistances on hot water and cooling water side, respectively. Thermal resistance of thermal bonding material is calculated considering differential element as shown in Fig. 2(a).
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Thermal resistance of differential element is given by R¼
d to ð1 cos /Þ þ wg k tbm d2to d/ cos / lpt
ð10Þ
where, R is thermal resistance of the differential element in terms of differential angle d/. The thermal resistances of all elements of TBM are in parallel. Therefore, the overall thermal resistance of TBM is obtained by integrating 1/R term for the differential element between the limits /max to /max. The derived equation for overall thermal resistance of TBM is Z /max 1 k tbm d2to cos / lpt Rthtbm ¼ 2 d/ ð11Þ d to ð1 cos /Þ þ wg 0 Another approach to obtain thermal resistance of thermal bonding material is by calculating equivalent/average thickness considering the area equivalence. Following equation gives equivalent/average thickness of thermal bonding material. p ½sin /max ð1 cos /max Þ 12 /max 180 sin /max cos /max d to ð12Þ wtbmav ¼ wg þ sin /max The thermal resistance of thermal bonding material calculated using Eq. (11) and other calculated by considering the approach of average thickness of thermal bonding material deviates within 10%.
0.6
Experimental Pressure Drop, dph (bar)
45 deg line
0.5
0.4
0.3
0.2
0.1
0.0 0.0
0.1
0.2
0.3
0.4
Predicted Pressure Drop, dph (bar)
Fig. 6. Experimental vs. simulated pressure drop.
0.5
0.6
M.V. Rane, M.S. Tandale / Applied Thermal Engineering 25 (2005) 2715–2729 Experimental Overall Heat Transfer Coefficient, Ui.h (kW/m2 K)
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3.0 45 deg line
2.5
2.0
1.5
1.0 1.0
1.5
2.0
Predicted Overall Heat Transfer Coefficient, Ui.h
2.5
3.0
(kW/m2 K)
Fig. 7. Experimental vs. predicted overall heat transfer coefficient.
6. Experimental validation of model The present model developed for straight tube TTHE is validated experimentally for waterto-water heat transfer by testing a typical module of straight tube TTHE. The experimental setup used for conducting experiments is explained in earlier section. The experimental and simulated results on pressure drop and overall heat transfer coefficient for straight tube TTHE are represented in Figs. 6 and 7. The results show good agreement between the results prediction by model and the experimental results. The average difference between the predicted and experimental results of pressure drop on hot water side is 2.3% and the maximum difference is 4.2%. The average difference between the predicted and experimental overall heat transfer coefficient is 2% and maximum difference is 6.2%.
7. Conclusions Five different serpentine layouts of TTHE have been experimentally evaluated for the effect of varying straight lengths between bends on thermo-hydraulic performance. Tubes used in all five serpentine layout TTHE are 9.525 mm OD and 43 mm bend diameter. Maximum overall heat transfer coefficient is obtained for the serpentine layout TTHE with seven bends when the performance is compared at same pumping power. Also, the overall heat transfer coefficient in serpentine layout TTHE with seven bends is higher than TTHE with straight layout by 17%.
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In water–water heat transfer, not all serpentine TTHE layouts are better than straight layout. The serpentine layout TTHE with three and nine bends have shown lower heat transfer performance than straight layout TTHE. However, at very low pumping power (below 3 W), serpentine layout with three bends has shown slightly better heat transfer performance than straight tube TTHE. The maximum difference in performance of optimum serpentine layout TTHE (seven bends) and nine bend serpentine TTHE, which is a non-optimum, is 30%. Thus, due care should be taken while designing TTHE with serpentine layout to maximize the benefits of this design. In case of serpentine layout TTHE, the experimental results indicate that there is a definite optimum for a number of bends for a particular application. In the present case, the optimum number of bends in serpentine layout is 7. An analytical model for simulation of straight tube TTHE in water–water heat transfer is validated experimentally. Effectiveness-NTU approach is used in the model for performance predictions. The average and maximum deviation between predicted and experimental values of overall heat transfer coefficient is 2% and 6.2%, respectively. Similarly, average and maximum deviation is pressure drop 2.3% and 4.2%, respectively.
References [1] M.V. Rane, M.S. Tandale, Tube–tube heat exchangers, Filed PCT/IN03/00377, 2003. [2] M.V. Rane, M.S. Tandale, An experimental study on various layouts of tube–tube heat exchanger in steam condensation, Experimental Thermal and Fluid Science, submitted for publication. [3] M.V. Rane, M.S. Tandale, Benefits of superheat recovery on chillers- case study for a hotel installation, Paper presented at 21st IIR International Congress of Refrigeration, Washington, DC, August 2003, pp. 17–22. [4] R.K. Shah, S.D. Joshi, Convective heat transfer in curved ducts, in: S. Kakak, R.K. Shah (Eds.), Handbook of Single-phase Convective Heat Transfer, first ed., John Wiley and Sons, 1987. [5] I.Y. Chen, J.C. Huang, C.C. Wang, Singe-phase and two-phase frictional characteristics of small U-tube wavy tubes, International Communication Heat Mass Transfer 31 (3) (2004) 303–314. [6] I.Y. Chen, S.K. Lai, C.C. Wang, Frictional performance of small diameter U-type wavy tubes, ASME Journal of Fluids Engineering 47 (2003) 2241–2249. [7] M.M. Ohadi, E.M. Sparrow, A. Walawalkar, A.I. Ansari, Pressure drop characteristics for a turbulent flow in a straight circular tube situated downstream of a bend, International Journal of Heat Mass Transfer 33 (4) (1990) 583–591. [9] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (2) (1976) 359–368. [10] R. Techo, R.R. Tickner, R.E. James, An accurate equation for the computation of the friction factor from smooth pipes from the Reynolds number, ASME Transaction Journal of Applied mechanics 32 (1965) 443. [11] R.J. Moffat, Describing the uncertainties in experimental results, Experimental Thermal and Fluid Science 1 (1988) 3–17. [12] D.F. Geary, Return bend pressure drop in refrigeration systems, ASHRAE Transactions 2342 (1980) 250–265.
Water-to-water heat transfer in tube–tube heat exchanger: Experimental and analytical study Milind V. Rane *, Madhukar S. Tandale Mechanical Engineering Department, Heat Pump Laboratory, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India Received 28 July 2004; accepted 5 January 2005
Abstract Tube–tube heat exchanger (TTHE) is a low cost, vented double wall heat exchanger which increases reliability by avoiding mixing of fluids exchanging heat. It can be potentially used for heat recovery from engine cooling circuit, oil cooling, desuperheating in refrigeration and air conditioning, dairy, and pharmaceutical industry, chemical industry, refinery, etc. These tube–tube heat exchangers are successfully demonstrated for superheat recovery water heating applications, condenser and evaporator in heat pumps, lube oil cooler for shipboard gas turbines, milk chilling and pasteurizing application. This paper presents an experimental study on various layouts of TTHE for water-to-water heat transfer. The theoretical and experimental results on this type of heat exchanger configuration could not be located in literature. Overall heat transfer coefficient and pumping power were experimentally determined for a fixed tube length and surface area of serpentine layouts with different number of bends and results are compared with straight tube TTHE. In the case investigated, serpentine layout TTHE with seven bends has shown optimum performance, with overall heat transfer coefficient 17% higher than straight tube TTHE. Two out of five serpentine layout TTHE have shown poor heat transfer performance than straight tube TTHE. The experimental results also indicate that there is a definite optimum for a number of bends in serpentine layout TTHE. An analytical model for prediction of thermo-hydraulic performance of straight layout has been developed and validated experimentally. 2005 Published by Elsevier Ltd.
*
Corresponding author: Tel.: +91 22 2576 7514; fax: +91 22 2572 4544. E-mail address: [email protected] (M.V. Rane).
1359-4311/$ - see front matter 2005 Published by Elsevier Ltd. doi:10.1016/j.applthermaleng.2005.01.007
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Keywords: Double wall heat exchanger; Serpentine layout; Straight tube; Analytical model
1. Introduction A tube–tube heat exchanger (TTHE) is a double wall tubular heat exchanger wherein two or more tubes are placed side-by-side and bonded thermally using thermal bonding material (TBM) for effective transfer of heat. Use of bends and straight lengths in tube–tube heat exchanger results in significant enhancement in heat transfer due to secondary flows induced in the bends. The secondary flows induced in bend leads to heat transfer enhancement in bend as well as in straight length downstream of bend without significant increase in pressure drop [1,2]. Dean was first to point out that the occurrence of a secondary flow at right angles to the main flow is due to centrifugal force [4]. The distorted flow condition by the induced secondary flow persists at a downstream distance of more than 50dtÆi for single-phase and 70dtÆi for two-phase [5]. Chen et al. [6] proposed empirical correlation for U-type wavy tubes with small diameter and short separation between consecutive bends (l/dtÆi = 1.93–7). Their correlation shows good agreements with the experimental data. However, extrapolations of correlation with wider operating range needs further examination to check their applicability. Recently, Chen et al. [5] have proposed a new correlation for friction factor applicable for wider separation between the consecutive bends (l/dtÆi = 0–30) but valid for limited range of Re (50–10,000). Ohadi et al. [7] have reported their study on effect of bend on pressure drop in a straight section downstream of a 180 bend. They found about 9% higher pressure drop in downstream section due to bend. Multi-stream Hampson heat exchanger with paired tubes reported by Kao [7] is helical coil type for three fluids. The paired tubes are soldered with tin–lead solder having thermal conductivity about 10% of copper, which may not be effective in liquid–liquid heat exchange due to its low thermal conductivity. In many heat transfer augmentation techniques, the augmentation is usually accompanied by significant increase in the pumping power required to overcome increase in pressure drop for the same heat transfer rate. But, in case of TTHE with serpentine layout the secondary flows induced due to bend continue their effect in the downstream portion of a bend [1,2]. Heat transfer enhancement in downstream section is maximum at the leading edge and diminishes along its length. Experimental and theoretical results on single-phase heat transfer on tube–tube heat exchanger configuration could not be located in literature. This paper experimentally investigates the thermo-hydraulic performance of serpentine layout TTHE with different number of bends (3, 6, 7, 8 and 9) in water-to-water heat transfer. Also, an experimental comparison of thermohydraulic performance of serpentine layout TTHE modules with straight tube TTHE is done. An analytical model for prediction of thermo-hydraulic performance of straight tube TTHE is developed and validated. In this type of heat exchanger, there is a wide choice of configurations to select depending on application like liquid–liquid, gas–liquid, two-phase etc. Fig. 1 shows different configurations of TTHE. Configuration 1–1 is preferred for high thermal conductivity tube material, 2–1 for gas–liquid application and configuration n–n for low thermal conductivity tube material. In some of the applications different diameter tubes are paired together allowing greater flexibility
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Nomenclature A heat transfer surface area, m2 BV ball valve C Cold/heat capacity, J/K d diameter of tube, m dp pressure drop, N/m2 dbend diameter of bend, m FS full scale f friction factor, dimensionless H Hot h heat transfer coefficient, W/m2 K k thermal conductivity, W/m K l length of tube, m length of tube sector acting as a fin, m lfin lpm liters per minute lst.section length of straight section of serpentine tube, m LMTD log mean temperature difference, degree m mass flow rate, kg/s NTU number of transfer units Nu Nusselt number, dimensionless PICCV pressure independent characterized control valve Pr Prandtl number, dimensionless Q heat transfer rate, W Re Reynolds number, dimensionless R, Rth thermal resistance, K/W r fouling resistance, m2 K/W t temperature, C TBM thermal bonding material U overall heat transfer coefficient, W/m2 K w thickness, m gap between adjacent tubes, m wg wpp.tot total pumping power, W Subscripts av average bend tube bend c cold f fouling h hot i inside o outside
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min max N pt t tbm Greek e gfs /
minimum maximum number of variables per tube tube thermal bonding material symbols effectiveness, dimensionless fin surface efficiency, dimensionless semi-fill angle subtended by thermal bonding material at tube centre, degree
H
C
TBM
(a)
H
H
C
TBM
(b)
H
C
C
H
H
C
TBM
(c)
Fig. 1. Sectional view of three TTHE configurations. (a) 1–1 TTHE, (b) 2–1 TTHE and (c) n–n TTHE.
in optimising the heat exchanger with respect to heat transfer coefficient and pressure drop. The configuration 2–1 shown in Fig. 1(b) is used in TTHE for recovery of superheat from a 60 TR chiller for one of the hotels in Mumbai [3].
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Some of the features of TTHE giving advantages over tube-in-tube and shell-and-tube heat exchangers are: (a) Possibility of using different material for tubes carrying fluids in order to reduce the cost. Reduction in material used by having two tubes used side-by-side, instead of one inside the other as the case in tube-in-tube heat exchangers. (b) For a particular design pressure, outer tube wall thickness is high which increases weight and hence cost of heat exchanger. In TTHE, tubes are placed side-by-side. Hence, diameter of tube replacing the outer tube is small. This reduces the thickness, weight and cost of the tubes. This along with reduced cost of headers leads to cheaper and reliable design in spite of small additional weight and cost due to TBM. (c) An ability of TTHE to handle fluids with fibrous materials, partial or complete extraction or introduction of fluids at intermediate temperature, increase or decrease the capacity of heat exchanger by increasing or decreasing number of tube sets, good accessibility of all tubes for ease of repair, in case of leakage.
2. Experimental setup Schematic diagram of the experimental setup for conducting water-to-water heat transfer experiments on TTHE modules is shown in Fig. 3. It includes a test section (TTHE module covered with insulation), an electric water heater, valves, pump and instrumentation for measurement. The experimental setup consists of two fluid circuits. The first circuit, as shown in Fig. 3, is closed loop for hot water. Hot water is generated in an electric water heater, which has a capacity of about 9 kW. Flow rate of hot water from water heater is controlled by adjusting valve and temperature of hot water at inlet to the test section is controlled by three-phase Variac. Hot water temperature at inlet and outlet of the test section is measured by K type thermocouples. The second circuit is cooling water circuit as shown in the upper half of the Fig. 3. This is open loop with the digital turbine meter for measuring cooling water flow rate and pressure independent characterized control valve (PICCV) for regulating the flow rate. The water flow rate is adjusted to different values and maintained constant by pressure independent characterized control valve. Thermocouples are placed in cooling water stream to measure temperatures at inlet and outlet of a test section. 2.1. Test section The test section comprising tube–tube heat exchanger module, is shown as a sectional view in Fig. 2(a). Various modules of TTHE are fabricated for test. TTHE modules being tested consist of two copper tubes of 9.525 mm OD, which are brazed all along their lengths with copper filler material. The copper filler, which will be referred in this paper as thermal bonding material (TBM), subtends semi-fill angle /max of 36.7 at the tube centre. The gap between the tubes, wg is measured at different sections along the length to calculate the average gap between the tubes of TTHE module. The simulation results show that for TTHE with copper tubes, a gap of up to
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(a)
(b)
Fig. 2. TTHE module. (a) Cross-sectional view of 1–1 TTHE module; (b) serpentine layout TTHE module with six bends.
1 mm has insignificant effect on heat transfer. However, with lower thermal conductivity TBM, the effect of gap will be considerable. The average gap between the tubes is less than 0.5 mm for all modules tested. This small gap between the tubes allow thermal bonding material to flow to other side of tubes during brazing. Hot water flows through one tube and cooling water through other. All modules during the tests are oriented such that the hot water tube is below the cooling water tube. This eliminates
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Fig. 3. Schematic of experimental setup for water-to-water heat transfer.
the effects, though insignificant, of variants other than number of bends on performance of modules. All modules are insulated thermally from their surroundings during tests by the closed cell foam insulation (thickness 25.4 mm and thermal conductivity 0.046 W/m K). 2.1.1. Straight layout 1–1 TTHE module (one tube for hot water and another tube for cooling water) fabricated using two copper tubes with 9.525 mm OD. These straight tubes are brazed all along their lengths with copper filler. 2.1.2. Serpentine layout A pair of copper tubes with 9.525 mm OD is first bent to a serpentine shape on tube bending machine. The ratio of bend diameter to tube diameter (dbend/dtÆi) is 5.29. These tubes are brazed all along their lengths. Five modules of serpentine layout with 3, 6, 7, 8 and 9 bends are fabricated giving different ratio of length of the straight section to tube diameter (lst.section/dtÆi). Fig. 2(b) shows serpentine layout TTHE with six bends. 2.2. Experimental method The cooling water inlet temperature during the test is 29 ± 0.5 C. The flow rate of water is adjusted by pressure independent characterized control valve and held constant irrespective of tap water pressure. The cooling water flow rate is changed from 3 to 10 lpm in step of about 1 lpm. Flow rate on two sides is kept same in all sets of readings. The temperature of hot water inlet to the test section is adjusted to 85 ± 0.1 C by changing heater input through three-phase Variac.
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2.2.1. Instrumentation Instruments used for measuring various parameters during the experimentation are: (a) Water flow rate is measured using digital turbine meter. Make: GPI turbine meter, Model No. S050 N1/200 , Mid-flow, accuracy: ±2% of reading in the range 3.8–37.9 lpm, range: 1.9–37.9 lpm. (b) Flow rate of cooling water below 3.8 lpm is measured by measuring weight of water using weighing balance with an accuracy of ±1% of reading. Make: PAG Oerlikon AG CH-Dietikon Precisa Balances, Model No. 87113 type 2300-9535/H6200D. The range and resolution of instrument is 0–6.2 kg and 0.1 g respectively. This was done since the accuracy of turbine meter is lower than ±2% for flow rate below 3.8 lpm. (c) The pressure losses are measured by digital differential pressure transducers. Make: HBM, Digibar, range: 0–1.2 bar, resolution: ±0.5% of the measurement, and accuracy: ±2%. The instrument was calibrated using accurate dial gauge having accuracy of 0.1% of FS. (d) The fluid temperatures are measured using K type thermocouples with an accuracy of ±0.3 C. The range and resolution of instrument is 20 to 300 C and 0.1 C, respectively. Thermocouples are calibrated using thermocouple calibrator in Instrumentation Laboratory. The bends in serpentine TTHE modules tested are not perfectly circular in cross-section due to the manufacturing process used. As a result of this, the tube cross-section became elliptical due to flattening. The maximum flattening of the bends of all modules tested is less than 8%. The flattening is calculated by following equation [12] flattening ¼
ðd tmax d tmin Þ 0.5 ðd tmax þ d t. min Þ
ð1Þ
Since 10% flattening results in very small 0.3% reduction in cross-sectional area; 8% flattening in the present case is expected to have insignificant effect on pressure drop.
3. Results and discussion Pressure drop and heat transfer results for the layouts tested in water-to-water heat transfer are shown in Figs. 4 and 5. 3.1. Pressure drop Fig. 4 represents variation in experimental pressure drop with mass flow rate on hot water side for all six modules of TTHE. In serpentine layouts, the pressure drop increases with number of bends. The straight layout TTHE has shown lowest pressure drop amongst all layouts tested, which is as expected.
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Pressure Drop on Hot Water Side, dph (bar)
7 Straight Serpentine (3 bends) Serpentine (6 bends) Serpentine (7 bends) Serpentine (8 bends)
6 5
Serpentine (9 bends)
4 3 2 1 0
2
4
6 8 Flow Rate of Water, mh(kg/min)
10
12
Fig. 4. Variations in pressure drop with mass flow rate of water.
Overall Heat Transfer Coefficient, Ui.h (kW/m2 K)
3.4 Straight Serpentine Serpentine Serpentine Serpentine Serpentine
3.2 3.0 2.8
(3 (6 (7 (8 (9
bends) bends) bends) bends) bends)
2.6 2.4 2.2 2.0 1.8 1.6 1.4
0
4
8
12
16
20
24
Total Pumping Power, Wpp.tot (W)
Fig. 5. Variations in experimental overall heat transfer coefficient with total pumping power.
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3.2. Overall heat transfer coefficient Fig. 5 represents variation of experimentally determined overall heat transfer coefficient with total pumping power for six modules tested. For a fixed pumping power, serpentine layout TTHE with seven bends has shown highest overall heat transfer coefficient. Its maximum value is higher than straight tube TTHE by 17%. When comparison is done amongst serpentine layouts, the overall heat transfer coefficient is highest in serpentine layout with seven bends and lowest with nine bends. For serpentine layout with three bends, the overall heat transfer coefficient is lower than serpentine layout with seven bends in this range of flow rate. Thus, the experimental results indicate that in serpentine layout TTHE, there is a definite optimum for a number of bends for a particular application. In serpentine layout with three and six bends, with dbend/dtÆi of 55.3 and 28.1, respectively, part of the straight sections does not offer enhancement in heat transfer. Effect of secondary flow diminishes long before the fluid enters the subsequent bend. In serpentine layouts with eight and nine bends, with dbend/dtÆi of 20.9 and 15.8, respectively, the secondary flow generated by the previous bend probably persists as the fluid enters in the next bend. Since the secondary flow is reversed in subsequent bends in a serpentine layout, pressure drop increases without commensurate increase in heat transfer. Benefits of the bends are not realized, since number of bends per unit length is large as in the case of eight and nine bends, the secondary flow is first neutralized as it passes the bend and reversed as it comes out. The consecutive bend interactions are so severe that the performance of the serpentine layout is worse than that of a straight tube TTHE. The quantities measured directly include the volume flow rate of water, inlet and outlet temperature of water. The uncertainty in measurement of volume flow rate of water is ±2% of reading (maximum uncertainty: ±0.2 lpm). The uncertainty of temperature measurement is ±0.3 C. According to the uncertainty analysis based on Kline and McClintock method illustrated by Moffat [11], the maximum uncertainties of overall heat transfer coefficient, heat transfer rate, and log mean temperature difference is 3.3%, 3% and 0.76%, respectively.
4. Model development An effectiveness-NTU method is used in the model developed for performance prediction of tube–tube heat exchanger. The present model developed for straight tube–tube heat exchanger incorporates following attributes: (a) Layout: straight. (b) Flow configuration: counter flow or parallel flow. (c) Geometric parameters of tubes: number, diameter, thickness, material on two sides. (d) Thermal bonding of tubes: material and its size (/), gap between the adjacent tubes. Appropriate parameters like length of fin, lfin (part of the tube transferring heat by fin effect), number of tubes on two sides, semi-fill angle / are included in the model to analyse most of the configurations (various configurations with different number of tubes) of tube–tube heat exchan-
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ger. The performance parameters like overall heat transfer coefficient, pressure drop, pumping power, cost, and size of heat exchanger are calculated for straight layout. Input parameters to the model are inlet temperatures and mass flow rates of water. Other input parameters necessary for the analysis are flow arrangement, number of tubes, tube material, tube diameter, tube thickness, thermal bonding material and its size. Following assumptions were made in the model development. (a) Steady state operation. (b) No heat loss to the surroundings. (c) No heat transfer in the direction of flow. (d) Uniform fluid distribution in all tubes in multiple tube tube–tube heat exchanger. (e) One dimensional flow of heat through part of the tube and thermal bonding material. (f) No phase change.
4.1. Heat transfer equations The net heat transfer depends on the waterside heat transfer coefficients, fouling factors, thermal resistance by tube walls, and thermal bonding material. The correlations for heat transfer coefficients and friction factors reported in the literature have been used in the model. Few important equations used in the model are given below. NTU is calculated by NTU ¼
UA C min
ð2Þ
Theoretical relations for effectiveness as a function of NTU and heat capacity ratio are available for different flow arrangements like counter flow or parallel flow. For counter flow, equation for effectiveness is e¼
1 exp½NTU ð1 C ratio Þ 1 C ratio exp½NTU ð1 C ratio Þ
ð3Þ
where, C ratio ¼
C min C max
The maximum possible heat transfer rate is calculated by Qmax ¼ C min ðthi tci Þ
ð4Þ
The actual heat transfer rate in heat exchanger is calculated by equation Q ¼ e C min ðthi tci Þ
ð5Þ
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4.2. Heat transfer coefficient The net heat transfer depends on heat transfer coefficients, fouling factors, thermal resistance by tube walls, and thermal bonding material. Gnielinskis correlation [9] is used for heat transfer coefficient calculation for transition region as well as fully developed turbulent flow for a straight smooth circular tube Nu ¼
f ðRe 2
1000Þ Pr f 0.5 1 þ 12.7 2 ðPr2=3 1Þ
ð6Þ
For 2300 6 Re 6 5 · 106 and 0.5 6 Pr 6 2000. It is modified version of second Petukhov correlation, which agrees with most reliable experimental data to an accuracy of ±5%. 4.3. Friction factor For friction factor in fully developed turbulent flow for a straight smooth circular tube, Prandtl, Karman, Nikuradse (PKN) correlation is classical correlation valid for wide range of Re (4 · 103 6 Re 6 107). The correlation is also used for comparison of recent correlations. h pffiffiffii 1 pffiffiffi ¼ 1.7372 ln Re f 0.3946 ð7Þ f Predictions of this correlation agree with the extensive experimental measurements within ±2 [4]. However, the PKN correlation is not explicit form; Techo, Tickner, James correlation [10] is used for friction factor calculations. 1 Re pffiffiffi ¼ 1.7372 ln ð8Þ 1.964 ln Re 3.8215 f This explicit form of PKN correlation agrees within ±0.1% of PKN correlation for 104 6 Re 6 2.5 · 108.
5. Overall heat transfer coefficient The overall heat transfer coefficient is obtained using following expression 1 1 1 1 1 þ rfh þ Rthh þ Rthtbm þ Rthc þ þ rfc ¼ UA hh Ah gfsh hc Ac gfsc
ð9Þ
RthÆtbm is thermal resistance of thermal bonding material. Thickness of thermal bonding material (measured in the direction of heat transfer) varies from minimum at / = 0 to maximum at the limiting value /max. RthÆh and RthÆc are thermal resistance of portion of tubes in contact with thermal bonding material on hot water and cooling water side, respectively. Similarly, rfÆh and rfÆc are fouling resistances on hot water and cooling water side, respectively. Thermal resistance of thermal bonding material is calculated considering differential element as shown in Fig. 2(a).
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Thermal resistance of differential element is given by R¼
d to ð1 cos /Þ þ wg k tbm d2to d/ cos / lpt
ð10Þ
where, R is thermal resistance of the differential element in terms of differential angle d/. The thermal resistances of all elements of TBM are in parallel. Therefore, the overall thermal resistance of TBM is obtained by integrating 1/R term for the differential element between the limits /max to /max. The derived equation for overall thermal resistance of TBM is Z /max 1 k tbm d2to cos / lpt Rthtbm ¼ 2 d/ ð11Þ d to ð1 cos /Þ þ wg 0 Another approach to obtain thermal resistance of thermal bonding material is by calculating equivalent/average thickness considering the area equivalence. Following equation gives equivalent/average thickness of thermal bonding material. p ½sin /max ð1 cos /max Þ 12 /max 180 sin /max cos /max d to ð12Þ wtbmav ¼ wg þ sin /max The thermal resistance of thermal bonding material calculated using Eq. (11) and other calculated by considering the approach of average thickness of thermal bonding material deviates within 10%.
0.6
Experimental Pressure Drop, dph (bar)
45 deg line
0.5
0.4
0.3
0.2
0.1
0.0 0.0
0.1
0.2
0.3
0.4
Predicted Pressure Drop, dph (bar)
Fig. 6. Experimental vs. simulated pressure drop.
0.5
0.6
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3.0 45 deg line
2.5
2.0
1.5
1.0 1.0
1.5
2.0
Predicted Overall Heat Transfer Coefficient, Ui.h
2.5
3.0
(kW/m2 K)
Fig. 7. Experimental vs. predicted overall heat transfer coefficient.
6. Experimental validation of model The present model developed for straight tube TTHE is validated experimentally for waterto-water heat transfer by testing a typical module of straight tube TTHE. The experimental setup used for conducting experiments is explained in earlier section. The experimental and simulated results on pressure drop and overall heat transfer coefficient for straight tube TTHE are represented in Figs. 6 and 7. The results show good agreement between the results prediction by model and the experimental results. The average difference between the predicted and experimental results of pressure drop on hot water side is 2.3% and the maximum difference is 4.2%. The average difference between the predicted and experimental overall heat transfer coefficient is 2% and maximum difference is 6.2%.
7. Conclusions Five different serpentine layouts of TTHE have been experimentally evaluated for the effect of varying straight lengths between bends on thermo-hydraulic performance. Tubes used in all five serpentine layout TTHE are 9.525 mm OD and 43 mm bend diameter. Maximum overall heat transfer coefficient is obtained for the serpentine layout TTHE with seven bends when the performance is compared at same pumping power. Also, the overall heat transfer coefficient in serpentine layout TTHE with seven bends is higher than TTHE with straight layout by 17%.
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In water–water heat transfer, not all serpentine TTHE layouts are better than straight layout. The serpentine layout TTHE with three and nine bends have shown lower heat transfer performance than straight layout TTHE. However, at very low pumping power (below 3 W), serpentine layout with three bends has shown slightly better heat transfer performance than straight tube TTHE. The maximum difference in performance of optimum serpentine layout TTHE (seven bends) and nine bend serpentine TTHE, which is a non-optimum, is 30%. Thus, due care should be taken while designing TTHE with serpentine layout to maximize the benefits of this design. In case of serpentine layout TTHE, the experimental results indicate that there is a definite optimum for a number of bends for a particular application. In the present case, the optimum number of bends in serpentine layout is 7. An analytical model for simulation of straight tube TTHE in water–water heat transfer is validated experimentally. Effectiveness-NTU approach is used in the model for performance predictions. The average and maximum deviation between predicted and experimental values of overall heat transfer coefficient is 2% and 6.2%, respectively. Similarly, average and maximum deviation is pressure drop 2.3% and 4.2%, respectively.
References [1] M.V. Rane, M.S. Tandale, Tube–tube heat exchangers, Filed PCT/IN03/00377, 2003. [2] M.V. Rane, M.S. Tandale, An experimental study on various layouts of tube–tube heat exchanger in steam condensation, Experimental Thermal and Fluid Science, submitted for publication. [3] M.V. Rane, M.S. Tandale, Benefits of superheat recovery on chillers- case study for a hotel installation, Paper presented at 21st IIR International Congress of Refrigeration, Washington, DC, August 2003, pp. 17–22. [4] R.K. Shah, S.D. Joshi, Convective heat transfer in curved ducts, in: S. Kakak, R.K. Shah (Eds.), Handbook of Single-phase Convective Heat Transfer, first ed., John Wiley and Sons, 1987. [5] I.Y. Chen, J.C. Huang, C.C. Wang, Singe-phase and two-phase frictional characteristics of small U-tube wavy tubes, International Communication Heat Mass Transfer 31 (3) (2004) 303–314. [6] I.Y. Chen, S.K. Lai, C.C. Wang, Frictional performance of small diameter U-type wavy tubes, ASME Journal of Fluids Engineering 47 (2003) 2241–2249. [7] M.M. Ohadi, E.M. Sparrow, A. Walawalkar, A.I. Ansari, Pressure drop characteristics for a turbulent flow in a straight circular tube situated downstream of a bend, International Journal of Heat Mass Transfer 33 (4) (1990) 583–591. [9] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (2) (1976) 359–368. [10] R. Techo, R.R. Tickner, R.E. James, An accurate equation for the computation of the friction factor from smooth pipes from the Reynolds number, ASME Transaction Journal of Applied mechanics 32 (1965) 443. [11] R.J. Moffat, Describing the uncertainties in experimental results, Experimental Thermal and Fluid Science 1 (1988) 3–17. [12] D.F. Geary, Return bend pressure drop in refrigeration systems, ASHRAE Transactions 2342 (1980) 250–265.