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The effect of flow, thermodynamic and geometrical characteristics on exergy loss in shell and coiled tube heat exchangers
Energy 91 (2015) 678e684
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
The effect of flow, thermodynamic and geometrical characteristics on exergy loss in shell and coiled tube heat exchangers Hamed Sadighi Dizaji, Samad Jafarmadar*, Mehran Hashemian Faculty of Mechanical Engineering, Urmia University, Urmia, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 April 2015 Received in revised form 21 August 2015 Accepted 26 August 2015 Available online xxx
This work presents experimental investigations on the effects of flow, thermodynamic and geometrical characteristics on exergy loss in shell and coiled tubes heat exchangers. Pressure drop and heat transfer characteristics in shell and coiled tube heat exchangers have been widely studied in the resent years. However, the effects of flow, thermodynamic and geometrical parameters on exergetic characteristics have not been explicitly and experimentally studied. Hence, the main scope of the present work is to clarify the effect of shell and coil side flow rates, inlet temperatures, coil pitch and coil diameter on exergy loss in shell and coiled tube heat exchangers. Both of the total exergy loss and dimensionless exergy loss are studied. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Shell and coiled tube heat exchanger Exergy loss Fluid properties Thermodynamic characteristics Geometry
1. Introduction Irreversibility and availability are two concepts that have found increasing use in recent years. These concepts are particularly applicable in the analysis of complex thermodynamic systems. Irreversibility and availability are very powerful tools in design and optimization studies of such systems [1]. Helically coiled tubes have wide applications in the industry because of their high heat transfer coefficients, low volume and size, narrow residence time distributions and simple manufacture method etc. Hence, knowledge about the heat transfer, pressure drop and exergetic characteristics in helically coiled tubes are very significant. Thermal and frictional characteristics of helically coiled tubes were extensively investigated in the past years. However, exergetic characteristics have not been explicitly and experimentally studied for shell and coiled tube heat exchangers. Hence, the main scope of the present work is to clarify the effect of flow, thermodynamic and geometrical parameters on exergy loss in shell and coiled tube heat exchangers. The flow moved through a helically coiled tube is affected by centrifugal forces. Centrifugal forces create secondary flows, and
* Corresponding author. E-mail addresses: [email protected] (H. Sadighi Dizaji), S. [email protected] (S. Jafarmadar), [email protected] (M. Hashemian). http://dx.doi.org/10.1016/j.energy.2015.08.084 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
they induce significant eddies in a cross-section of the coiled tube. Indeed, as described in Wu et al. [2] study, centrifugal forces drive the fluid flow toward the outer wall and then returns by flowing back along the wall. Centrifugal forces, secondary flows and eddies can enhance the exergy loss in helically coiled tubes. Investigations on shell and coiled tube heat exchangers as well as exergetic parameters are summarized as follows. Ko [3] offered optimal coil curvature ratio in a helical coiled tube with different combination of design parameters. The System analyzed by thermodynamic second low was based on minimal entropy generation principle for fully developed laminar flow and constant wall heat flux. Salimpour [4,5] experimentally studied the heat transfer characteristics of shell and coiled tube heat exchanger and proposed some correlations to predict the shell-side and tubeside Nusselt number. Kumar et al. [6] investigated on heat transfer and pressure drop of tube-in-tube helically coiled heat exchanger. Keε model was used to evaluate the turbulent flow. Ghorbani et al. [7] evaluated the effects of coil pitch and tube diameters on shellside heat transfer coefficient of a shell and coiled tube heat exchanger. Their findings showed that, the effect of tube diameter on shell-side heat transfer coefficient is negligible. Besides, their results indicated that the shell side heat transfer coefficient increases with the increase of coil pitch. Pandey and Nema [8] conducted experimental research on exergy loss in corrugated plate heat exchanger with different types of plate. Naphon [9] investigated on entropy generation and exergy loss in a concentric micror [10] analyzed the heat transfer rate fin tube heat exchanger. Zacha
H. Sadighi Dizaji et al. / Energy 91 (2015) 678e684
Nomenclature A c d D Dh De Dh e E k ṁ Max Min NTU p Pr q Q Rc
coiled tube area, m2 specific heat, J/kg C coiled tube diameter, m shell diameter, m shell side hydraulic diameter, m d )0.5 Dean number, Re(2R c 2 D 2pR d2 p1 hydraulic diameter, Dþ2pR cd op1 c o dimensionless exergy loss exergy loss (exergy change), W thermal conductivity, W/m C mass flow rate, kg/s Maximum minimum number of thermal units coil pitch, m Prandtl number, mC k heat transfer rate, W flow rate, LPM coil radius, m
in the outer side of the coiled tube in several cases with different combination of geometrical and flow parameters. Hashemi [11] used CuO-oil based nanofluid flow inside the helically coiled tube with constant wall heat flux. Experimental investigations showed that, using of coiled tube instead of straight tube causes heat transfer enhancement as well as more pressure drop. Besides, analogy of two heat transfer enhancement method showed that the employment of helically coiled tube instead of straight tube preferred to the adding additives to the base fluid. Mohammed and Narrein [12] numerically investigated the effects of using different geometrical parameters with the combination of nanofluid on heat transfer and fluid flow characteristics in a helically coiled tube heat exchanger. It was found that the heat transfer rate can be increased by reducing the helix radius, increasing the inner tube diameter and decreasing the annulus diameter. Jamshidi [13] experimentally concluded that the increasing coil diameter, coil pitch and fluid flow rate leads to higher heat transfer rate in shell and coiled tube heat exchangers. Pan et al. [14] performed a comprehensive study of thermal and hydraulic performances of shell and tube exchangers, and presented the detailed thermal and hydraulic calculations on the shell and tube heat exchangers with implementing conventional intensification techniques. According to the Kumar et al. [15] study the use of nanofluid in coiled tubes creates stronger secondary flow through the tube. The second flows properly mix nano-particles and also avoid particles concentrations which lead to higher heat transfer rate and also more pressure drop. According to the literature review no experimental investigation has been performed to study the effect of flow, thermodynamic and geometrical parameters on exergy loss in shell and helically coiled heat exchangers. In the present work, the effect of shell and coil side flow rates, hot and cold water inlet temperatures, coil diameter and coil pitch on exergy loss experimentally evaluated for the shell and coiled tube heat exchanger. 2. Experiments 2.1. Experimental apparatus and tubes geometry A general view of the experimental set-up is shown in Fig. 1. An electrical heater (inside the hot water tank), rheostat and a
Re s T U V W X
679
Reynolds number, VD y specific entropy, J/kg. K temperature, K overall heat transfer coefficient, (W/m2C) water mean velocity, m/s total uncertainty in the measurement independent variable
Greece symbols n kinematic viscosity, m2/s p g dimensionless pitch, 2pR c Subscripts c cold fluid e environment condition h hot fluid i inner o outer in inlet out outlet
thermostat maintain the hot water inlet temperature at around a constant value. The heated water is pumped from the hot water tank, and then it passes the control valve, goes into a Rota-meter, enters the helically coiled tube and finally it returns into the hot water tank. A cooling unit maintains the cold water inlet temperature at around a constant value. The cooling unit consists of an evaporator (inside the cold water tank), compressor, condenser, refrigerant, expansion valve, thermostat and a fan (the fan is used when lower temperatures are needed). The cooled water is pumped from the cold water tank and then it passes the control valve, goes into a rotameter, enters the shell side of heat exchanger, and finally it returns into the cold water tank. The hot and cold water inlet and outlet temperatures were recorded at fully steady state condition using EXTECH data logger (SDL200) with K type thermocouples (accuracy ±0.5 C and resolution 0.1 C). Besides, all Rota-meters were calibrated for hot and cold water by using a stopwatch and measuring cylinders. As seen in Fig. 1(c) the test section (which presents a new simple method to make a shell and coiled tube heat exchanger for research applications) consists of a shell tube, a coiled tube, two insulated grooved end plates and four screwed steel rods. The shell of heat exchanger was placed between the end-plates and screwed steel rods were used to hold and adjust the position of the end-plates. The coiled tube was constructed by copper material with 9 mm inner diameter and 12 mm outer diameter and the outer tube (shell) was made from PVC. Helical tubes in this study have 12 turns. A schematic illustration of the coiled tube is shown in Fig. 2. 2.2. Experiments procedure Different conditions considered in this study are presented in Table 1. In first step, geometrical and thermodynamic parameters (inlet temperatures) were kept constant and the effects of shell and coil side flow rates were investigated. For this purpose, each shell side flow rate (3, 4, 5, 6 and 7 LPM) was experimented with five different coil side flow rates (3, 3.5, 4, 4.5 and 5 LPM). It is noted that, used water pumps can't supply more than around 6 LPM to coil side of test section because of the high pressure drop through the coiled tube compared to straight tube. All selected amounts for other parameters such as temperatures are proportional with the
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Fig. 1. (a) Experimental setup and (b) a schematic illustration of the test set-up: 1-test section, 2-Rotameter, 3-warm water tank, 4-dimmer and thermostat and heater, 5-water pump, 6-condenser, 7-compressor, 8-cold water tank, 9-evaporator, 10- coiled tube and (c) a schematic illustration of test section.
used related devices. In the second step, shell and coil side flow rates were fixed at around 3 LPM and the effects of hot and cold water inlet temperatures were studied. Each shell side (cold water) inlet temperature (around 8, 18 and 25 C) was tested with three
various coil side inlet temperature (around 40, 60 and 80 C). Finally, both of the flow and thermodynamic parameters were fixed and the effect of coil pitch and coil diameter on exergy loss were investigated. 2-cm layer of the glass wool insulation were used to prevent heat loss to surrounding from the outer tube (shell). During the experiments, inlets and outlets bulk temperatures were measured at steady state condition. 2.3. Uncertainty of measurements
Fig. 2. A schematic illustration of the coiled tube.
Measurement uncertainties can be due to the measuring instrument, environment condition, operator and other sources. In this experiment, the uncertainty of experimental data results was evaluated by Kline [16] method. The uncertainties in calculating a
H. Sadighi Dizaji et al. / Energy 91 (2015) 678e684
Eh and Ec are the exergy change for hot fluid and cold fluid respectively, and are calculated as follows:
Table 1 Various test conditions (variable parameters are bold in each row). Qc LPM
Qh LPM
De (coil)
Th,in C
Tc,in C
Pr
P (mm)
Rc (mm)
8 8 8 8 8
e e e e e
12 12 12 12 12
55 55 55 55 55
The effect of shell and coil side flow rate 3 4 5 6 7
3e5 3e5 3e5 3e5 3e5
2600e4800 2600e4800 2600e4800 2600e4800 2600e4800
40 40 40 40 40
e e e
3 3 3
40e80 40e80 40e80
8 18 25
e e
5 5
40 40
8 8
2e10 2e10 2e10
12 12 12
55 55 55
vRþ WRþ ¼ @ w vX1 1
!2 þ
vRþ w vX2 2
e e
12e24 12e24
55 35
!2 þ…þ
_ c ðsc out sc in Þg Ec ¼ Te fm
(5)
vRþ wn vXn
T out Tin
(6)
Substituting Eq. (6) into Eq. (4), Eq. (5) and Eq. (3) yields:
result (Wþ R ) due to some independent variables are evaluated by following equation:
0
(4)
sout sin ¼ cpc ln
The effect of geometrical parameters 3 3
_ h ðsh out sh in Þg Eh ¼ Te fm
For liquids it can be assumed that the specific heat is constant and the entropy change can be calculated as below.
The effect of shell and coil side inlet temperatures 3 3 3
681
!2 112 A
T _ h cph ln ho Eh ¼ Te m Thi
(7)
T _ c cpc ln co Ec ¼ Te m Tci
(8)
T T _ h cph ln ho þ m _ c cpc ln co E ¼ Te m Thi Tci
(9)
Dimensionless exergy loss (x) can be calculated from Eq. (10) [17,18].
(1) Uncertainty results details are summarized in Table 2.
e¼
E Te Cmin
Cmin ¼ Min {Ch ¼ ṁhcph and Cc ¼ ṁccpc}
(10)
(11)
2.4. Exergy loss calculation method Exergy is defined as the maximum useful work that can be achieved from the reversible system in a specified environment. For heat exchangers which do not involve shaft work, the exergy given out by one flow is compared with the exergy gained with the other flow. Exergy loss (E) can be calculated as described below. For a given steady control volume, exergy balance can be expressed as:
X
Ein ¼
X
Eout
X
Eproduct
(2)
In present study, heat exchanger is adiabatic and it can be assumed that the amount of qh is equal with the amount qc. Exergy loss in a steady control volume with two different types of working fluids can be written as follows: E ¼ Eh þ Ec
(3)
Table 2 Maximum uncertainty of parameters. Parameter
Unit
Uncertainty in the temperature measurement
Hot fluid inlet temperature Hot fluid outlet temperature Cold fluid inlet temperature Cold fluid outlet temperature
Comment
C
C C C C
±0.5 ±0.5 ±0.5 ±0.5
(1.2%) (1.2%) (6%) (6%)
Uncertainty in the measurement of volume flow rate
LPM
Water (shell side) Water (coil side)
LPM LPM
Uncertainties in calculating a result
%
Exergy loss
%
±9.23
Uncertainty in reading values of table (r,k, …)
%
±0.1e0.2
±0.5 (16%) ±0.5 (16%)
3. Results and discussions 3.1. The effect of hot and cold water flow rate on exergy loss Fig. 3(a) presents exergy loss (E) versus the Dean number. According to the Table 1 the coil diameter and coil pitches are 110 mm and 12 mm respectively. Also, hot and cold water inlet temperatures were kept constant at around 40 C and 8 C respectively. Exergy loss (E) increases with the increase of shell or coil side flow rate. The slope of exergy loss augmentation due to Dean number enhancement is severe for higher amounts of shell side flow rate. Maximum and minimum exergy loss enhancement occurs at shell side flow rate of 7 LPM and 3 LPM respectively. Also, it can be said that when the shell side flow rate is more than the coil side flow rate, the effect of the amount of coil side flow rate on exergy loss is greater. For example, at shell side flow rate of 6 LPM or 7 LPM, which are more than the coil side flow rates for all points (coil side flow rate changes from 3 LPM to 5 LPM) coil side flow rate has a significant effect on exergy loss. But at shell side flow rate of 3 LPM which is less than the coil side flow rates (3, 3.5, 4, 4.5, 5 LPM), the effect of Dean number on exergy loss is minor. The relationship between dimensionless exergy loss (e) calculated from Eq. (10) and Dean number is shown in Fig. 3(b). Curves behavior in dimensionless exergy loss (e) depends on both of the exergy loss (E) and Cmin (see Eq. (11)). For shell side flow rate of 5, 6 and 5 LPM, Cmin is evaluated using of the coil side mass flow rate. For these cases, as exergy loss (E) increases, Cmin increases too, but the ratio of E to the Cmin which is indicative of dimensionless exergy loss (e) decreases. It means that, the enhancement of Cmin is more than the enhancement of exergy loss (E). For shell side flow rate of 3 LPM and three last points of 4 LPM the theorem are different. For
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Fig. 3. The effect of shell and coil flow rates on a) exergy loss b) dimensionless exergy loss.
these cases, Cmin is evaluated using of the shell side flow rate which has less amount of mass flow rate in comparison with the coil side flow rate, and despite that the exergy loss (E) increases with the increase of Dean number but the amount of Cmin is constant. To this reason, dimensionless exergy loss (e) decreases with the increase of Dean number for these cases. Indeed, as seen in Fig. 3(b) dimensionless exergy loss can be increased or decreased with the increase of Dean number, it depends on Cmin in Eq. (10). Hence, it isn't possible to present an explicitecomprehensive correlation for dimensionless exergy loss as a function of flow rates. However, ever any changes in coil or shell side flow rate influence significantly on dimensionless exergy loss. 3.2. The effect of hot and cold water inlet temperatures on exergy loss
hot and cold water inlet temperatures. Experimental results indicate that as hot water (coil side) inlet temperature increases both of the exergy loss and dimensionless exergy loss increases. Moreover, results show that the exergy loss (E and e) decreases with the increase of cold water (shell side) inlet temperature. By increasing the hot water inlet temperature, the difference between hot and cold water inlet temperature (DTin ¼ Th,in Tc,in) increases, but by increasing the cold water inlet temperature, difference between hot and cold water inlet temperature decreases. Hence, it can be concluded that, the exergy loss increases with the increase of DTin, which can be due to the hot water inlet temperature enhancement or cold water inlet temperature decrement. Indeed, the enhancement of DTin causes more heat transfer rate between the cold water (coil side) and hot water (shell side). Hence, the exergy loss due to heat transfer irreversibility increases.
c m
Prandtl number ( pk ) is a potential indicator of specific heat, thermal conductivity and viscosity as the main thermodynamic characteristics of the working fluid. Hence, hot and cold water inlet temperatures are varied in order to get different amounts of water Prandtl number; and the effects of water inlets temperatures on exergy loss are evaluated. Other parameters (coil side and shell side flow rate, coil pitch and coil diameter) are fixed in the constant values in this section as presented in Table 1. Fig. 4(a) and Fig. 4(b) show the variation of exergy loss and dimensionless exergy loss by
3.3. The effect of coil pitch and coil diameter on exergy loss 3.3.1. First mode (shell side and coil side flow rates are fixed) In this section, flow rates and inlet temperatures are fixed and the effect of coil pitch and coil diameter on exergy loss are studies. The desired coil diameters are 0.11 m and 0.07 m which each of them is investigated with three different pitches (12 mm, 18 mm and 24 mm). Both shell side and coil side flow rates were kept
Fig. 4. The effect of hot and cold water inlet temperatures on a) exergy loss b) dimensionless exergy loss.
H. Sadighi Dizaji et al. / Energy 91 (2015) 678e684
683
Fig. 5. The effects of coil pitch and coil diameter on a) exergy loss b) dimensionless exergy loss. Shell and coil side flow rates are constant.
constant at 3LPM. Hot water inlet temperature is 40 C and cold water inlet temperature is around 8 C for all cases in this section. The relationship between exergy loss and coil pitch is shown in Fig. 5 for first mode. According to Fig. 5(a), as coil pitch or coil diameter increases, exergy loss (E) increases. Exergy loss enhancement due to the increase of coil pitch or coil diameter can be described as follow. At higher amounts of coil pitch, more and better contact occurs between the shell side water flow and the coiled tube, and the result is more heat transfer rate through the heat exchanger [12]. Besides, in a fixed coil turns (coil turns in this study is 12), the length of coiled tube with higher coil diameter is more than the coiled tube with less coil diameter. Hence, the residence time of hot water in heat exchanger increases, and the cold fluid can earn more heat transfer from the hot water in the coiled tube. As mentioned before, more heat transfer rate causes more exergy loss through the heat exchanger. Hence the exergy loss due to heat transfer irreversibility increases by increasing the coil pitch or coil diameter which is in agreement by the represented results in Fig. 5(a). As seen in Fig. 5 the trend curve of exergy loss (E) and dimensionless exergy loss (e) are similar in this mode. Because the denominator of Eq. (10) is constant for this mode (flow rates are fixed) and obviously dimensionless exergy loss (calculated with Eq. (10)) increases as exergy loss (E) increases. Hence, dimensionless exergy loss (e) increases with the increase of coil pitch or coil diameter because of the same reasons which were described above for exergy loss (E). 3.3.2. Second mode (shell side Re and coil side De are constant) It should be noted that each coiled tube creates different shell side hydraulic diameter because of their different geometrical characteristics (see Eq. (12)). Therefore, a defined shell side water flow rate (for example 3LPM) creates different and exclusive shell side Reynolds number for each case (see Eq. (13)). It is noted that, in present paper, shell side hydraulic diameter is calculated from Eq. (12) used by Saeedinia et al. [19]. However, Salimpour et al. [5] employed another form of Eq. (12) that is dimensionally inhomogeneous (the units of the two terms in the numerator do not match). According to Eq. (14), a defined coil side water flow rate creates different and exclusive coil side Dean number for each coil diameter as well.
Dh ¼
D2 2pRc d2o p1 D þ 2pRc do p1
(12)
Reshell side ¼
V Dh y
De ¼ Recoil side
(13)
d 2Rc
0:5 (14)
Hence, in the second mode, shell side and coil side water flow rate were proportional changed in order to get the same shell side Reynolds number (around 3300) and the same coil side Dean number (around 3000) for all coiled tubes. Obviously different values of shell and coil side water flow rate are required for each coiled tube. Fig. 6 shows the effect of coil pitch and coil diameter on exergy loss and dimensionless exergy loss for the second mode. As seen in Fig. 6, the results are different from the results in Fig. 5 especially for dimensionless exergy loss. Both exergy loss (E) and dimensionless exergy loss increase with the increase of coil pitch. Exergy loss (E) increases with the increase coil diameter. But dimensionless exergy loss (e) decreases with the increase of coil diameter. This phenomenon is explained as follows. First of all, it is noted that, denominator of Eq. (10) was the same for both coiled tubes in the first mode, but it has different value for each coiled tube in this mode. Indeed, in order to get the same Dean number for two coiled tubes with different coil diameters, different values of coil side water flow rate is required. The required coil side water flow rate (Recoil side) for coiled tube with 2Rc ¼ 0.11 m is more than the required flow rate for coiled tube with 2Rc ¼ 0.07 m to get the same Dean number (see Eq. (14)). Hence both numerator and denominator of Eq. (10) increase with the increase of coil diameter. In other words, dimensionless exergy loss (e) for this mode increases with the increase of exergy loss (E) and decreases with the increase of coil side water flow rate (Cmin). Therefore a competition between numerator (E) and denominator (Cmin) of Eq. (10) is created. In this case, the enhancement of Cmin (denominator) due to increment of coil diameter is more than the enhancement of E (numerator). So, dimensionless exergy loss decreases with the increase of coil diameter which is in agreement by the represented results in Fig. 6(b). It can be concluded that, Cmin has a significant effect on the curve behavior of dimensionless exergy loss.
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H. Sadighi Dizaji et al. / Energy 91 (2015) 678e684
Fig. 6. The effects of coil pitch and coil diameter on a) exergy loss b) dimensionless exergy loss. Shell side Re and coil side De are constant.
4. Conclusion This paper experimentally investigates the effect of flow, thermodynamic and geometric parameters on exergetic characteristics in shell and coiled tube heat exchangers. The key findings from the experimental study are described as below. Exergy loss increases with the increase of shell or coil side flow rate. Dimensionless exergy loss can increase or decrease with the increase of flow rates. It depends on Cmin. Both of the exergy loss and dimensionless exergy loss increase with the increase of coil side inlet temperature and decrease of shell side inlet temperature. The effect of coiled tube geometry on exergy loss was investigated in two modes. In first mode, flow rates and inlet temperatures were kept constant, and in the second mode Re and De were kept constant instead of flow rates. Indeed, in the second mode, dimensionless exergy loss (e) depends on both of the exergy loss (E) and Cmin, but in the first mode Cmin are constant for all cases. Exergy loss and dimensionless exergy loss increase with the increase of coil pitch and coil diameter in first mode. But in second mode, a competition between E and Cmin is created and the enhancement of dimensionless exergy loss due to coil diameter is minor in comparison with first mode. References [1] Holman GPW. Heat transfer. 6th ed. McGraw-Hill; 1986. n B. Pressure drop and convective heat transfer of water [2] Wu Z, Wang W, Sunde and nanofluids in a double-pipe helical heat exchanger. Appl Therm Eng 2013;60:266e74. [3] Ko TH. Thermodynamic analysis of optimal curvature ratio for fully developed laminar forced convection in a helical coiled tube with uniform heat flux. Int J Therm Sci 2006;45:729e37.
[4] Salimpour MR. Heat transfer characteristics of a temperature-dependentproperty fluid in shell and coiled tube heat exchangers. Exp Therm Fluid Sci 2008;35:1190e5. [5] Salimpour MR. Heat transfer coefficients of shell and coiled tube heat exchangers. Exp Therm Fluid Sci 2008;33:203e7. [6] Kumar V, Faizee B, Mridha M, Nigam KDP. Numerical studies of a tube-in-tube helically coiled heat exchanger. Chem Eng Proc 2008;47:2287e95. [7] Ghorbani N, Taherian H, Gorji M, Mirgolbabaei H. Experimental study of mixed convection heat transfer in vertical helically coiled tube heat exchangers. Exp Therm Fluid Sci 2010;34:900e5. [8] Pandey SD, Nema VK. An experimental investigation of exergy loss reduction in corrugated plate heat exchanger. Energy 2011;36:2997e3001. [9] Naphon P. Study on the exergy loss of the horizontal concentric micro-fin tube heat exchanger. Int Comm Heat Mass Transf 2011;38:229e35. [10] Zachar A. Investigation of natural convection induced outer side heat transfer rate of coiled-tube heat exchangers. Int J Heat Mass Transf 2012;55: 7892e901. [11] Hashemi SM, Akhavan-Behabadi MA. An empirical study on heat transfer and pressure drop characteristics of CuOebase oil nanofluid flow in a horizontal helically coiled tube under constant heat flux. Int J Heat Mass Transf 2012;39: 144e51. [12] Mohammed HA, Narrein K. Thermal and hydraulic characteristics of nanofluid flow in a helically coiled tube heat exchanger. Int Com Heat Mass 2012;39: 1375e83. [13] Jamshidi N, Farhadi M, Ganji DD, Sedighi K. Experimental analysis of heat transfer enhancement in shell and helical tube heat exchangers. Appl Therm Eng 2013;51:644e52. [14] Pan M, Jamaliniya S, Smith R, Bulatov I, Gough M, Higley T, et al. New insights to implement heat transfer intensification for shell and tube heat exchangers. Energy 2013;57:208e21. [15] Kumar PCM, Kumar J, Tamilarasan R, Nathan SS, Suresh S. Heat transfer enhancement and pressure drop analysis in a helically coiled tube using Al2O3/water nanofluid. J Mech Sci Tech 2014;28:1841e7. [16] Kline SJ, McClintock FA. Describing uncertainties in single-sample experiments. Mech Eng 1953:3e8. [17] Akpinar EK, Bicer Y. Investigation of heat transfer and exergy loss in a concentric double pipe exchanger equipped with swirl generator. Int J Therm Sci 2005;44:598e608. [18] Akpinar EK. Evaluation of heat transfer and exergy loss in a concentric double pipe exchanger equipped with helical wires. Energy Conver Manag 2006;47: 3473e86. [19] Saeedinia M, Akhavan-Behabadi MA, Nasr M. Experimental study on heat transfer and pressure drop of nanofluid flow in a horizontal coiled wire inserted tube under constant heat flux. Exp Therm Fluid Sci 2012;36:158e68.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
The effect of flow, thermodynamic and geometrical characteristics on exergy loss in shell and coiled tube heat exchangers Hamed Sadighi Dizaji, Samad Jafarmadar*, Mehran Hashemian Faculty of Mechanical Engineering, Urmia University, Urmia, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 April 2015 Received in revised form 21 August 2015 Accepted 26 August 2015 Available online xxx
This work presents experimental investigations on the effects of flow, thermodynamic and geometrical characteristics on exergy loss in shell and coiled tubes heat exchangers. Pressure drop and heat transfer characteristics in shell and coiled tube heat exchangers have been widely studied in the resent years. However, the effects of flow, thermodynamic and geometrical parameters on exergetic characteristics have not been explicitly and experimentally studied. Hence, the main scope of the present work is to clarify the effect of shell and coil side flow rates, inlet temperatures, coil pitch and coil diameter on exergy loss in shell and coiled tube heat exchangers. Both of the total exergy loss and dimensionless exergy loss are studied. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Shell and coiled tube heat exchanger Exergy loss Fluid properties Thermodynamic characteristics Geometry
1. Introduction Irreversibility and availability are two concepts that have found increasing use in recent years. These concepts are particularly applicable in the analysis of complex thermodynamic systems. Irreversibility and availability are very powerful tools in design and optimization studies of such systems [1]. Helically coiled tubes have wide applications in the industry because of their high heat transfer coefficients, low volume and size, narrow residence time distributions and simple manufacture method etc. Hence, knowledge about the heat transfer, pressure drop and exergetic characteristics in helically coiled tubes are very significant. Thermal and frictional characteristics of helically coiled tubes were extensively investigated in the past years. However, exergetic characteristics have not been explicitly and experimentally studied for shell and coiled tube heat exchangers. Hence, the main scope of the present work is to clarify the effect of flow, thermodynamic and geometrical parameters on exergy loss in shell and coiled tube heat exchangers. The flow moved through a helically coiled tube is affected by centrifugal forces. Centrifugal forces create secondary flows, and
* Corresponding author. E-mail addresses: [email protected] (H. Sadighi Dizaji), S. [email protected] (S. Jafarmadar), [email protected] (M. Hashemian). http://dx.doi.org/10.1016/j.energy.2015.08.084 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
they induce significant eddies in a cross-section of the coiled tube. Indeed, as described in Wu et al. [2] study, centrifugal forces drive the fluid flow toward the outer wall and then returns by flowing back along the wall. Centrifugal forces, secondary flows and eddies can enhance the exergy loss in helically coiled tubes. Investigations on shell and coiled tube heat exchangers as well as exergetic parameters are summarized as follows. Ko [3] offered optimal coil curvature ratio in a helical coiled tube with different combination of design parameters. The System analyzed by thermodynamic second low was based on minimal entropy generation principle for fully developed laminar flow and constant wall heat flux. Salimpour [4,5] experimentally studied the heat transfer characteristics of shell and coiled tube heat exchanger and proposed some correlations to predict the shell-side and tubeside Nusselt number. Kumar et al. [6] investigated on heat transfer and pressure drop of tube-in-tube helically coiled heat exchanger. Keε model was used to evaluate the turbulent flow. Ghorbani et al. [7] evaluated the effects of coil pitch and tube diameters on shellside heat transfer coefficient of a shell and coiled tube heat exchanger. Their findings showed that, the effect of tube diameter on shell-side heat transfer coefficient is negligible. Besides, their results indicated that the shell side heat transfer coefficient increases with the increase of coil pitch. Pandey and Nema [8] conducted experimental research on exergy loss in corrugated plate heat exchanger with different types of plate. Naphon [9] investigated on entropy generation and exergy loss in a concentric micror [10] analyzed the heat transfer rate fin tube heat exchanger. Zacha
H. Sadighi Dizaji et al. / Energy 91 (2015) 678e684
Nomenclature A c d D Dh De Dh e E k ṁ Max Min NTU p Pr q Q Rc
coiled tube area, m2 specific heat, J/kg C coiled tube diameter, m shell diameter, m shell side hydraulic diameter, m d )0.5 Dean number, Re(2R c 2 D 2pR d2 p1 hydraulic diameter, Dþ2pR cd op1 c o dimensionless exergy loss exergy loss (exergy change), W thermal conductivity, W/m C mass flow rate, kg/s Maximum minimum number of thermal units coil pitch, m Prandtl number, mC k heat transfer rate, W flow rate, LPM coil radius, m
in the outer side of the coiled tube in several cases with different combination of geometrical and flow parameters. Hashemi [11] used CuO-oil based nanofluid flow inside the helically coiled tube with constant wall heat flux. Experimental investigations showed that, using of coiled tube instead of straight tube causes heat transfer enhancement as well as more pressure drop. Besides, analogy of two heat transfer enhancement method showed that the employment of helically coiled tube instead of straight tube preferred to the adding additives to the base fluid. Mohammed and Narrein [12] numerically investigated the effects of using different geometrical parameters with the combination of nanofluid on heat transfer and fluid flow characteristics in a helically coiled tube heat exchanger. It was found that the heat transfer rate can be increased by reducing the helix radius, increasing the inner tube diameter and decreasing the annulus diameter. Jamshidi [13] experimentally concluded that the increasing coil diameter, coil pitch and fluid flow rate leads to higher heat transfer rate in shell and coiled tube heat exchangers. Pan et al. [14] performed a comprehensive study of thermal and hydraulic performances of shell and tube exchangers, and presented the detailed thermal and hydraulic calculations on the shell and tube heat exchangers with implementing conventional intensification techniques. According to the Kumar et al. [15] study the use of nanofluid in coiled tubes creates stronger secondary flow through the tube. The second flows properly mix nano-particles and also avoid particles concentrations which lead to higher heat transfer rate and also more pressure drop. According to the literature review no experimental investigation has been performed to study the effect of flow, thermodynamic and geometrical parameters on exergy loss in shell and helically coiled heat exchangers. In the present work, the effect of shell and coil side flow rates, hot and cold water inlet temperatures, coil diameter and coil pitch on exergy loss experimentally evaluated for the shell and coiled tube heat exchanger. 2. Experiments 2.1. Experimental apparatus and tubes geometry A general view of the experimental set-up is shown in Fig. 1. An electrical heater (inside the hot water tank), rheostat and a
Re s T U V W X
679
Reynolds number, VD y specific entropy, J/kg. K temperature, K overall heat transfer coefficient, (W/m2C) water mean velocity, m/s total uncertainty in the measurement independent variable
Greece symbols n kinematic viscosity, m2/s p g dimensionless pitch, 2pR c Subscripts c cold fluid e environment condition h hot fluid i inner o outer in inlet out outlet
thermostat maintain the hot water inlet temperature at around a constant value. The heated water is pumped from the hot water tank, and then it passes the control valve, goes into a Rota-meter, enters the helically coiled tube and finally it returns into the hot water tank. A cooling unit maintains the cold water inlet temperature at around a constant value. The cooling unit consists of an evaporator (inside the cold water tank), compressor, condenser, refrigerant, expansion valve, thermostat and a fan (the fan is used when lower temperatures are needed). The cooled water is pumped from the cold water tank and then it passes the control valve, goes into a rotameter, enters the shell side of heat exchanger, and finally it returns into the cold water tank. The hot and cold water inlet and outlet temperatures were recorded at fully steady state condition using EXTECH data logger (SDL200) with K type thermocouples (accuracy ±0.5 C and resolution 0.1 C). Besides, all Rota-meters were calibrated for hot and cold water by using a stopwatch and measuring cylinders. As seen in Fig. 1(c) the test section (which presents a new simple method to make a shell and coiled tube heat exchanger for research applications) consists of a shell tube, a coiled tube, two insulated grooved end plates and four screwed steel rods. The shell of heat exchanger was placed between the end-plates and screwed steel rods were used to hold and adjust the position of the end-plates. The coiled tube was constructed by copper material with 9 mm inner diameter and 12 mm outer diameter and the outer tube (shell) was made from PVC. Helical tubes in this study have 12 turns. A schematic illustration of the coiled tube is shown in Fig. 2. 2.2. Experiments procedure Different conditions considered in this study are presented in Table 1. In first step, geometrical and thermodynamic parameters (inlet temperatures) were kept constant and the effects of shell and coil side flow rates were investigated. For this purpose, each shell side flow rate (3, 4, 5, 6 and 7 LPM) was experimented with five different coil side flow rates (3, 3.5, 4, 4.5 and 5 LPM). It is noted that, used water pumps can't supply more than around 6 LPM to coil side of test section because of the high pressure drop through the coiled tube compared to straight tube. All selected amounts for other parameters such as temperatures are proportional with the
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Fig. 1. (a) Experimental setup and (b) a schematic illustration of the test set-up: 1-test section, 2-Rotameter, 3-warm water tank, 4-dimmer and thermostat and heater, 5-water pump, 6-condenser, 7-compressor, 8-cold water tank, 9-evaporator, 10- coiled tube and (c) a schematic illustration of test section.
used related devices. In the second step, shell and coil side flow rates were fixed at around 3 LPM and the effects of hot and cold water inlet temperatures were studied. Each shell side (cold water) inlet temperature (around 8, 18 and 25 C) was tested with three
various coil side inlet temperature (around 40, 60 and 80 C). Finally, both of the flow and thermodynamic parameters were fixed and the effect of coil pitch and coil diameter on exergy loss were investigated. 2-cm layer of the glass wool insulation were used to prevent heat loss to surrounding from the outer tube (shell). During the experiments, inlets and outlets bulk temperatures were measured at steady state condition. 2.3. Uncertainty of measurements
Fig. 2. A schematic illustration of the coiled tube.
Measurement uncertainties can be due to the measuring instrument, environment condition, operator and other sources. In this experiment, the uncertainty of experimental data results was evaluated by Kline [16] method. The uncertainties in calculating a
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Eh and Ec are the exergy change for hot fluid and cold fluid respectively, and are calculated as follows:
Table 1 Various test conditions (variable parameters are bold in each row). Qc LPM
Qh LPM
De (coil)
Th,in C
Tc,in C
Pr
P (mm)
Rc (mm)
8 8 8 8 8
e e e e e
12 12 12 12 12
55 55 55 55 55
The effect of shell and coil side flow rate 3 4 5 6 7
3e5 3e5 3e5 3e5 3e5
2600e4800 2600e4800 2600e4800 2600e4800 2600e4800
40 40 40 40 40
e e e
3 3 3
40e80 40e80 40e80
8 18 25
e e
5 5
40 40
8 8
2e10 2e10 2e10
12 12 12
55 55 55
vRþ WRþ ¼ @ w vX1 1
!2 þ
vRþ w vX2 2
e e
12e24 12e24
55 35
!2 þ…þ
_ c ðsc out sc in Þg Ec ¼ Te fm
(5)
vRþ wn vXn
T out Tin
(6)
Substituting Eq. (6) into Eq. (4), Eq. (5) and Eq. (3) yields:
result (Wþ R ) due to some independent variables are evaluated by following equation:
0
(4)
sout sin ¼ cpc ln
The effect of geometrical parameters 3 3
_ h ðsh out sh in Þg Eh ¼ Te fm
For liquids it can be assumed that the specific heat is constant and the entropy change can be calculated as below.
The effect of shell and coil side inlet temperatures 3 3 3
681
!2 112 A
T _ h cph ln ho Eh ¼ Te m Thi
(7)
T _ c cpc ln co Ec ¼ Te m Tci
(8)
T T _ h cph ln ho þ m _ c cpc ln co E ¼ Te m Thi Tci
(9)
Dimensionless exergy loss (x) can be calculated from Eq. (10) [17,18].
(1) Uncertainty results details are summarized in Table 2.
e¼
E Te Cmin
Cmin ¼ Min {Ch ¼ ṁhcph and Cc ¼ ṁccpc}
(10)
(11)
2.4. Exergy loss calculation method Exergy is defined as the maximum useful work that can be achieved from the reversible system in a specified environment. For heat exchangers which do not involve shaft work, the exergy given out by one flow is compared with the exergy gained with the other flow. Exergy loss (E) can be calculated as described below. For a given steady control volume, exergy balance can be expressed as:
X
Ein ¼
X
Eout
X
Eproduct
(2)
In present study, heat exchanger is adiabatic and it can be assumed that the amount of qh is equal with the amount qc. Exergy loss in a steady control volume with two different types of working fluids can be written as follows: E ¼ Eh þ Ec
(3)
Table 2 Maximum uncertainty of parameters. Parameter
Unit
Uncertainty in the temperature measurement
Hot fluid inlet temperature Hot fluid outlet temperature Cold fluid inlet temperature Cold fluid outlet temperature
Comment
C
C C C C
±0.5 ±0.5 ±0.5 ±0.5
(1.2%) (1.2%) (6%) (6%)
Uncertainty in the measurement of volume flow rate
LPM
Water (shell side) Water (coil side)
LPM LPM
Uncertainties in calculating a result
%
Exergy loss
%
±9.23
Uncertainty in reading values of table (r,k, …)
%
±0.1e0.2
±0.5 (16%) ±0.5 (16%)
3. Results and discussions 3.1. The effect of hot and cold water flow rate on exergy loss Fig. 3(a) presents exergy loss (E) versus the Dean number. According to the Table 1 the coil diameter and coil pitches are 110 mm and 12 mm respectively. Also, hot and cold water inlet temperatures were kept constant at around 40 C and 8 C respectively. Exergy loss (E) increases with the increase of shell or coil side flow rate. The slope of exergy loss augmentation due to Dean number enhancement is severe for higher amounts of shell side flow rate. Maximum and minimum exergy loss enhancement occurs at shell side flow rate of 7 LPM and 3 LPM respectively. Also, it can be said that when the shell side flow rate is more than the coil side flow rate, the effect of the amount of coil side flow rate on exergy loss is greater. For example, at shell side flow rate of 6 LPM or 7 LPM, which are more than the coil side flow rates for all points (coil side flow rate changes from 3 LPM to 5 LPM) coil side flow rate has a significant effect on exergy loss. But at shell side flow rate of 3 LPM which is less than the coil side flow rates (3, 3.5, 4, 4.5, 5 LPM), the effect of Dean number on exergy loss is minor. The relationship between dimensionless exergy loss (e) calculated from Eq. (10) and Dean number is shown in Fig. 3(b). Curves behavior in dimensionless exergy loss (e) depends on both of the exergy loss (E) and Cmin (see Eq. (11)). For shell side flow rate of 5, 6 and 5 LPM, Cmin is evaluated using of the coil side mass flow rate. For these cases, as exergy loss (E) increases, Cmin increases too, but the ratio of E to the Cmin which is indicative of dimensionless exergy loss (e) decreases. It means that, the enhancement of Cmin is more than the enhancement of exergy loss (E). For shell side flow rate of 3 LPM and three last points of 4 LPM the theorem are different. For
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Fig. 3. The effect of shell and coil flow rates on a) exergy loss b) dimensionless exergy loss.
these cases, Cmin is evaluated using of the shell side flow rate which has less amount of mass flow rate in comparison with the coil side flow rate, and despite that the exergy loss (E) increases with the increase of Dean number but the amount of Cmin is constant. To this reason, dimensionless exergy loss (e) decreases with the increase of Dean number for these cases. Indeed, as seen in Fig. 3(b) dimensionless exergy loss can be increased or decreased with the increase of Dean number, it depends on Cmin in Eq. (10). Hence, it isn't possible to present an explicitecomprehensive correlation for dimensionless exergy loss as a function of flow rates. However, ever any changes in coil or shell side flow rate influence significantly on dimensionless exergy loss. 3.2. The effect of hot and cold water inlet temperatures on exergy loss
hot and cold water inlet temperatures. Experimental results indicate that as hot water (coil side) inlet temperature increases both of the exergy loss and dimensionless exergy loss increases. Moreover, results show that the exergy loss (E and e) decreases with the increase of cold water (shell side) inlet temperature. By increasing the hot water inlet temperature, the difference between hot and cold water inlet temperature (DTin ¼ Th,in Tc,in) increases, but by increasing the cold water inlet temperature, difference between hot and cold water inlet temperature decreases. Hence, it can be concluded that, the exergy loss increases with the increase of DTin, which can be due to the hot water inlet temperature enhancement or cold water inlet temperature decrement. Indeed, the enhancement of DTin causes more heat transfer rate between the cold water (coil side) and hot water (shell side). Hence, the exergy loss due to heat transfer irreversibility increases.
c m
Prandtl number ( pk ) is a potential indicator of specific heat, thermal conductivity and viscosity as the main thermodynamic characteristics of the working fluid. Hence, hot and cold water inlet temperatures are varied in order to get different amounts of water Prandtl number; and the effects of water inlets temperatures on exergy loss are evaluated. Other parameters (coil side and shell side flow rate, coil pitch and coil diameter) are fixed in the constant values in this section as presented in Table 1. Fig. 4(a) and Fig. 4(b) show the variation of exergy loss and dimensionless exergy loss by
3.3. The effect of coil pitch and coil diameter on exergy loss 3.3.1. First mode (shell side and coil side flow rates are fixed) In this section, flow rates and inlet temperatures are fixed and the effect of coil pitch and coil diameter on exergy loss are studies. The desired coil diameters are 0.11 m and 0.07 m which each of them is investigated with three different pitches (12 mm, 18 mm and 24 mm). Both shell side and coil side flow rates were kept
Fig. 4. The effect of hot and cold water inlet temperatures on a) exergy loss b) dimensionless exergy loss.
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683
Fig. 5. The effects of coil pitch and coil diameter on a) exergy loss b) dimensionless exergy loss. Shell and coil side flow rates are constant.
constant at 3LPM. Hot water inlet temperature is 40 C and cold water inlet temperature is around 8 C for all cases in this section. The relationship between exergy loss and coil pitch is shown in Fig. 5 for first mode. According to Fig. 5(a), as coil pitch or coil diameter increases, exergy loss (E) increases. Exergy loss enhancement due to the increase of coil pitch or coil diameter can be described as follow. At higher amounts of coil pitch, more and better contact occurs between the shell side water flow and the coiled tube, and the result is more heat transfer rate through the heat exchanger [12]. Besides, in a fixed coil turns (coil turns in this study is 12), the length of coiled tube with higher coil diameter is more than the coiled tube with less coil diameter. Hence, the residence time of hot water in heat exchanger increases, and the cold fluid can earn more heat transfer from the hot water in the coiled tube. As mentioned before, more heat transfer rate causes more exergy loss through the heat exchanger. Hence the exergy loss due to heat transfer irreversibility increases by increasing the coil pitch or coil diameter which is in agreement by the represented results in Fig. 5(a). As seen in Fig. 5 the trend curve of exergy loss (E) and dimensionless exergy loss (e) are similar in this mode. Because the denominator of Eq. (10) is constant for this mode (flow rates are fixed) and obviously dimensionless exergy loss (calculated with Eq. (10)) increases as exergy loss (E) increases. Hence, dimensionless exergy loss (e) increases with the increase of coil pitch or coil diameter because of the same reasons which were described above for exergy loss (E). 3.3.2. Second mode (shell side Re and coil side De are constant) It should be noted that each coiled tube creates different shell side hydraulic diameter because of their different geometrical characteristics (see Eq. (12)). Therefore, a defined shell side water flow rate (for example 3LPM) creates different and exclusive shell side Reynolds number for each case (see Eq. (13)). It is noted that, in present paper, shell side hydraulic diameter is calculated from Eq. (12) used by Saeedinia et al. [19]. However, Salimpour et al. [5] employed another form of Eq. (12) that is dimensionally inhomogeneous (the units of the two terms in the numerator do not match). According to Eq. (14), a defined coil side water flow rate creates different and exclusive coil side Dean number for each coil diameter as well.
Dh ¼
D2 2pRc d2o p1 D þ 2pRc do p1
(12)
Reshell side ¼
V Dh y
De ¼ Recoil side
(13)
d 2Rc
0:5 (14)
Hence, in the second mode, shell side and coil side water flow rate were proportional changed in order to get the same shell side Reynolds number (around 3300) and the same coil side Dean number (around 3000) for all coiled tubes. Obviously different values of shell and coil side water flow rate are required for each coiled tube. Fig. 6 shows the effect of coil pitch and coil diameter on exergy loss and dimensionless exergy loss for the second mode. As seen in Fig. 6, the results are different from the results in Fig. 5 especially for dimensionless exergy loss. Both exergy loss (E) and dimensionless exergy loss increase with the increase of coil pitch. Exergy loss (E) increases with the increase coil diameter. But dimensionless exergy loss (e) decreases with the increase of coil diameter. This phenomenon is explained as follows. First of all, it is noted that, denominator of Eq. (10) was the same for both coiled tubes in the first mode, but it has different value for each coiled tube in this mode. Indeed, in order to get the same Dean number for two coiled tubes with different coil diameters, different values of coil side water flow rate is required. The required coil side water flow rate (Recoil side) for coiled tube with 2Rc ¼ 0.11 m is more than the required flow rate for coiled tube with 2Rc ¼ 0.07 m to get the same Dean number (see Eq. (14)). Hence both numerator and denominator of Eq. (10) increase with the increase of coil diameter. In other words, dimensionless exergy loss (e) for this mode increases with the increase of exergy loss (E) and decreases with the increase of coil side water flow rate (Cmin). Therefore a competition between numerator (E) and denominator (Cmin) of Eq. (10) is created. In this case, the enhancement of Cmin (denominator) due to increment of coil diameter is more than the enhancement of E (numerator). So, dimensionless exergy loss decreases with the increase of coil diameter which is in agreement by the represented results in Fig. 6(b). It can be concluded that, Cmin has a significant effect on the curve behavior of dimensionless exergy loss.
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Fig. 6. The effects of coil pitch and coil diameter on a) exergy loss b) dimensionless exergy loss. Shell side Re and coil side De are constant.
4. Conclusion This paper experimentally investigates the effect of flow, thermodynamic and geometric parameters on exergetic characteristics in shell and coiled tube heat exchangers. The key findings from the experimental study are described as below. Exergy loss increases with the increase of shell or coil side flow rate. Dimensionless exergy loss can increase or decrease with the increase of flow rates. It depends on Cmin. Both of the exergy loss and dimensionless exergy loss increase with the increase of coil side inlet temperature and decrease of shell side inlet temperature. The effect of coiled tube geometry on exergy loss was investigated in two modes. In first mode, flow rates and inlet temperatures were kept constant, and in the second mode Re and De were kept constant instead of flow rates. Indeed, in the second mode, dimensionless exergy loss (e) depends on both of the exergy loss (E) and Cmin, but in the first mode Cmin are constant for all cases. Exergy loss and dimensionless exergy loss increase with the increase of coil pitch and coil diameter in first mode. But in second mode, a competition between E and Cmin is created and the enhancement of dimensionless exergy loss due to coil diameter is minor in comparison with first mode. References [1] Holman GPW. Heat transfer. 6th ed. McGraw-Hill; 1986. n B. Pressure drop and convective heat transfer of water [2] Wu Z, Wang W, Sunde and nanofluids in a double-pipe helical heat exchanger. Appl Therm Eng 2013;60:266e74. [3] Ko TH. Thermodynamic analysis of optimal curvature ratio for fully developed laminar forced convection in a helical coiled tube with uniform heat flux. Int J Therm Sci 2006;45:729e37.
[4] Salimpour MR. Heat transfer characteristics of a temperature-dependentproperty fluid in shell and coiled tube heat exchangers. Exp Therm Fluid Sci 2008;35:1190e5. [5] Salimpour MR. Heat transfer coefficients of shell and coiled tube heat exchangers. Exp Therm Fluid Sci 2008;33:203e7. [6] Kumar V, Faizee B, Mridha M, Nigam KDP. Numerical studies of a tube-in-tube helically coiled heat exchanger. Chem Eng Proc 2008;47:2287e95. [7] Ghorbani N, Taherian H, Gorji M, Mirgolbabaei H. Experimental study of mixed convection heat transfer in vertical helically coiled tube heat exchangers. Exp Therm Fluid Sci 2010;34:900e5. [8] Pandey SD, Nema VK. An experimental investigation of exergy loss reduction in corrugated plate heat exchanger. Energy 2011;36:2997e3001. [9] Naphon P. Study on the exergy loss of the horizontal concentric micro-fin tube heat exchanger. Int Comm Heat Mass Transf 2011;38:229e35. [10] Zachar A. Investigation of natural convection induced outer side heat transfer rate of coiled-tube heat exchangers. Int J Heat Mass Transf 2012;55: 7892e901. [11] Hashemi SM, Akhavan-Behabadi MA. An empirical study on heat transfer and pressure drop characteristics of CuOebase oil nanofluid flow in a horizontal helically coiled tube under constant heat flux. Int J Heat Mass Transf 2012;39: 144e51. [12] Mohammed HA, Narrein K. Thermal and hydraulic characteristics of nanofluid flow in a helically coiled tube heat exchanger. Int Com Heat Mass 2012;39: 1375e83. [13] Jamshidi N, Farhadi M, Ganji DD, Sedighi K. Experimental analysis of heat transfer enhancement in shell and helical tube heat exchangers. Appl Therm Eng 2013;51:644e52. [14] Pan M, Jamaliniya S, Smith R, Bulatov I, Gough M, Higley T, et al. New insights to implement heat transfer intensification for shell and tube heat exchangers. Energy 2013;57:208e21. [15] Kumar PCM, Kumar J, Tamilarasan R, Nathan SS, Suresh S. Heat transfer enhancement and pressure drop analysis in a helically coiled tube using Al2O3/water nanofluid. J Mech Sci Tech 2014;28:1841e7. [16] Kline SJ, McClintock FA. Describing uncertainties in single-sample experiments. Mech Eng 1953:3e8. [17] Akpinar EK, Bicer Y. Investigation of heat transfer and exergy loss in a concentric double pipe exchanger equipped with swirl generator. Int J Therm Sci 2005;44:598e608. [18] Akpinar EK. Evaluation of heat transfer and exergy loss in a concentric double pipe exchanger equipped with helical wires. Energy Conver Manag 2006;47: 3473e86. [19] Saeedinia M, Akhavan-Behabadi MA, Nasr M. Experimental study on heat transfer and pressure drop of nanofluid flow in a horizontal coiled wire inserted tube under constant heat flux. Exp Therm Fluid Sci 2012;36:158e68.