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Columbia International Publishing American Journal of Heat and Mass Transfer (2016) Vol. 3 No. 5 pp. 352-381 doi:10.7726/ajhmt.2016.1020 Review ______________________________________________________________________________________________________________________________ *Corresponding e-mail: [email protected] 1 Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Khuzestan, Islamic Republic of Iran. 352 A Comprehensive Review on the Nanofluids Application in the Tubular Heat Exchangers Maysam Molana 1* Received: 30 August 2016; Published online: 1 October 2016 © Columbia International Publishing 2016. Published at www.uscip.us Abstract This paper focuses on the nanofluids implementation in the tubular heat exchangers namely, shell and tube, double pipe and coiled tube. The author thinks that a comprehensive review of performed studies in this area can demonstrate advantages and disadvantages of nanofluids application in the heat exchangers. All available papers are reflected in this paper including experimental and numerical studies with all of their important features and findings. The most considered paper confirmed the Nusselt number enhancement with the use of nanofluids in the heat exchangers. Also, nanofluids implementation in the heat exchangers resulted in an increase in the required pumping power, in the most cases. Keywords: Nanofluids; Tubular heat exchangers; Nusselt number; Reynolds number 1. Introduction The heat exchanger is critical process equipment playing a vital role in all industries, approximately. Their main purpose of the heat exchanger using is to exchange heat between two or more fluids at different temperatures. This facilitates cooling and heating easily. Also, their applications are so wide in industry, such as power production (Vidhi et al., 2014; Hsieh et al., 2014), chemical and food processes (Rainieri et al., 2014; D’Addio et al., 2012 ), electronics (Zhu et al., 2013; Lee and Cho, 2002), waste heat recovery (Rohde et al., 2013; Hatami et al., 2015), refrigeration (Nakagawa et al., 2011; Kang et al., 2007), air conditioning (Nasif and Al-Waked, 2014; Siegel and Nazaroff, 2003) and space applications (Sivasakthivel et al., 2014; Hamada et al., 2007). About 26% of the industrial energy is wasted in the form of hot gas or fluid energy is emitting heat in the environment which is the major reason for global warming (Shahrul et al., 2014, Teke et al., 2010). Hence, implementation of heat exchangers to recover this energy is necessary.

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Page 1: A Comprehensive Review on the Nanofluids Application in ...paper.uscip.us/ajhmt/ajhmt.2016.1020.pdf · basis for any capacity and operating conditions. This is contrary to many other

Columbia International Publishing American Journal of Heat and Mass Transfer (2016) Vol. 3 No. 5 pp. 352-381 doi:10.7726/ajhmt.2016.1020

Review

______________________________________________________________________________________________________________________________ *Corresponding e-mail: [email protected] 1 Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz,

Khuzestan, Islamic Republic of Iran.

352

A Comprehensive Review on the Nanofluids Application in the Tubular Heat Exchangers

Maysam Molana1*

Received: 30 August 2016; Published online: 1 October 2016 © Columbia International Publishing 2016. Published at www.uscip.us

Abstract This paper focuses on the nanofluids implementation in the tubular heat exchangers namely, shell and tube, double pipe and coiled tube. The author thinks that a comprehensive review of performed studies in this area can demonstrate advantages and disadvantages of nanofluids application in the heat exchangers. All available papers are reflected in this paper including experimental and numerical studies with all of their important features and findings. The most considered paper confirmed the Nusselt number enhancement with the use of nanofluids in the heat exchangers. Also, nanofluids implementation in the heat exchangers resulted in an increase in the required pumping power, in the most cases. Keywords: Nanofluids; Tubular heat exchangers; Nusselt number; Reynolds number

1. Introduction The heat exchanger is critical process equipment playing a vital role in all industries, approximately. Their main purpose of the heat exchanger using is to exchange heat between two or more fluids at different temperatures. This facilitates cooling and heating easily. Also, their applications are so wide in industry, such as power production (Vidhi et al., 2014; Hsieh et al., 2014), chemical and food processes (Rainieri et al., 2014; D’Addio et al., 2012 ), electronics (Zhu et al., 2013; Lee and Cho, 2002), waste heat recovery (Rohde et al., 2013; Hatami et al., 2015), refrigeration (Nakagawa et al., 2011; Kang et al., 2007), air conditioning (Nasif and Al-Waked, 2014; Siegel and Nazaroff, 2003) and space applications (Sivasakthivel et al., 2014; Hamada et al., 2007). About 26% of the industrial energy is wasted in the form of hot gas or fluid energy is emitting heat in the environment which is the major reason for global warming (Shahrul et al., 2014, Teke et al., 2010). Hence, implementation of heat exchangers to recover this energy is necessary.

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Kakac and Liu (2002) explained heat exchanger types and applications in their noteworthy book: Heat exchangers may be classified according to the following main criteria:

1- Recuperators / regenerators 2- Transfer processes: direct contact and indirect contact 3- Geometry of construction: tubes, plates, and extended surfaces 4- Heat transfer mechanisms: single-phase and two-phase 5- Flow arrangements: parallel, counter and cross flows.

The main goal of this study is the investigation of nanofluids application in tubular heat exchangers (shell and tube, double pipe and coil tube). All available papers are reflected in this paper including experimental and numerical studies. The author thinks that a comprehensive review of performed studies in this area can demonstrate advantages and disadvantages of using nanofluids in heat exchangers. Nanofluids (nanoparticles suspended in a base fluid) have attracted a wide attention of researchers all around the world. The higher thermal properties of nanofluids are so promising to use as a heat transfer fluid. It is likely that these modern fluids can improve the heat transfer characteristics and be implemented instead of the poor heat transfer fluids. There are numerous studies in this area (Jand and Choi, 2006; Salavati et al., 2015; Tso and Chao, 2015; Li et al., 2015; Lou and Yang, 2015). Also, Wang and Mujumdar (2008a; 2008b) have reviewed all physical properties of nanofluids, comprehensively.

2. Shell and Tube Heat Exchangers Shell and tube heat exchangers are most used exchanger in all over the world. Their applications varied from HVAC systems (Kakac and Liu, 2002), automotive (T’Joen et al., 2009), process application (Nieh et al., 2014), power plants and oil and gas industries [19-23] (Zilio and Mancin, 2015; Llopis et al., 2008; Anisur et al., 2014; Zeng et al., 2012; Zhang et al., 2013), refrigeration systems (Sarkar, 2011) and so on. The main components of a shell and tube heat exchanger are (Fig. 1):

Shell Front head Rear head Tubes; Tube sheet; Baffles; and Nozzles

Other components include tie-rods and spacers; pass partition plates, impingement plate, longitudinal baffle, sealing strips, supports, and foundation.

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Fig. 1. A schematic of a shell and tube heat exchanger

A number of shell side and tube side arrangements are used in shell and tube heat exchangers depending on heat duty, pressure drop, pressure level, fouling, manufacturing techniques, cost, corrosion control, and cleaning problems. Shell and tube heat exchangers are designed on a custom basis for any capacity and operating conditions. This is contrary to many other types of heat exchangers (Kakac and Liu, 2002).

Walvekar et al. (2015) studied the heat transfer performance of nanofluids turbulent flow in a shell and tube heat exchanger, experimentally. They dispersed carbon nanotubes with 20 nm outer diameter and 35 µm length in distilled water. Nanotubes volume concentration was between 0.051 to 0.085%. Their results showed an enhancement of 7%-202% compared to water which they attributed to high thermal conductivity and surface area of CNT nanoparticles. Kumaresan et al. (2013) performed an experiment to study convective heat transfer characteristics of multi-walled nanofluids including carbon nanotubes and a mixture of water and ethylene glycol as base fluid in a shell and tube heat exchanger. Volume concentration was in the pure water to 0.45% range. Their interesting results could be summarized as follows:

- The migration of carbon nanotubes does not allow the thermal boundary layer to develop at the faster rate.

- The value of the Prandtl number decreases, as the temperature increases for all the nanofluids with various MWCNT concentrations due to a substantial decrease in the viscosity of the nanofluids.

- The conventional correlations are not able to predict the value of Nusselt number for the nanofluids as its value increases with decrease in the Reynolds number at various MWCNT concentrations.

- The results of average heat transfer coefficient evaluated for various dimensionless length is useful in order to optimize the length of the heat exchanger for maximum heat transfer.

Effect of different nanoparticle shapes on a shell and tube heat exchanger using different baffle angles and operated with nanofluids has investigated, experimentally by Elias et al. (2014). They assumed different nanoparticle shape including cylindrical, bricks, blades, and platelets of

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Boehmite alumina (ᵞ-AlOOH) up to 1% volume concentration. They observed that among all the shapes, nanofluids having cylindrical shape showed better overall heat transfer coefficient and a lower overall heat transfer coefficient was found for blades and platelets shapes of the nanoparticles. Also, the entropy minimization rate was found higher for cylindrical shape compared to any other shapes at 20o baffle angle. Although the degrading behavior of entropy generation happens for all nanoparticle shapes with the increase of nanoparticle volume fraction, entropy generation rate is different in various nanoparticle shapes (Fig. 2).

Fig. 2. Effect of different nanoparticle shapes on entropy generation of nanofluids (Elias et al.,

2014)

Raja et al. (2012) conducted an experimental investigation to take into account the effect of wire coil insert in heat transfer and pumping power characteristics of Al2O3-water nanofluids in a shell and tube heat exchanger. They found that coil insert help to heat transfer enhancement and this enhancement is even more when using nanofluids. An important result of their study is the negligible effect of nanoparticles on a need to pumping power in same Peclet number, up to 1.5% volume concentration. Figure 3 shows the system need to pumping power versus Peclet number in different concentration. In a numerical study done by Leong et al. (2012), a shell and tube heat recovery exchanger operated with Cu-water-EG nanofluids was modeled. Their results showed a controversial phenomenon in degrading power pumping as an increase in volume concentration (Fig. 4). Therefore, lower pumping power is needed when nanofluids is used in the heat recovery exchanger. About 10.99% less power or energy was observed at 1% nanoparticle volume fraction compared to that of ethylene glycol base fluid. They explained this as in other studies, comparison between base fluid and nanofluids pressure drop was conducted at constant Reynolds’s number which affects the

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nanofluids mass flow rate. Higher mass flow rate is needed to produce the same value of Reynolds number since the viscosity of nanofluids increased with the particle volume fraction. Subsequently, more pumping power is needed. However, in the present analysis, the coolant mass flow was kept constant. As a result, the coolant velocity decreases with particle volume fractions. Afshoon and Fakhar (2014) solved flow field and heat transfer of 30 nm copper nanoparticle dispersed in water in turbulent flow regime, numerically. They found a maximum enhancement in heat transfer about 32% at the maximum volume concentration (0.236%) compared with water. However, heat transfer enhancement at 0.078% is an optimum case. Since, its percentage increase in pressure drop is less than the percentage increase in heat transfer coefficient. Therefore, the highest enhancement is not the best thermal performance, necessarily and it is strongly dependent on trade-off between the values of heat transfer enhancement and probable enhancement in need to pumping power. So, industrial designers should pursuit optimum case rather than the maximum enhancement case.

Fig. 3. Pumping power of alumina – water nanofluids against Peclet number with coil insert for

different percentage of volume concentrations (Raja et al., 2012)

Sarkar (2011) investigated different nanofluids in shell and tube gas cooler in transcritical CO2 refrigeration systems, analytically. They considered four different 50 nm nanoparticles: Al2O3, TiO2, CuO and Cu dispersed in water with maximum 2% volume concentration. Results demonstrated improves the gas cooler effectiveness, cooling capacity and COP with nearly same pump power, increase in cooling COP with an increase in compressor discharge pressure, nanofluids mass flow rate, gas cooler length and volume fraction. Also, the maximum cooling COP improvement of transcritical CO2 cycle is 26%. 24.4%. 20.7% and 16.5% for alumina, titanium oxide, copper oxide and copper all in water nanofluids, respectively.

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Fig. 4. Effect of copper volume fraction on the coolant pressure drop (Leong et al., 2012)

Fig. 5. The enhancement of Nusselt number as a function of Reynolds Number

Figure 5 shows enhancement behavior of nanofluids in shell and tube heat exchangers as a function of Reynolds number, available in the literature. One can see that the slopes of curvatures are so different. For example, Leong et al. (2012) observed a rough enhancing manner in the Nusselt number. On the other hand, Ramesh & Vivekananthan (2014) observed an about constant Nusselt

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number with any increase in Reynolds number. Furthermore, their results give the Nusselt number in a disappointing order of value. The reason of such incredible difference maybe is about the used Re range in two studies. Also, it could because of the complex geometry of the shell and tube heat exchangers. Nevertheless, almost all studies demonstrate considerable enhancement in the Nusselt number by nanofluids implementation.

3. Double Pipe heat Exchangers A double pipe heat exchanger is one of the simplest types of exchangers up to now. It consists of two concentric pipes with different inner and outer diameters having two specific spaces for hot and cold fluids. The major application of this type of heat exchanger is for sensible heating or cooling of process fluids where small heat transfer areas (to 50 square meters). This configuration is also very suitable when one or both fluids are at high pressure. The major disadvantage is that double pipe heat exchangers are bulky and expensive per unit of transfer surface (Kakac and Liu, 2002).

A double pipe heat exchanger can play a vital role in many applications such as HVAC systems (Kurata et al., 2007) petrochemical industry (Sheikholeslami et al., 2015), refrigeration (Krishna et al., 2012), solar water heater (Natarajan and Sathish, 2009), and bioprocess industry (Agarwal et al., 2014).

Chun et al. (2008) studied the effect of alumina nanoparticles dispersed in transformer oil in a double pipe heat exchanger, up to 1% volume concentration, experimentally with laminar flow regime. Their results show that nanofluids give a better thermal performance compared with base fluid. They investigated surface properties of nanoparticles, particle loading, and particle shape. They guessed that heat transfer enhancement of nanofluids may be caused by the high concentration of nanoparticles in the wall side by the particle migration.

Fig. 6. A typical twisted tape (Maddah et al., 2014a)

Maddah et al. (2014a) conducted an experiment to investigate the effect of twisted-tape turbulators and TiO2-water nanofluids on heat transfer in a double pipe heat exchanger. Their twisted tapes were made from the aluminum sheet with tape thickness of 1mm, a width of 5mm, and length of 120 cm (Fig. 6). Titanium dioxide nanoparticles with a diameter of 30 nm and a volume concentration of 0.01% (very dilute nanofluids) were prepared. They found that by using of nanofluids and twisted tape, heat transfer coefficient was about 10 to 25% higher than base fluid (Fig. 7). They concluded that the collisions occurring between nanoparticles and the base fluid molecules on the one hand and the impacts of the particles on the heat exchanger wall, on the other

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hand, result in an enhancement in energy. The friction between the wall and fluid increases if nanofluids are dealt with and, therefore heat transfer improves.

Fig. 7. The effect of volume concentration and twisted tape, TiO2 – water on the efficiency at

different Reynolds number (Maddah et al., 2014a)

Reddy et al. (2015) investigated the heat transfer coefficient and friction factor of ethylene glycol-water based TiO2 (21 nm) nanofluids in a double pipe heat exchanger with and without helical coil insert, in a turbulent flow regime, experimentally. They observed that a 7.85% enhancement in heat transfer increased to 17.71% when using of helical coil inserts. Therefore, there is a combined effect of coil inserts and nanofluids. Also, they proposed two predicting correlations for Nusselt number and friction factor (Eq. 1 & 2).

037.076.05.08.0 1)1(PrRe007523.0

d

PNu

(1) 041.0

723.22377.0 1)1(Re3250.0

d

Pf

(2)

Where, 4000<Re<15000, 0<<0.02%, 24.45<Pr<32.85, 0<P/d<2.5 (=0, P/d=0 for the plain tube) In another experimental study, Prasad et al. (2014) considered Al2O3-water nanofluids in a U-type heat exchanger with helical tape inserts. The maximum Nusselt number enhancement was 32.91% compared to water. Also, they developed two correlations (Eq. 3 & 4) for the Nusselt number and

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friction factor are obtained as functions of the Reynolds number, Prandtl number, volume concentration and aspect ratio.

02.086.24.08.0 1)1(PrRe096.0

d

PNu

(3) 04.0

46.224.0 1)1(Re284.0

d

Pf

(4)

Where, 3000<Re<30000, 0<<0.03%, 5.12<Pr<6.54, 0<P/d<20. Sarafraz and Hormozi (2015) studied forced convective heat transfer using biological nanofluids in a double-pipe heat exchanger, experimentally. Nanofluids were prepared at volume fractions of 0.1%, 0.5%, and 1% and well dispersed in ethylene-glycol/water, in three flow regime: laminar, transient and turbulent. They showed that enhanced parameters in turbulent flow regime are so greater than the other regimes (Fig. 8). Also, they proposed a new correlation for thermal conductivity of nanofluids, based on the temperature and volume concentration of nanoparticles.

661.30)(00114.0981.0 CTk

k o

bf

nf

(5)

Fig. 8. The comparison between the enhancement parameter at different Reynolds numbers and

volume fractions (Sarafraz and Hormozi, 2015)

Wu et al. (2013) studied conducted an experiment to investigate the Pressure drop and convective heat transfer of water and Al2O3-water nanofluids in a double pipe helical heat exchanger. They observed that for both laminar flow and turbulent flow, no anomalous heat transfer enhancement was found. Also, Secondary flow intensity mitigation due to nanofluids may neutralize the benefit

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from the thermal conductivity increase. They proposed two accurate correlations for laminar and turbulent flow in helically coiled tubes, as follows:

4.0375.06.0775.0

:flowlaminarfor

f

n

bf

nf

bf

nf

bf

nf

bf

nf

C

C

k

k

h

h

(6) 4.045.06.085.0

:flowturbulentfor

f

n

bf

nf

bf

nf

bf

nf

bf

nf

C

C

k

k

h

h

(7)

Also, they considered the figure of merit for the heat transfer coefficient ratio of the nanofluids over the base fluid is adopted to compare the heat transfer performance of the nanofluids to that of the base fluid. If r >1, the nanofluids are beneficial for the heat transfer coefficient. They found that “the figure of merit based on the constant Reynolds number can be misleading and should not be used to evaluate heat transfer enhancement because the net result for the constant Reynolds number comparison is a combination of the nanofluids property effect and the flow velocity effect. Possible additional effects of nanoparticles, e.g., Brownian motion, thermophoresis, and diffusiophoresis, on the convective heat transfer characteristics of the nanofluids were negligible compared to the dominant thermophysical properties of the nanofluids” (Hashemi and Akhavan-Behabadi, 2012).

Fig. 9. The Nusselt number increment versus the Reynolds number using nanofluids in the double

pipe heat exchangers

Figure 9 demonstrates the Nusselt number increment against the Reynolds number for nanofluids using in the double pipe heat exchangers, in the literature. All of the considered studies show a consistent enhancement behavior of heat transfer. The reason of this consistency in the literature

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may be arouse from simplicity of geometry of the double pipe heat exchangers compared to the shell and tube heat exchangers. We can conclude that the Nusselt number increases with any increase in the Reynolds number and this increase is considerable for the turbulent regime compared to the laminar regime.

4. Coil Tube Heat Exchangers Today, implementation of helical (coil) tubes in heat exchangers are widely accepted as a passive heat transfer enhancement technique in heat and mass transfer applications, because of their secondary flows gives higher rates of heat and mass transfer rates. The other their benefits are ease of manufacture and compact design. The heat transfer and pressure drop characteristics of this geometry of tube are studied, experimentally and numerically [107-108] (Kurnia et al., 2011; Naphon and Wongwises, 2006). For example, Prabhanjan et al. (2004) compared the heat transfer rates between a helically coiled and a straight tube heat exchanger. Their results show that the geometry of heat exchanger and water bath temperature affected the heat transfer coefficient. Figure 10 shows the different types of tubes implemented in heat exchangers. In this case, such as the other type of heat exchangers, one more important heat transfer enhancement technique is using nanofluids. Regarding the promising heat transfer characteristics of nanofluids, Hashemi and Akhavan-Behabadi (2012) investigated heat transfer and pressure drop characteristics of CuO-oil nanofluids in a horizontal helically coiled tube under constant heat flux, experimentally. They dispersed 10 nm CuO nanoparticles in oil with weight concentration range 0.5% to 2%, in a laminar flow regime. Their results showed that at the same flow conditions and for a given nanofluids with constant particle concentration, helical tube enhances the heat transfer rates compared to that of the straight tube, significantly. Also, they observed an enhancement about 78% in heat transfer coefficient compared to base fluid for the helical tube at Reynolds number 0f 82.2. Finally, they proposed a correlation for Nusselt number prediction for CuO-oil nanofluids flow with weight concentrations less than 2% in the hydrodynamically fully developed laminar flow regime with Reynolds number smaller than 125 and Prandtl number range of 700 to 2050:

180.0286.0346.0 )1(PrRe73.41 Nu (8) Fakoor Pakdaman et al. (2013) used the overall performance index to evaluate thermo-physical properties of MWCNT/heat transfer oil nanofluids flow inside vertical helically coiled tubes, experimentally. There are some problems in using of nanofluids reported in the literature that pressure drop enhancement may be larger than heat transfer enhancement. This is because of viscosity rise due to nanoparticles presence. To find optimum work conditions, one can use overall performance index and taking into account the effects of heat transfer and pressure drop enhancements, simultaneously. This parameter is defined as follow:

bf

bf

p

p

h

h

~

~*

*

(9)

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Where *h and *~p represent mean heat transfer coefficient and pressure drop of the flow resulted

by applying heat transfer enhancement techniques, respectively. Moreover, bfh and bfp~ are the

mean heat transfer coefficient and pressure drop change of the base fluid, respectively. When the performance index is greater than 1, it demonstrates that the heat transfer technique is more in the favor of heat transfer enhancement rather than in the favor of pressure drop increasing. Thus, the heat transfer methods with performance index greater than 1 may be feasible choices in practical applications (Saeednia et al., 2012). Their results show that remarkably high performance index was calculated for nanofluids in the helically coiled tube. The maximum value of overall performance index is 6.4 for 0.4% weight concentration of nanofluids that yield these methods a good choice in practical applications (Fig. 11).

Fig. 10. Computational domain for (a) straight tube, (b) conical spiral tube, (c) in-plane spiral tube,

and (d) helical spiral tube (Sasmito et al., 2011)

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Fig. 11. Variation of the overall performance index with the Reynolds number for the downward

flow of the nanofluids inside helical coil No. 1 (Fakoor-Pakdaman et al., 2013)

Akhavan-Behabadi et al. (2015) designed an experimental setup to study the heat transfer and pressure drop characteristics of MWCNT-water nanofluids inside horizontal coiled wire inserted tube. They observed 85% enhancement in heat transfer and 475% penalty in pressure drop using nanofluids in the range of 0.05% to 0.2% of nanoparticles volume concentration, surprisingly. Finally, they introduced two new correlations using the results of the experiments to predict the Nusselt number and friction factor of the nanofluids flow inside coiled wire inserted tubes:

8125.00761.06877.00442.06837.0 11)1(PrRe1763.0

d

e

d

PNu

(10) 79.002.0

44.021.0 11)1(Re7026.0

d

e

d

Pf

(11) 10000<Re<20000, 4.5<Pr<6.5, 1.70<p/d<2.83, 0.113<e/d<0.170. Bahremand et al. (2014) conducted and experimental and nume rical investigation on helically coiled tube under constant wall heat flux and turbulent flow regime using two-phase Eulerian-Lagrangian approach. They dispersed 10 nm Ag nanoparticles in water with 0 to 0.03% volume concentrations as very dilute nanofluids. They found that Enhanced heat transfer and pressure drop increase for coils with greater curvature ratios. Also, they observed that the nanoparticles do not change the axial velocity and turbulent kinetic energy significantly. Their results showed that for nanofluids with greater particle volume concentration, the effect of nanoparticle diameter on increment of mean heat transfer coefficient becomes more significant. Also, they developed two correlations using multiple regressions analysis of MATLAB for estimating the ratio of mean heat transfer coefficient and pressure drop of nanofluids to water in helical tubes.

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4283.0

041.0

0089.00371.0

10221.1

p

Bf

nf d

h

h

(12)

1553.00551.0446.2

Bf

nf

p

p

(13)

Where, 14000<Re<40000, 0.03%<<0.4%, 0.02< <0.05 and 10 nm< pd<50 nm.

Also, Saeednia et al. (2012) developed two another predicting correlations during their experimental study, using the experimental data and the least square method. Their correlations can predict the present experimental data effectively.

14.0448.0358.0324.0636.0 )()()(PrRe467.0 m

s

d

e

d

pNu

(14)

58.0362.0943.0708.0 )()()(Re7.198m

s

d

e

d

pf

(15) Where, 1.79<p/d<2.14 and 0.064<e/d<0.107. We can see the expectable manner of increase in the Nusselt number as a function of the Reynolds number in the coiled tube heat exchangers, in figure 12. The details of all available studies in this area are collected in Table 1.

Fig. 12. The increase in the Nusselt number as a function of the Reynolds number in the coiled tube

heat exchangers

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Table1. The details of all available studies on the nanofluids implementation in the tubular heat exchangers.

References Type of Study

Type of Exchanger

Base Fluid

Nanoparticles Nanoparticl

e Size

Volume Fraction

Range (%)

Nanofluids Reynolds

Range

Nanofluids Flow

Regime

Maximum Heat

Transfer Enhancemen

t (%)

Findings

Khodammrezaee et al. (2010)

Numerical Shell&Tube EG Al2O3 <100 nm Not mentioned Not

mentioned Not mentioned 325

The effect of increasing in shear stress in comparison with the extreme increasing of heat transfer coefficient (325%) is negligible.

Ramesh & Vivekananthan

(2014) Experimental Shell&Tube EG Al2O3 20 nm 0.2-2.5 2000-4000 Laminar 30

Nanofluids change the flow structure so that besides of thermal conductivity increment, chaotic movements, and dispersion fluctuations of nanoparticles especially

near the tube wall leads to increase in the energy exchange rates and augments heat transfer rate.

Walvekar et al. (2015)

Experimental Shell&Tube Water CNT 20 nm 35 µm

0.051-0.085 2750-4850 Turbulent 202 Heat transfer enhancement is a function of temperature and concentration.

Parametthanuwat et al. (2011)

Experimental Shell&Tube Water Ag <100 nm 0.5-1.5 Not

mentioned Not mentioned

Not mentioned but prominent

Oleic acid as surfactant raises the effectiveness of the nanofluids.

Patel et al. (2014)

Numerical Shell&Tube Water Not mentioned Not mentioned 0-1 Not

mentioned Laminar

Not mentioned but prominent

CFX model is validated by comparison to the experimental results within 10% error.

Ghozatloo et al. (2013)

Experimental Shell&Tube Water Graphene Not mentioned 0-1 1940 Laminar 23.9 By increasing the concentration of graphene from, the heat transfer coefficient

increased by 15.3% at 25°C, whereas, at 38°C, an enhancement of 23.9% on heat transfer coefficient occurred.

Santhosh Cibi et al. (2014)

Experimental Shell&Tube Water Graphite Not mentioned 0.025-0.075 Not

mentioned Laminar Not mentioned The heat transfer coefficient increases gradually as the concentration increases.

Elias et al. (2014)

Numerical Shell&Tube Water

-EG Boehmite alumina Not mentioned 0-1

Not mentioned

Laminar Not mentioned Entropy generation decreases with the increase of volume concentration for all baffle

angles and segmental baffle.

Bhanuteja & Azad (2013)

Numerical Shell&Tube Water Ag, Al2O3,CuO,

SiO2, TiO2 Not mentioned 2-4

Not mentioned

Turbulent Not mentioned SiO2 nanofluids obtained highest pressure drop and Ag nanofluids gives better result

by obtaining lowest pressure drop.

Shahrul et al. (2014a)

Analytical Shell&Tube Water

ZnO CuO

Fe3O4, TiO2 Al2O3

50 40 36 21 20

0-0.03 Not

mentioned Turbulent

Not mentioned but prominent

Energy effectiveness of the shell and tube heat exchanger can be increased approximately from 31% to 44% using different nanofluids.

Shahrul et al. (2014b)

Analytical Shell&Tube Water

Al Al2O3

Fe3O4, TiO2

40 20 36 21

0-0.04 Not

mentioned Turbulent

17 14 13 10

Using nanofluids in the heat exchanger systems of all sectors, a lot of heat emissions can be reduced.

Raja et al. (2012)

Experimental Shell&Tube Water Al2O3 40.3 0.5-1.5 Not

mentioned Laminar 33.5 The superior thermal characteristics of nanofluids obtained with the aid of coil insert.

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Lotfi et al. (2012)

Experimental Shell&Tube Water MWCNT Not mentioned Not mentioned Not

mentioned Not mentioned Not mentioned

The heat transfer enhances in the presence of MWCNT in comparison with the base fluid

Shahrul et al. (2014c)

Analytical Shell&Tube Water MWCNT Not mentioned 0.02-0.1 Not

mentioned Turbulent 17

With the reduced heat emissions, global warming and greenhouse effects can be reduced by using MWCNT-W nanofluids as working fluid in shell & tube heat

exchanger system.

Godson et al. (2014)

Experimental Shell&Tube Water Ag 54 0.01-0.04 5000-25000 Turbulent 12.4

A maximum enhancement in the convective heat transfer coefficient of 12.4% and effectiveness of 6.14% is recorded. The apparent increase in the heat transfer

coefficient is due to the enhanced thermo-physical properties, and delayed development of boundary layer in the entrance regions.

Kirubadurai & Ramesh (2014)

Numerical Shell&Tube Water Silicon Nitride 50 0-5 3385-4027 Turbulent Not mentioned 11% effectiveness enhancement is obtained.

Farajollahi et al. (2010)

Experimental Shell&Tube Water Al2O3

TiO2 25 10

0.3-2 0.15-0.75

Not mentioned

Turbulent 15 24

TiO2/water and Al2O3/water nanofluids possess better heat transfer behavior at the lower and higher volume concentrations, respectively. Competition of thermal conductivity and particle size of both nanoparticles may be the source of these

differences for heat transfer performances.

Albadr et al. (2013)

Experimental Shell&Tube Water Al2O3 30 0.3-2 75000-175000

Turbulent 62.6 Friction factor increases with the increase in concentration, because of the increase in

the viscosity of the nanofluids

Arvind (2015) Experimental Shell&Tube Water Aluminium

Nitride Not mentioned 0.4-0.8

Not mentioned

Not mentioned Not mentioned but prominent

Nitride-water nanofluids are used because of its high melting point, low density and high structural stability. An increase of 9.68% of effectiveness is obtained, where

aluminum nitride nanoparticles are used than with water.

Leong et al. (2012)

Numerical Shell&Tube Water

EG Cu Not mentioned

0-2.5 0-1

2330-2400 Laminar 10.11

16

Less coolant pumping power (10.99%) is needed for heat recovery exchanger operated with ethylene glycol nanofluids containing 1% copper nanofluids compared

to base fluid.

Afshoon & Fakhar (2014)

Numerical Shell&Tube Water CuO 30 0.015-0.236 6000-31000 Turbulent 32 The best volumetric concentration is 0.078%, because its percentage increase in

pressure drop is less than the percentage increase in heat transfer coefficient.

Sarkar (2011) Analytical Shell&Tube Water

Al2O3

TiO2

CuO Cu

50 0-2 Not

mentioned Turbulent

Not mentioned but prominent

The nanofluids may effectively use as coolant in shell-and-tube gas cooler to improve the performance of transcritical CO2 refrigeration cycle.

Guerrieri et al. (2012)

Numerical Shell&Tube Water

-PG Al2O3

CuO 10 0-0.15

Not mentioned

Turbulent Not mentioned but prominent

The propylene glycol based nanofluids have low thermal conductivity compared to water based nanofluids.

Marode & Keche (2015)

Experimental Shell&Tube Water Al2O3 Not mentioned 0-0.1 19000-100000

Turbulent Not mentioned but prominent

Thermal analysis has been carried out for different design with two fluids and on the basis of comparative results is made which one give the best heat transfer rates.

Anoop et al. (2013)

Experimental Shell&Tube Water SiO2 20 2-6 Not

mentioned Not mentioned Not mentioned No anomalous enhancement in heat transfer coefficient values was observed.

Tiwari (2015) Experimental Shell&Tube Water Al2O3 44 0.5-3 10000-11000 Turbulent Not mentioned but prominent

Less coolant pumping power is needed for heat exchanger operated with nanofluids compared to the base fluid.

Kumaresan et al. (2013)

Experimental Shell&Tube Water

-EG MWCNT

30-50 nm 10-20 µm

0-0.45 500-5500 Laminar 150

Nusselt number increases with decrease in the Reynolds number as the concentration increases. Significant enhancement in the convective heat transfer coefficient in the

entrance region was observed. The possible reason for the abnormal enhancement in the heat transfer coefficient for the shorter length of the test section is due to the

migration of the carbon nanotubes. This migration of carbon nanotubes does not allow the thermal boundary layer to develop at the faster rate.

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Senthilraja & Vijayakumar

(2013) Experimental Double Pipe Water CuO 27 0.1-0.3 2000-22000 Turbulent

Not mentioned but prominent

The convective heat transfer coefficient increases with an increase in time also the Nusselt number increases with increasing the liquid flow rate.

Chun et al. (2008)

Experimental Double Pipe Transformer

Oil Al2O3 7-43 0-1 100-500 Laminar 25

Experimental correlation was proposed for an alumina-transformer oil nanofluids system.

Moshizi et al. (2014)

Analytical Double Pipe Water Al2O3 10 2-10 Not

mentioned Not mentioned Not mentioned

The heat transfer coefficient enhancement in the case of heat generation is much more that in the case of heat absorption.

Turkyilmazoglu (2015)

Analytical Double Pipe Water

Cu CuO

Al2O3

TiO2

Ag

Not mentioned 0-0.5 Not

mentioned Laminar Not mentioned

The anomalous heat transfer enhancement as observed in the experiments and numerical solutions of nanofluids flow occurring in the circular concentric shapes is

mainly due to the velocity slip mechanism.

Reddy & Rao (2014)

Experimental Double Pipe Water

-EG TiO2 21 0.0004-0.02 4000-15000 Turbulent 17.71 Generalized correlations are proposed for Nusselt number and friction factor.

Reddy et al. (2015)

Experimental Double Pipe Water TiO2

ZnO 21 0.002-0.004 1600-6100

Turbulent and Laminar

66.12 78.30

Effectiveness of the heat exchangers increases considerably when nanofluids are used as heat transfer media.

Prasad et al. (2014)

Experimental Double Pipe Water Al2O3 50 0.01-0.03 3000-30000 Turbulent 32.91 5% heat transfer enhancement for water flowing in a heat exchanger at a Reynolds

number of 30000.

Mohammed et al. (2013)

Numerical Double Pipe Water

Al2O3

CuO SiO2 ZnO

20-50 1-4 10000-50000 Turbulent 411 The Nusselt number increases with decreasing the nanoparticle diameter. SiO2

nanofluids has the highest Nusselt number value, followed by Al2O3, ZnO, and CuO while pure water has the lowest Nusselt number.

Wu et al. (2013) Experimental Double Pipe Water Al2O3 20 0.78% wt- 7.04% wt

1000-10000 Laminar

Turbulent 3.43

Figure of merit based on the constant Reynolds number can be misleading and should not be used for heat transfer enhancement comparison. No anomalous heat transfer

enhancement was found

Chavda et al. (2014)

Experimental Double Pipe Water Al2O3 50 0.001-0.01 Not

mentioned Not mentioned

Not mentioned but prominent

Increasing working fluid heat transfer with an increase in volume concentration.

Maddah et al. (2014a)

Experimental Double Pipe Water TiO2 30 0-0.01 10000-30000 Turbulent 20 When using twisted tape and nanofluids, the heat transfer coefficient was about 10 to

25 percent higher than when they were not used. It was also observed that the heat transfer coefficient increases with operating temperature and mass flow rate.

Bozorgan & Bozorgan

(2012) Numerical Double Pipe EG

Al2O3

TiO2 Not mentioned 0-10

Not mentioned

Laminar Not mentioned As the probability of collision between nanoparticles and the heat exchanger wall

increases, due to using higher concentration of coolants, the total heat transfer coefficient increases.

Senthilraja et al. (2014)

Experimental Double Pipe Water CuO 27 0.05-0.15 3000-20000 Turbulent Not mentioned but prominent

The convective heat transfer coefficient of the nanofluids was increased with increasing the electric field intensity the nanofluids volume concentration.

Maddah et al. (2014b)

Experimental Double Pipe Water Al2O3 20-22 0.2-0.9 5000-21000 Turbulent 52 Generalized correlations were developed for the estimation of Nusselt number, friction factor and thermal performance factor under turbulent flow conditions.

Zamzamian & Jamal-Abadi

(2013) Numerical Double Pipe EG Al2O3 50 0.1-1

Not mentioned

Laminar 23.7 Nusselt number of the nanofluids for different nanoparticle concentrations as well as various operating temperatures was found to increase up to 23.7% using 1.0% wt of

nanoparticles.

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Huminic &Huminic [70]

Numerical Double Pipe Water CuO TiO2

24 0.5-3 Not

mentioned Laminar

14 19

The convective heat transfer coefficient of the nanofluids and water increased with increasing of the mass flow rate and with the Dean number.

Duangthongsuk & Wongwises

[71] Experimental Double Pipe Water TiO2 21 0-0.2 4000-18000 Turbulent 11 The use of the nanofluids has a little penalty in pressure drop.

Sozen et al. [72] Experimental Double Pipe Water Al2O3- Fly ash 14 0-4 Not

mentioned Turbulent 6.3

The improvement in the performance of PFHE was observed to be as high as 31.2%, whereas that of CFHE was 6.9%.

Khedkar et al. [73]

Experimental Double Pipe Water TiO2 20 2-3 300-4000 Laminar Not mentioned but prominent

The average heat transfer rates for nanofluids are higher than those for the water, and this increases with the concentration of nanofluids composition.

Sarafraz & Hormozi [35]

Experimental Double Pipe Water

-EG

Biological Nanoparticles including Ag

40-50 0.1-1 1000-10000 Laminar

Transient Turbulent

67 A remarkable enhancement of heat transfer coefficient up to 67% at vol. %=1.

Bahiraei & Hangi [74]

Numerical Double Pipe Water Mn–Zn ferrite

magnetic 10-30 1-5 4000-30000 Turbulent

Not mentioned but prominent

Magnetic field increases the pressure drop and enhances the heat transfer whose effect becomes more prominent at lower Reynolds numbers.

Borazjani et al. [75]

Numerical Double Pipe Water Al2O3 Not mentioned 0-4 100-80000 Turbulent Not mentioned but prominent

Increase of energy efficiency ratio, thus power to pump decrease for a given heat transfer rate.

Demir et al. [76] Numerical Double Pipe Water Al2O3

TiO2 21 0-4 0-80000 Turbulent

Not mentioned but prominent

Nanofluids behave more like a pure fluid than a liquid–solid mixture.

Luciu et al.[77] Experimental Double Pipe Water Al2O3 47 0-4 200-1700 Laminar Not mentioned but prominent

Experimental data have clearly shown a low Nusselt number due to the high conductivity number for this fluid, and high convection transfer coefficient.

Sonawane et al. [78]

Experimental Double Pipe Water Al2O3 20 2-3 300-4000 Laminar Not mentioned The heat transfer characteristics of nanofluids improve with Reynolds number

significantly as compared to base fluid.

Khedkar et al. [79]

Experimental Double Pipe Water Al2O3 Not mentioned 1-7.5 1000-5000 Turbulent 16 It observed that, 3 % nanofluids shown optimum performance with overall heat

transfer coefficient 16% higher than water.

Aghayari rt al. [98]

Experimental Double Pipe Water Al2O3 20 0.1-0.3 10000-27000 Turbulent 24 The heat transfer coefficient increases with the operating temperature and

concentration of nanoparticles.

Radhakrishnan et al. [99]

Experimental Double Pipe Water Al2O3 22 0-0.1 8000-60000 Turbulent 20 Performance evaluation criteria were found for water and nanofluids ant it was

observed that rectangular baffled twisted tape performs better than other twisted tapes.

Halelfadl et al. [100]

Experimental Double Pipe Water MWCNT 9 nm

1.5 µm 0-0.026 500-2500 Laminar 12

The enhancement of the thermal conductivity and the average convective heat transfer of nanofluids increased with the aspect ratio of nanotubes.

Amani and Abbasian Arani

[101] Experimental Double Pipe Water TiO2 10 0.2-2 8000-49000 Turbulent Not mentioned Nanofluids show significant increment in the both of heat transfer and pressure drop.

Kannadasan et al. [80]

Experimental Coil Tube Water CuO 10-15 0.1-0.2 Not

mentioned Turbulent 49 A slight improve in the thermal performance factor using nanofluids.

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Zamzamian (2014)

Experimental Coil Tube EG Al2O3 Not mentioned 1-5 100-3700 Laminar Not mentioned Adding nanoparticles leads to increase entropy generation in the cases that fluid flow

(pressure drop) irreversibility is dominant

Falahat (2012) Analytical Coil Tube Water Al2O3 Not mentioned 0-4 500-10000 Laminar Not mentioned Total entropy generation at the fixed Reynolds number, decreases.

Akbaridoust et al. (2013)

Experimental Numerical

Coil Tube Water CuO 68 0.1-0.2 100-1000 Laminar Not mentioned Utilization of the base fluid in the helical tube with greater curvature compared to the

use of nanofluids in straight tubes enhanced heat transfer more effectively.

Akhavan-Behabadi et al.

(2015) Experimental Coil Tube Water MWCNT

5-20 nm 1-20 µm

0.063-0.251 100-2000 Laminar 80 The Nusselt numbers of nanofluids in helical coils were up to 60% higher than that for

the base fluid in such geometries.

Mukeshkumar et al. (2012)

Experimental Coil Tube Water Al2O3 45-50 0.4-0.8 5200-8600 Laminar 42 Al2O3 nanofluids can be applied as coolant in a helically coiled tube at 0.1% and 0.4%

particle volume concentrations without significant pressure drop.

Khairul et al. (2013)

Analytical Coil Tube Water

CuO Al2O3

SiO2 ZnO

40 20 -

50

1-4 6600-7800 Turbulent Not mentioned but prominent

CuO/water nanofluids indicate significant heat transfer performance for helically coiled heat exchanger. SiO2/water nanofluids show lower heat transfer coefficient by

increasing the volume fraction of nanoparticles. This is due to the lower density of SiO2/water nanofluids.

Narrein & Mohammed

(2013) Numerical Coil Tube

Water-EG-

Engine Oil

Al2O3

SiO2 CuO ZnO

25 40 80 60

1-4 Not

mentioned Laminar

Not mentioned but prominent

The Nusselt number is highest using CuO–water nanofluids in this study. In addition, rotation can be used to enhance the heat transfer rates.

Sasmito et al. (2011)

Numerical Coil Tube Water Al2O3

CuO 45 0-3 1000 Laminar 15

Nanoparticles up to 1% improve significantly the heat transfer performance; however, further addition tends to deteriorate heat transfer performance.

Fakoor Pakdaman et al.

(2013) Experimental Coil Tube

Engine Oil

MWCNT 5-20 nm 1-10 µm

0.1-0.4 10-2000 Laminar Not mentioned but prominent

Pressure drop of the 0.4% wt. nanofluids is up to 31% higher than that of the base fluid at the Reynolds number of almost 1800.

Fakoor Pakdaman et al.

(2012) Experimental Coil Tube Oil MWCNT

5-20 nm 1-10 µm

0.1-0.4 10-2000 Laminar 15 High overall performance index of up to 6.4 was obtained for the simultaneous

utilization of both heat transfer enhancement techniques

Akhavan-Behabadi et al.

(2012) Experimental Coil Tube Water MWCNT 5-20 0.05-0.2 10000-20000 Turbulent 85 Average, 85% enhancement in heat transfer and 475% penalty in pressure drop.

Aly (2014) Numerical Coil Tube Water Al2O3 40 0.5-2 10000-30000 Turbulent Not mentioned but prominent

The friction factor increases with the increase in the curvature ratio and almost there is no pressure drop penalty with increasing the concentration up to 2%.

Bahremand et al. (2014)

Experimental Numerical

Coil Tube Water Ag 10 0-0.03 14000-40000 Turbulent Not mentioned but prominent

Enhanced heat transfer and pressure drop increase for coils with greater curvature ratios

Khairul et al. (2014a)

Analytical Coil Tube Water CuO

Al2O3

ZnO 25 1-4 4500-13000 Turbulent 7.4

CuO/water nanofluid, the heat transfer enhancement and reduction of entropy generation rate were obtained about 7.14% and 6.14%, respectively. The heat transfer

coefficient was improved with the increasing of concentration and volume flow rate, while entropy generation rate went down.

Jamshidi et al. (2012)

Numerical Coil Tube Water Al2O3 Not mentioned 1-3 200-2600 Laminar Not mentioned Using nanofluids don't change the optimized shape factors but temperature

dependent properties alter the optimum particle volume fraction.

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Srinivas & Vinod (2013)

Experimental Coil Tube Water Al2O3 20-30 0.15-0.75 Not

mentioned Laminar

Turbulent Not mentioned but prominent

Energy savings are more in laminar and turbulent conditions of flow than transition regime, and percentage savings increase with increase in concentration. higher stirrer

speed and shell-side temperature also resulted in more energy savings.

Khairul et al. (2014b)

Numerical Coil Tube Water CuO Not mentioned 1-4 Not

mentioned Laminar 14.24

The heat transfer coefficient increased significantly by 5.90%, 8.72%, 11.50% and 14.24% respectively for 1%, 2%, 3% and 4% compare to water.

Falahat (2011) Analytical Coil Tube Water Al2O3 Not mentioned 1-4 <320000 Turbulent Not mentioned In the sense of thermodynamic performance, adding nanoparticles to the base fluid is

efficient only when the heat transfer irreversibility is dominant.

Mohammed & Narrein (2012)

Numerical Coil Tube Water CuO 25 0-4 Not

mentioned Turbulent Not mentioned

The heat transfer can be enhanced by reducing the helix radius, increasing the inner tube diameter and decreasing the annulus diameter.

Hashemi & Akhavan behabadi

(2012)

Experimental Coil Tube Oil CuO 50 0.5-2 10-150 Laminar 78.4

Nanofluids have better heat transfer characteristics when they flow in helical tube rather than in the straight tube. The maximum heat transfer enhancement of 18.7%

and 30.4% is obtained for nanofluids flow with 2 wt.% concentration inside the straight tube and helical tube, respectively.

Saeednia et al. (2012)

Experimental Coil Tube Oil CuO 50 0.07-0.3 10-120 Laminar 45 In average, 45% increase in heat transfer coefficient and 63% penalty in the pressure drop was observed at the highest Reynolds number inside the wire coil inserted tube

with the highest wire diameter.

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5. Conclusion This paper has devoted to review the all available literature about nanofluids application in the tubular heat exchangers including shell and tube, double pipe, and coiled tube types. 79 relevant studies has considered in details. 60% of them are experimental studies and remainder is numerical and analytical studies. 34% of all considered papers are about shell and tube heat exchangers, 38% and 28% of them are about double pipe and coiled tube types, respectively. Water is most common heat transfer fluids in the relevant literature by 87% following by Ethylene Glycol as base fluid by 8%. The most popular nanoparticles are alumina, copper oxide and carbon nanotubes by 52%, 20%, and 11% usage, respectively. In this regards, following points are useful:

The most studies show that there is a considerable enhancement in the Nusselt number with any increase in the Reynolds number.

Nanofluids implementation in the heat exchangers resulted in an increase in the required pumping power, in the most cases.

The observed maximum heat transfer enhancement is 325%, 411% and 85% in shell and tube, double pipe, and coiled tube heat exchangers, respectively.

The maximum heat transfer enhancement occurs at the highest used volume concentration, in the most cases.

Future research should be focused more on the role of the nanoparticles shape on the thermal performance and pumping power. Also, the boiling phenomena ought to be considered. Another nanoparticles material such as non-oxide and non-metallic composition could be taking into account.

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Nomenclature P………………………………………………………………………………………………………….……….….….…helical pitch, m C………………………………………………..…………………………………specific heat at constant pressure, (J/kg.K) D………………………………………………….........................…………………………….……………..……….pipe diameter, m d…………………………………………………......................……………………………...…………….. helical coil diameter, m dp……………………………………..…………………………..………………………….…………………..particle diameter, nm e…………………………………………………………………………...………………….…………………………wire diameter, m f……………………………………………………………..……………………………….……………………………….friction factor h……………………………………………………...…….…………….…. convective heat transfer coefficient, (W/m2K) h*……………………………………………………………….……………………………..……. mean heat transfer coefficient

k………………………….……………………………………………………..………….……thermal conductivity, 1 1Wm k

Nu………………………………………………………………………..……………………….……….……..……Nusselt number T......................................................................................................................................................................Temperature, oC Pr……………………………………………………………………………….………………………..………………Prandtl number Re…………………………………….……………………………………….………………………………………Reynolds number Greek symbols …………………………………………...………………………………………………......particle volume concentration, % …………………………………………………...………………………………………………………….dynamic viscosity, Pa s …………………………………………………………………..……………………………………..……………..density, (kg/m3) …………………………………………………………………….……………………………………overall performance index

*~p ……………………………………………………………..…………………..….…...mean pressure drop of the flow, Pa ……………………………………………………………..…………..……………………………….……….curvature ratio, d/D Subscripts nf ……………………………………………………………………………………..………………………………………….nanofluid bf ………………………………………………………………………………………………………..…………………….....base fluid m……………………………………………………………………………………………………………………...………………...….bulk s………………………………………………………………………………………………………………….……………..tube surface