Measurement and correlation of frictional pressure drop of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube

international journal of refrigeration 32 (2009) 1756–1764

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Measurement and correlation of frictional pressure drop of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube Hao Penga, Guoliang Dinga,*, Weiting Jianga, Haitao Hua, Yifeng Gaob a

Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, China International Copper Association Shanghai Office, 381 Huaihaizhong Road, Shanghai 200020, China

b

article info

abstract

Article history:

The objective of this paper is to investigate the effect of nanoparticle on the frictional

Received 26 February 2009

pressure drop characteristics of refrigerant-based nanofluid flow boiling inside a horizontal

Received in revised form

smooth tube, and to present a correlation for predicting the frictional pressure drop of

19 May 2009

refrigerant-based nanofluid. R113 refrigerant and CuO nanoparticle were used for

Accepted 7 June 2009

preparing refrigerant-based nanofluid. Experimental conditions include mass fluxes from

Published online 17 June 2009

100 to 200 kg m2 s1, heat fluxes from 3.08 to 6.16 kW m2, inlet vapor qualities from 0.2 to 0.7, and mass fractions of nanoparticles from 0 to 0.5 wt%. The experimental results show

Keywords:

that the frictional pressured drop of refrigerant-based nanofluid increases with the

Heat exchanger

increase of the mass fraction of nanoparticles, and the maximum enhancement of fric-

Smooth tube

tional pressure drop is 20.8% under above conditions. A frictional pressure drop correlation

Horizontal tube

for refrigerant-based nanofluid is proposed, and the predictions agree with 92% of the

Experiment

experimental data within the deviation of 15%.

Measurement

ª 2009 Elsevier Ltd and IIR. All rights reserved.

Coefficient Friction Flow Boiling Refrigerant Additive Particle

Chute de pression due au frottement d’un nanofluide fonde´ sur un frigorige`ne en e´bullition en e´coulement a` l’inte´rieur d’un tube lisse horizontal : mesures et corre´lation Mots cle´s : E´changeur de chaleur ; Tube lisse ; Tube horizontal ; Expe´rimentation ; Mesure ; Coefficient ; Frottement ; E´coulement ; E´bullition ; Frigorige`ne ; Additif ; Particule

* Corresponding author. Tel.: þ86 21 34206378; fax: þ86 21 34206814. . E-mail address: [email protected] (G. Ding). 0140-7007/$ – see front matter ª 2009 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2009.06.005

international journal of refrigeration 32 (2009) 1756–1764

Nomenclature d D FPD G m P DP q T x

diameter of nanoparticle (m) diameter of tube (m) nanoparticle impact factor mass flux (kg m2 s1) mass flow rate (kg s1) pressure (Pa) pressure drop (Pa) heat flux (W m2) temperature ( C) vapor quality

Greek symbols e void fraction r density (kg m3)

1.

Introduction

In recent years, refrigerant-based nanofluids formed by suspending nanoparticles in pure refrigerants have been used as a new kind of working fluid to improve the performance of refrigeration systems (Wang et al., 2003, 2007; Bi et al., 2008). The presence of nanoparticles may have effects on the pressure drop characteristics of refrigerants flow boiling inside tubes, and then have impacts on the overall performance of the heat exchangers of refrigeration systems. Therefore, the pressure drop characteristics of refrigerant-based nanofluids must be known for the design and optimization of the heat exchangers in refrigeration systems using refrigerant-based nanofluids. The researches on the pressure drop characteristics of nanofluids can be divided into two categories. One is to investigate the single-phase pressure drop characteristics of nanofluids, and the other is to investigate the phase-change pressure drop characteristics of nanofluids. For the single-phase pressure drop characteristics of nanofluids, experimental studies (Chein and Chuang, 2007; He et al., 2007; Lee and Mudawar, 2007) and simulation study (Li and Kleinstreuer, 2008) have been reported in literatures. Experiments on the single-phase pressure drop of CuO/H2O nanofluid in micro-channel heat sink showed that the presence of nanoparticle causes a slight increase in pressure drop (Chein and Chuang, 2007). Experiments on the single-phase pressure drop of TiO2/H2O nanofluid flowing upward through a vertical pipe showed that the pressure drop of nanofluid is a little larger than that of the host fluid at a given Reynolds number (He et al., 2007). Experiments on the single-phase pressure drop of Al2O3/H2O nanofluid in micro-channel showed that the pressure drop of nanofluid is larger than that of the host fluid, and increases with the increase of nanoparticle concentration at the same Reynolds number (Lee and Mudawar, 2007). Li and Kleinstreuer (2008) simulated the fully developed pressure gradient of CuO/H2O nanofluid flow inside micro-channels. The simulation results show that: (i) comparing to the host fluid at a given Reynolds number, the

s 4 u

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surface tension (N m1) volume fraction of nanoparticles mass fraction of nanoparticles

Subscripts frict frictional i inside L liquid mom momentum n nanoparticles r refrigerant static static total total V vapor

pressure gradient enhancements are less than 2% and 5% at nanoparticle volume fractions of 1% and 4%, respectively; (ii) comparing to the host fluid at a given mean velocity, the pressure gradient enhancements are less than 5% and 15% at nanoparticle volume fractions of 1% and 4%, respectively. All these researches show that the single-phase pressure drop of nanofluid is larger than that of the host fluid, and the enhancement of the pressure drop is related to the nanoparticle concentration. Comparing to the researches on the single-phase pressure drop characteristics of nanofluids, there are much fewer researches on the phase-change pressure drop characteristics of nanofluids. A literature survey shows that the phasechange pressure drop of nanofluid is mentioned only by the paper of Bartelt et al. (2008). In the paper, the authors found that the presence of nanoparticle has an insignificant effect on the pressure drop of refrigerant/nanolubricant mixture (R-134a/POE/CuO nanofluid) flow boiling inside a horizontal tube, but no experimental data of the pressure drop were provided. The reason for such insignificant effect might be that the presence of lubricant oil can significantly enhance the pressure drop of refrigerant flow boiling inside tube (Zurcher et al., 1997; Hu et al., 2008) and conceal the effect of nanoparticle on the pressure drop. A definite conclusion of the nanoparticle effect on the pressure drop characteristics of nanofluid may not be obtained by the only report on the pressure drop characteristics of refrigerant/nanolubricant mixture (Bartelt et al., 2008), and more experiments on the effect of nanoparticle on the phase-change pressure drop of nanofluid are needed. The purpose of this study is to investigate the frictional pressure drop characteristics of refrigerant-based nanofluid flow boiling inside a smooth tube at different nanoparticle concentrations, mass fluxes, heat fluxes and inlet vapor qualities, to analyze the effect of nanoparticle on the frictional pressure drop characteristics of refrigerant-based nanofluid, and to present a correlation for predicting the frictional pressure drop of refrigerant-based nanofluid flow boiling inside the smooth tube.

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reduce heat loss to the surroundings. Heat losses from the pre-heater and the test section are less than 2.0%. The differential pressure transducer to measure the pressure drop of refrigerant-based nanofluid is installed between the inlet and outlet of the test section. The mass flux of refrigerant-based nanofluid is controlled by adjusting the rotational speed of the variable-frequency pump or adjusting the opening of the valve in the by-pass of the pump. The heat flux is controlled by varying the heat addition to the test section. The inlet vapor quality of the test section is controlled by varying the heat addition to the preheater. The evaporation pressure is controlled by adjusting the temperature of the cool water bath. Test conditions cover different mass fluxes, heat fluxes, inlet vapor qualities and nanoparticle concentrations, as tabulated in Table 1. All signals of temperature, pressure, pressure difference and mass flow rate are collected by an Agilent 34970A data acquisition system and transmitted to a computer after the system reaches stable conditions.

ΔP

P T 11

2

·

10

1 4 3 9 7

8

5

6

Fig. 1 – Schematic of experimental facility. 1-test section; 2-temperature constant controller; 3-cool water bath; 4-refrigerant-based nanofluid charge device; 5-sight glass; 6-variable-frequency pump; 7-vacuum or nitrogen charge port; 8-volume flow meter; 9-sight glass; 10-mixing chamber; 11-pre-heater.

2.

3. Preparation and characterization of refrigerant-based nanofluid

Experimental apparatus

Similar to that used by Peng et al., in press, the experimental facility used for testing the pressure drop characteristics of refrigerant-based nanofluid consists of a variable-frequency pump, a volume flow meter, a mixing chamber, a pre-heater, a test section, a cool water bath and a device for the charge of refrigerant-based nanofluid, as schematically shown in Fig. 1. The liquid-phase refrigerant-based nanofluid from the cool bath is pumped by the variable-frequency pump, flows through the volume flow meter, the mixing chamber and the pre-heater, and then enters the test section at a known mass flux and vapor quality. After the evaporation in the test section, the refrigerant-based nanofluid enters the cool water bath to be condensed. The test section is a straight smooth copper tube with an outside diameter of 9.52 mm and thickness of 0.70 mm. The total length of the test tube is 1500  2.0 mm, while the effective heating length is 1400  2.0 mm. The electrical heating tape is wrapped around the outside of the test tube, and the heat addition to the test section is varied by adjusting the input power to the electric heating tape. The test section is insulated with glass wool and double layers of rubber foam to

Preparation of refrigerant-based nanofluid is an essential step in investigating the pressure drop characteristics of refrigerant-based nanofluid. In the present study, CuO was used as the nanoparticle while R113 was used as the host refrigerant. The reason for choosing CuO nanoparticle is that it has stable physical properties and wide application (Zeinali Heris et al., 2006; Chein and Chuang, 2007; Karthikeyan et al., 2008; Li and Kleinstreuer, 2008; Lv and Liu, 2008). Despite R113 is not widely used, the difference of the physical properties between R113 and other widely used refrigerants (e.g., R410A) is quite smaller than that between refrigerants and non-refrigerant fluids (e.g., water), so the pressure drop characteristics of R113-based nanofluid may reflect those of other refrigerantbased nanofluids to a certain extent. Moreover, R113 is in liquid state at ambient temperature and pressure while the widely used refrigerants such as R410A are in vapor state at ambient temperature and pressure, so it is much easier to prepare well-dispersed nanofluid based on R113. Therefore, R113 is chosen as the host fluid in our experiments, just as Ding et al. (2009) and Peng et al., in press did. The properties of refrigerant R113 and CuO nanoparticle are given in Tables 2 and 3, respectively. The average diameter of CuO nanoparticles used in the present study is 40 nm, and the TEM (transmission electron microscope) photograph of CuO nanoparticles is shown in Fig. 2.

Table 1 – Test conditions of the test tube. Mass flux (kg m2 s1) 100  10 150  10 200  10

Heat flux (kW m2)

Inlet vapor quality

Vapor quality change

Absolute pressure of outlet (kPa)

3.08 4.62 6.16

0.2–0.7 0.2–0.7 0.2–0.7

0.15 0.15 0.15

78.25 78.25 78.25

Mass fraction of nanoparticles (wt%) 0, 0.1, 0.2, 0.5

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Table 2 – Properties of refrigerant R113. Property

Unit

Value or format

Chemical Formula Molecular mass Normal boiling point Critical temperature Critical pressure

g/mol  C  C MPa

Cl2FC-CClF2 187.37 47.6 214.1 3.39

CuO/R113 nanofluids with three different nanoparticle concentrations (0.1 wt%, 0.2 wt%, and 0.5 wt%) were prepared in our experiments to study the pressure drop characteristics. The required mass of CuO nanoparticles was weighed by a digital electronic balance with a measurement range of 10 mg w 210 g and a maximum error of 0.1 mg. Then the weighed CuO nanoparticles were put into the weighed R113 to form the CuO/R113 mixture. The maximum uncertainty of the nanoparticle concentration in the test tube is determined by the measurement uncertainty of the mass of CuO nanoparticles and refrigerant R113. For target nanoparticle concentrations of 0.1 wt%, 0.2 wt% and 0.5 wt%, the maximum uncertainties of the nanoparticle concentrations in the test tube are 0.0013 wt%, 0.0025 wt% and 0.0063 wt%, respectively. A surfactant may cause the sorption and agglutination phenomenon during nanofluid boiling heat transfer process (Liu and Liao, 2008), and affect the pressure drop characteristics of the nanofluid. In order to avoid the disturbance of surfactant, tests were done on nanofluid without surfactant, as done by Das et al. (2003), Liu et al. (2007), Zeinali Heris et al. (2007) and Trisaksri and Wongwises (2009). Ultrasonic vibration was used for 30 min in order to stabilize the dispersion of the nanoparticles. Experimental observation shows that the stable dispersion of CuO nanoparticles can be kept for more than 12 h without coagulation or deposition (Peng et al., in press). This is much longer than the duration of each test which is less than 4 h. Moreover, the flow effect of the fluid and the disturbance effect of the bubbles in the flow boiling process of the refrigerant-based nanofluid can prevent the deposition of nanoparticles (Das et al., 2003; Liu et al., 2007). Therefore, the change of nanoparticle concentration during a single experiment can be ignored. Tests of pressure drop were repeated for three times under several test conditions, and it shows that the deviations among the three tested pressure drops under each condition are less than 5%. The small deviations indicate that the experiment has good repeatability and the change of nanoparticle concentration can be ignored.

Table 3 – Properties of CuO nanoparticle. Property Molecular mass Average particle diameter Density Thermal conductivity Isobaric specific heat

Unit g/mol nm kg m3 W m1 K1 J kg1 K1

Value 79.54 40 6320 32.9 550.5

Fig. 2 – TEM photograph of CuO nanoparticles.

4.

Data reduction and uncertainties

4.1.

Frictional pressure drop

The frictional pressure drop DPr,n,frict of refrigerant-based nanofluid flow boiling inside tube can be calculated by Eq. (1): DPr;n;frict ¼ DPr;n;total  DPr;n;static  DPr;n;mom

(1)

The total pressure drop DPr,n,total is measured by the differential pressure transducer. For a horizontal tube, the static pressure drop DPr,n,static ¼ 0. The momentum pressure drop DPr,n,mom is calculated by Eq. (2), and it was always less than 5% of the total pressure drop at the test conditions during the experiments. ( DPr;n;mom ¼ D

G2 x2 G2 ð1  xÞ2 þ 3rr;n;V ð1  3Þrr;n;L

) (2)

where, G is the mass flux of refrigerant-based nanofluid, kg m2 s1; x is the vapor quality; rr,n,V and rr,n,L are the vaporphase and liquid-phase densities of refrigerant-based nanofluid, respectively, kg m3; 3 is the void fraction and can be estimated from the drift flux model for horizontal tubes (Steiner, 1993), as shown in Eq. (3). 3¼

"

  x 1x ð1 þ 0:12ð1  xÞÞ þ rr;n;V rr;n;V rr;n;L   1=4 #1 1:18ð1  xÞ gsr;n rr;n;L  rr;n;V þ 1=2 Grr;n;L x

(3)

where, sr,n is the surface tension of refrigerant-based nanofluid, N m1. The surface tension of refrigerant-based nanofluid sr,n can be replaced by the surface tension of pure refrigerant because the effect of nanoparticles on the surface tension of nanofluid can be ignored (Das et al., 2003). The vapor-phase density of refrigerant-based nanofluid rr,n,V can be replaced by the vapor-phase density of pure refrigerant because most of nanoparticles exist in the liquid-phase refrigerant-based

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Table 4 – Uncertainties of parameters. Parameter

Uncertainty 

Temperature, T ( C) Pressure, P (kPa) Mass flow rate, m (kg s1) Power input (W) Mass flux, G (kg m2 s1) Heat flux, q (W m2) Pressure drop, DP (kPa)

0.1  C 0.1% 1.5% 0.5% 1.54% 4.94% 0.1 kPa

nanofluid. The liquid-phase density of refrigerant-based nanofluid rr,n,L is calculated by Eq. (4): rr;n;L ¼

ð1  x þ xuÞrr;L rn urr;L þ ð1  xÞð1  uÞrn

(4)

where, rr,L is the liquid-phase density of pure refrigerant; rn is the density of nanoparticle; u is the mass fraction of nanoparticles.

4.2.

Local vapor quality

The local vapor quality x of refrigerant-based nanofluid flow boiling inside tube is defined as follows: x¼

mr;;n;V mr;n;V þ mr;n;L

(5)

where, mr,n,V represents the mass flow rate of refrigerantbased nanofluid vapor phase, kg s1; mr,n,L represents the mass flow rate of refrigerant-based nanofluid liquid phase, kg s1. The local vapor quality x of refrigerant-based nanofluid flow boiling inside tube can be calculated as Peng et al., in press did.

4.3.

Uncertainties

The uncertainties of parameters including pressure drop are listed in Table 4. The uncertainties of parameters are estimated based on the analysis of error propagation reported by Moffat (1998).

5.

Results and discussion

Experimental data of the frictional pressure drop of CuO/R113 nanofluid versus the vapor quality at three mass fluxes of 100, 150 and 200 kg m2 s1 are shown in Fig. 3(a)–(c), respectively. It can be seen that the frictional pressure drop of CuO/R113 nanofluid is larger than that of pure R113 refrigerant, and increases with the increase of the mass fraction of nanoparticles. For example, when the mass flux is 100 kg m2 s1 and the vapor quality is 0.275, the frictional pressure drop increases 20.8% with the change of the mass fraction of nanoparticles from 0 to 0.5 wt%. It can also be seen from the figures that the frictional pressure drop increases with the increase of vapor quality of CuO/R113 nanofluid at a certain mass fraction of nanoparticles under the present test conditions. With the increase of vapor quality, the flow regime transforms toward the annular flow, so the frictional pressure drop is increased.

Fig. 3 – Frictional pressure drop of CuO/R113 nanofluid versus local vapor quality at different mass fluxes: (a) G [ 100 kg mL2 sL1; (b) G [ 150 kg mL2 sL1; (c) G [ 200 kg mL2 sL1.

In order to investigate the effect of nanoparticle on the frictional pressure drop quantitatively, the ratio of the frictional pressure drop of refrigerant-based nanofluid to that of pure refrigerant is defined as nanoparticle impact factor FPD:

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Fig. 4(a)–(c) show the nanoparticle impact factor FPD changing with the vapor quality at different mass fluxes. FPD are in the range of 1.05 w 1.21, 1.04 w 1.19 and 1.02 w 1.12 at mass fluxes of 100, 150 and 200 kg m2 s1, respectively. It can be seen from Fig. 4(a)–(c) that FPD increases with the increase of mass fraction of nanoparticles at each mass flux. The enhancement of the frictional pressure drop can reach 20.8%, 18.5% and 11.8% at mass fluxes of 100, 150 and 200 kg m2 s1, respectively, when the mass fraction of nanoparticles is 0.5 wt%. The reasons for occurring this phenomenon may include: 1) the viscosity of nanofluid increases with the increase of mass fraction of nanoparticles (He et al., 2007; Namburu et al., 2007; Choi et al., 2008; Nguyen et al., 2008), causing the enhancement of FPD with the increase of mass fraction of nanoparticles; 2) the collision among the nanoparticles as well as the friction between the nanoparticles and the inside tube wall increase with the increase of mass fraction of nanoparticles, causing the enhancement of FPD with the increase of mass fraction of nanoparticles. Fig. 4(a)–(c) show that the nanoparticle impact factor FPD at low and high vapor qualities (x < 0.5 and x > 0.7) is larger than that at intermediate vapor qualities (0.5 < x < 0.7). The reasons for this phenomenon may include: 1) the presence of nanoparticles promotes the transition of flow pattern to annular flow at low vapor qualities and delays the transition of flow pattern from annular to dryout flow at high vapor qualities, which leads to the obvious enhancement of the frictional pressure drop; 2) the flow pattern is kept as annular flow at intermediate vapor qualities, thus the influence of nanoparticles on flow pattern is weak, which leads to the inapparent enhancement of the frictional pressure drop. Fig. 4(a)–(c) also show that the nanoparticle impact factor FPD decreases with the increase of mass flux at given vapor quality and mass fraction of nanoparticles. It is conjectured that the increase of mass flux promotes annular flow, concealing the influence of nanoparticles on the frictional pressure drop.

6. Frictional pressure drop correlation for refrigerant-based nanofluid

Fig. 4 – Nanoparticle impact factor FPD of CuO/R113 nanofluid versus local vapor quality at different mass fluxes: (a) G [ 100 kg mL2 sL1; (b) G [ 150 kg mL2 sL1; (c) G [ 200 kg mL2 sL1.

FPD ¼ DPr;n;frict =DPr;frict

(6)

where, DPr,n,frict is the frictional pressure drop of refrigerantbased nanofluid, Pa; and DPr,frict is the frictional pressure drop of pure refrigerant, Pa.

To develop the frictional pressure drop correlation for refrigerant-based nanofluid, an effective method is to use the nanoparticle impact factor to correct the frictional pressure drop of pure refrigerant. It can be seen from experimental results that the nanoparticle impact factor is related to the nanoparticle concentration, the mass flux, and the vapor quality. Furthermore, the pressure drop of particle-liquid mixture flowing inside a tube is directly proportional to the diameter and density of the particle, and inversely proportional to the tube diameter (Wasp et al., 1977). Therefore, the nanoparticle impact factor should be expressed as the function of the nanoparticle concentration, the physical properties of nanoparticle including the average diameter and density of nanoparticle, the mass flux, and the vapor quality. Using the experimental data shown in Fig. 4, we can get the nanoparticle impact factor equation as follows:

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Fig. 5 – Comparison of the experimental nanoparticle impact factors with the predicted values by the nanoparticle impact factor equation.

 dn r FPD ¼ exp 4  2:19  107  þ 37:26  n  0:63  G Di rr;L

  217:73  x  ð1  xÞ

Fig. 7 – Comparison of the experimental frictional pressure drops with the predicted values by the nanoparticle impact factor equation combining Friedel correlation.

(7)

where, 4 is the volume fraction of nanoparticles; dn is the average diameter of nanoparticles; Di is the inside diameter of the smooth tube; rn is the density of nanoparticle; rr,L is the liquid-phase density of pure refrigerant.

Fig. 6 – Comparison between the experimental frictional pressure drops of pure R113 and the predicted values by the existing frictional pressure drop correlations.

Fig. 5 presents the comparison of the experimental nanoparticle impact factors FPD with the predicted values by the nanoparticle impact factor equation. The predictions agree with 99% of the experimental nanoparticle impact factors within the deviation of 5%, and the maximum deviation is 5.1% and the mean deviation is 2.1%. The frictional pressure drop of refrigerant-based nanofluid can be calculated by Eq. (8): DPr;n;frict ¼ FPD $DPr;frict

(8)

In Eq. (8), the frictional pressure drop of pure refrigerant DPr,frict can be calculated by the existing frictional pressure drop correlations using the properties of pure refrigerant. To select a suitable frictional pressure drop correlation for calculating DPr,frict in Eq. (8), the experimental frictional pressure drops of pure R113 are compared with the predictions of the existing classical frictional pressure drop correlations including Lockhart and Martinelli correlation (Lockhart and Martinelli, 1949), Friedel correlation (Friedel, 1979), and Mu¨ller-Steinhagen and Heck correlation (Mu¨llerSteinhagen and Heck, 1986), as shown in Fig. 6. It can be seen from Fig. 6 that the predicted frictional pressure drops of pure R113 agree well with the experimental data within the deviation of 35% w 20%, and Friedel correlation has the best accuracy. Therefore, the nanoparticle impact factor equation combining Friedel correlation is recommended for predicting the frictional pressure drop of refrigerant-based nanofluid. Fig. 7 shows the comparison of the experimental frictional pressure drops of refrigerant-based nanofluid with the predicted values by the nanoparticle impact factor equation combining Friedel correlation. It is shown that the predictions of nanoparticle impact factor equation combining Friedel correlation agree with 92% of the experimental data within the deviation of 15%, and the mean and maximum

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deviations of the predictions from the experimental data are 10.2% and 19.4%, respectively. The physical properties of nanoparticle and refrigerant are included in the nanoparticle impact factor equation, so the nanoparticle impact factor equation combining Friedel correlation can be used to other kinds of refrigerant-based nanofluids. But this frictional pressure drop correlation has been verified only by one kind of refrigerant-based nanofluid in the present study, and more verifications are needed in the future in order to ensure the accuracy of this correlation for other kinds of refrigerant-based nanofluids.

7.

Conclusions

1) The frictional pressure drop of refrigerant-based nanofluid flow boiling inside the horizontal smooth tube is larger than that of pure refrigerant, and increases with the increase of the mass fraction of nanoparticles. The maximum enhancement of frictional pressure drop can reach 20.8% under the experimental conditions. The nanoparticle impact factor FPD at low and high vapor qualities (x < 0.5 and x > 0.7) is larger than that at intermediate vapor qualities (0.5 < x < 0.7). The nanoparticle impact factor FPD decreases with the increase of mass flux at given vapor quality and mass fraction of nanoparticles. 2) A nanoparticle impact factor equation is proposed. The nanoparticle impact factors predicted by the equation are in good agreement with 99% of the experimental data within the deviation of 5%, and the maximum and mean deviations are 5.1% and 2.1%, respectively. 3) A frictional pressure drop correlation for refrigerant-based nanofluid is proposed, and the predicted frictional pressure drops agree with 92% of the experimental data within the deviation of 15%.

Acknowledgements The authors gratefully acknowledge the support from the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-05-0403) and International Copper Association.

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