Water Nanofluid or Helical Coiling

Article pubs.acs.org/IECR

Multiwalled Carbon Nanotube/Water Nanofluid or Helical Coiling Technique, Which of Them Is More Effective? Mostafa Kahani, Saeed Zeinali Heris,* and Seyed Mahmoud Mousavi Chemical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Khorasan Razavi, Iran ABSTRACT: A set of experiments were performed to investigate the effect of two different techniques of heat transfer enhancement: nanofluidics and helical coiling. The convection heat transfer behavior of multiwalled carbon nanotube (MWCNT)/water nanofluids through helical coiled tubes with different geometries was reported. Solutions of 0.1, 0.3, and 0.5% particle weight concentration of MWCNT in distilled water were prepared using a two-step method, and the effects of a wide range of different parameters such as Reynolds and Helical numbers, geometrical parameters of the coils, and nanofluid weight fractions were studied. It was observed that by increasing the Reynolds number or weight concentration of nanofluid, the Nusselt number increases considerably. The maximum thermal performance factor at 4.24 was achieved in this study. Also, the helical coiling technique showed better performance than nanofluidics in these experiments. In addition, the empirical correlations were developed for Nusselt number and pressure drop in terms of Helical number, Prandtl number, and weight concentration fit to the experimental data within +25% and −20%.

1. INTRODUCTION Heating or cooling fluids play a vital role in many industrial sectors, including energy supply and production, transportation, and electronics. Thus, development of advanced heat transferring fluids is clearly essential to improving the effective heat transfer behavior of conventional fluids, and various techniques have been proposed to reach this goal. One of the most suitable methods which has been used is to add nanoparticles of highly thermally conductive materials like carbon, metal, and metal oxides into heat transfer fluids to enhance thermal performance of highly efficient equipment.1,2 The synthesis, physical properties, and convective heat transfer of nanofluids have been considered by many researchers.3−9 Nanofluids have great potentials in heat transfer enhancement applications because of their intriguing properties such as considerable increase in thermal conductivity and prevention of clogging in microchannels.10 Also, nanofluids have been used as a new working medium in different applications.11−15 Carbon nanotubes (CNTs) are excellent candidates as dispersions for preparing thermal conductivity enhanced nanofluids due to their very high thermal conductivity and very large aspect ratio.16,17 However, the CNTs always form aggregates owing to very strong van der Waals interactions, nonreactive surface properties, and very large specific surface areas and aspect ratios.18 Assael et al.19 have observed a thermal conductivity enhancement of 38% for 0.6 vol% CNTs in water stabilized by SDS and CTAB. Ding et al.20 have reported a maximum enhancement of 79% at 1.0 wt % MWCNT dispersed in water with SDBS as a surfactant and also 350% enhancement in heat transfer coefficient for 0.5 wt % aqueous MWCNT suspension flowing through a horizontal tube. Faulkner et al.21 have investigated the convective heat transfer of CNT/water nanofluid in a microchannel. Their results showed an enhanced heat transfer coefficient of CNT/water at the highest concentration. On the other hand, helical coiled circular tubes have received attention in the literature due to their frequent use in heat © 2013 American Chemical Society

exchangers, chemical reactors, and other devices. They offer more efficient heat transfer, reduced back mixing, and smaller space requirements compared with straight tubes.22 Unlike the flow in straight pipe, fluid motion in a curved pipe is not parallel to the curved axis of the bend, owing to the presence of a secondary motion caused by secondary flow. The secondary flow is induced due to the difference in the centrifugal force caused by fluid elements moving with different axial velocities. The facts concerning the working principle of curved tubes and the reasons for its enhanced performance are well established as mentioned: (a) generation of secondary flow due to unbalanced centrifugal forces; (b) enhanced cross-sectional mixing; (c) reduction in axial dispersion; (d) improved heat-transfer coefficient; (e) improved mass-transfer coefficient.23 In our previous work, the effects of curvature ratio and coil pitch spacing for Al2O3/water nanofluid laminar flow on heat transfer behavior and pressure drop through helical coils have been investigated experimentally.24 The empirical data showed that reducing the curvature ratio or increasing the pitch spacing of the coil lead to incrementing the heat transfer rate and pressure drop. Besides, a detailed comparative study between metal oxide nanoparticles on thermal characteristics of nanofluid flow through helical coils has been done by Kahani et al.25 The results confirmed that Al2O3/water nanofluid which has greater thermal conductivity and also smaller particle size shows better thermal performance compared with TiO2/water nanofluid. Fakoor Pakdaman et al.26 have obtained high overall performance index of up to 6.4 for MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes. AkhavanBehabadi et al.27 have emphasized that utilizing vertical helical coiled tubes instead of straight ones enhances the heat transfer Received: Revised: Accepted: Published: 13183

April 6, 2013 August 13, 2013 August 15, 2013 August 15, 2013 dx.doi.org/10.1021/ie4010942 | Ind. Eng. Chem. Res. 2013, 52, 13183−13191

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematics of the experimental apparatus.

reported that utilization of base fluid in helical tube with greater curvature ratio compared to the use of nanofluid in straight tubes enhanced heat transfer more effectively. In the present investigation, thermal performance of MWCNT/water nanofluid flow inside helical coiled tubes was examined in an attempt to answer the following question: Nanofluids or helical coils, which of them is more effective to enhance heat transfer rate?

rate remarkably. Besides, nanofluid flows showed much higher Nusselt numbers compared to the base fluid flow. They used MWCNT in heat transfer oil to run their experiments and reported that the Nusselt numbers acquired for the heat transfer oil inside tested helical coils were 3−7 times higher than the values evaluated for the base fluid inside straight tubes with a similar length of the coils. Last but not the least, Akbaridoust et al.28 have investigated the pressure drop and the convective heat transfer behavior of CuO/water nanofluid flows in helical coiled numerically and experimentally. Also, they employed dispersion model to make the observed difference between numerical and experimental results negligible and

2. MATERIALS AND PROCEDURES 2.1. Experimental Apparatus. The schematics of the experimental apparatus are shown in Figure 1. The flow loop 13184

dx.doi.org/10.1021/ie4010942 | Ind. Eng. Chem. Res. 2013, 52, 13183−13191


Article

consisted of test sections, a cooler, a pump, a manometer, a dampener, a flow measuring unit, and thermocouples. As shown in Table 1, three copper helical coiled tubes (HCT) with different geometries and a straight tube were used in the test sections. Table 1. Dimensions of Helical Coils and Straight Tube d (mm)

tube HCT-I HCT-II HCT-III straight tube

7

t (mm)

0.5

L (mm)

D (mm)

λ

b (mm)

N

140 70 70

20 10 10

24 42 24

3 6 6

1318.8

Figure 2. TEM images of MWCNTs powder.

CNTs and also it reduces the presence of aggregates, as well as to adjust the pH of the nanofluid, it was employed by other researchers too.13,14,20,30,34 The optimum value of GA is crucial for minimizing the agglomeration and sedimentation of nanoparticles in the fluids. An appropriate amount of MWCNT and GA powders were added to distilled water using a magnetic stirrer for 2 h. Then, the suspensions were taken under sonication for 30 min by Hielscher ultrasonic processor (UP400S).The nanofluid in 0.1, 0.3, and 0.5 wt % concentrations was prepared. Also, the samples were kept in the stationary state for at least 6 days and were found them quite stable without visually observable sedimentation. In addition, the density of prepared nanofluids was measured once nanofluid prepared and also after 6 days. The reasonable agreement was achieved between the results which emphasizes the stable behavior of nanofluids without considerable sedimentation. 2.3. Theoretical Consideration. Experimental convective heat transfer coefficient and Nusselt number for nanofluid were calculated from the following equations:

To obtain a constant-heat flux boundary condition, the electric resistance was utilized around the heat transfer section. All the tests were performed under the same input power (100 W), and the tubes were covered by two thick layers of rock wool and fiberglass sheets as well. Two (PT100-type) thermocouples were inserted into the calming and mixing chambers of the flow at the inlet and the outlet of each test section for measuring the bulk temperatures of working fluids and other thermocouples from the same type were inserted through the little soldered tubes on the surface of the each test section at different points over the tubes. Plus, the accuracy of the all thermocouples was ±0.1%. A differential U-tube manometer was fitted across the test section to measure the pressure drop along the tubes. Also, a bypass line to adjust the flow rate was fabricated. To minimize the vibration and to ensure steady flow, a flow dampener was located before the test section. The working fluid leaving the test section was pumped through a heat exchanger (cooler) in which water was used as cooling fluid, then entered the flow measuring apparatus, and again flowed back to the reservoir tank. Each measurement was repeated at least two times. The essential parameters that were measured include electric input power, flow rate, bulk temperatures (inlet and outlet), outer wall temperatures, and pressure drops of working fluid along the coils. 2.2. Nanofluid Preparation. The specifications of the MWCNTs which were used in this study are listed in Table 2,

h(exp) =

outer diameter (nm)

length (μm)

actual density (kg/m3)

CP (J/kg·K)

k (W/m·K)

>95

10−20

∼30

2100

530

∼2000

A(Tw − Tb)M

(1)

h(exp)d (2) k where (Tw − Tb)M is the logarithmic mean temperature difference. After computing Nu(exp), the values are compared with Nu(theory) which can be calculated from Manlapaz and Churchill35 equation as follows: Nu(exp) =

Table 2. Physical Characteristics of MWCNTs Powder purity (%)

mC ̇ p(Tb1 − Tb2)

⎧⎡ ⎪ ⎪⎢ 4.63 NuC = ⎨⎢4.36 + 1342 ⎪ 1+ ⎪⎢⎣ PrHe 2 ⎩

(

and the morphological characterizations of powders obtained using transmission electron microscopy (TEM) are shown in Figure 2. TEM images clearly show that the CNT core is hollow with multiple layers almost parallel to the CNT axis. It is known that CNTs have a hydrophobic surface, which is prone to aggregation and precipitation in water in the absence of a surfactant.29,30 Gum arabic (GA) with a concentration of half weight percent of the MWCNTs was employed as the dispersant. The GA which is a complex mixture of glycoproteins and polysaccharides was used in experiments because of its high thermal stability compared with other counterparts such as sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfonate (SDBS), N-hydroxysuccinimide (NHS), and chitosan.1,31−33Since the GA surfactant plays an important role in dispersing and stabilizing of different kind of

⎡ He + 1.86⎢ ⎢⎣ 1 + 1.15 Pr

⎤3 ⎥ 2⎥ ⎥⎦

)

⎫1/3 ⎤3/2 ⎪ ⎪ ⎥ ⎬ ⎥⎦ ⎪ ⎪ ⎭

(3)

Also, four important dimensionless parameters on the nanofluid flow through helical coils, including Reynolds number (Re), Dean number (De), Prandtl number (Pr), and Helical number (He) are defined as follows:

13185

Re = ρUd/ ̅ μ

(4)

De = Re(d /D)1/2

(5)


Industrial & Engineering Chemistry Research Pr = μC P/k

Article

uncertainty of nanofluid specific heat calculation only depends on the uncertainty of nanofluid volume concentration (Uφ). The nanoparticles volume measurement error is UVs = ± 1.0 × 10−2, and also, the total volume of nanofluid error is UVt = ±10/ 2500 = ±4 × 10−3, so the maximum volume concentration error is calculated at Uϕ = ±[UVs2 + (−UVt)2]1/2 = ±1.07 × 10−3 and then the specific heat uncertainty is measured at UCp = (2Uϕ) = ±2.14 × 10−2. In addition, Patel model36 predictions successfully match a wide range variety of experimental data which are available in literature by a reasonable uncertainty.36 On the basis of these observations and applying 4.0% uncertainty on thermal conductivity, the maximum uncertainty of the Nusselt number calculated taking into account the above considerations is obtained at 6.14%.

(6)

1/2 ⎡ ⎛ b ⎞2 ⎤ ⎟ ⎥ He = De⎢1 + ⎜ ⎝ 2πD ⎠ ⎦ ⎣

(7)

36

Plus, the Patel model was applied for determination of nanofluid effective thermal conductivity as follows: ⎡ ⎤ k pφrf ⎥ k nf = k f ⎢1 + k f (1 − φ)rp ⎦⎥ ⎣⎢

(8)

The liquid particle size (rf) or average molecular size of water which used for calculations is 20 nm. Besides, the Ebrahimnia− Bajestan correlation37 was used in order to predict the dynamic viscosity of MWCNT/water nanofluid as follows: μnf = μf (1 + 22.7814φ − 9748.4φ 2 + 1 000 000φ3)

4. EXPERIMENTAL RESULTS AND DISCUSSION At the beginning, a set of experiments with distilled water were performed to establish the accuracy and reliability of the experiments. Figure 3 shows the measured Nusselt number of

(9)

where φ is the volume fraction of the CNTs. Equation 9 is applicable for the CNTs volume fractions less than 1%. The physical properties of the prepared nanofluids were calculated from water and nanoparticle characteristics at mean inlet and outlet bulk temperature using following equations for density and specific heat: ρnf = φρs + (1 − φ)ρf

(10)

Cp = φCp + (1 − φ)Cp nf

p

f

(11)

3. UNCERTAINTY OF EXPERIMENTS Equation 12 is a common relation which used for prediction of experimental errors:38 X ∂P UPi = i UXi P ∂Xi (12)

Figure 3. Comparison between theoretical and experimental Nusselt numbers of distilled water flow inside tubes.

in which Xi is the measurable parameter, P is the calculated quantity from the measurable parameter, UXi is the measured error, and UPi is the maximum error of a parameter. The influence of all errors in calculation of goal function can be summarized as follows:39

distilled water in helical coils in comparison with the theoretical one (eq 3) for laminar flow under constant flux condition. As it is shown, the deviation of the experimental data from the theoretical one is within −12% and +32%, and a reasonable agreement between experimental and theoretical correlation results is obtained which emphasizes the reliability of experimental results. In addition, in order to evaluate the repeatability of the results, some nanofluid samples selected randomly and the experiments repeated two times; one immediately after nanofluid preparation and other one after 6 days. The comparison results are shown in Figure 4. As it can be seen as well from this figure, there is a suitable agreement between the results of two different samples which confirms the sufficient reproducibility of experiments. 4.1. Nusselt Number. The variation of Nusselt number as a function of Reynolds number for distilled water and nanofluid flows through straight tube and helical coils are shown in Figure 5. It can be seen that the Nusselt number of nanofluid is greater than distilled water and is intensified by increasing Reynolds number and weight fraction of nanopowders. The superior thermal conductivity of nanofluid as compared to water and also reduction of boundary layer thickness as reported in previous literature40,41 are the main reasons to describe this kind of trend. Moreover, at higher Reynolds number, the

2 ⎡⎛ ⎞2 ⎛ X ∂P X ∂P ⎞ max UP = ±⎢⎜ 1 U1⎟ + ⎜ 2 U2⎟ + ... ⎢⎣⎝ P ∂X1 ⎠ ⎝ P ∂X 2 ⎠ 0.5 ⎛ Xi ∂P ⎞2 ⎤ UXi⎟ ⎥ +⎜ ⎝ P ∂Xi ⎠ ⎥⎦

(13)

The uncertainty of the experimental data may have resulted from measuring errors of parameters such as mass flow rate, inlet and outlet temperature difference, the logarithmic mean temperature difference between surface and fluid, and also the thermal conductivity and specific heat of nanofluid. It can be calculated using eq 13 for the Nusselt number: max UNu = ±[(Uṁ )2 + (UCp)2 + (U(Tb1− Tb2))2 + ( −U(Tw − Tb)M)2 + ( −Uk)2 ]0.5

(14)

Flow rates were measured directly from the taken time to fill a glass vessel of known volume with 4.0% uncertainty in measurement. Also, the uncertainty of the temperature difference is calculated at 0.74%. Considering eq 11, the 13186



Article

Table 3. Comparison between Heat Transfer Rate of Nanofluid Flows through HCT-III Considering the GA Effect h (W/m2·K) Re 620

3180

concentration wt %

with surfctant (GA)

without surfactant (GA)

deviation (%)

0.1 0.3 0.5 0.1 0.3 0.5

1499.2 1702.3 2090.8 4052.3 4636.6 5090.0

1512.5 1722.4 2138.9 4126.9 4730.7 5146.5

−0.89 −1.18 −2.3 −1.84 −2.03 −1.11

Figure 4. Comparison results for investigation of the repeatability of experiments.

dispersion effects and chaotic movement of the CNTs intensifies the mixing fluctuations and changes temperature profile to a flatter profile similar to turbulent flow and causes increase in heat transfer rate.42 In addition, in order to investigate the effect of GA on thermal performance of nanofluid flows through helical coils, a set of experiments were done without surfactant too. On the basis of the data in Table 3, it can be observed that GA has not any considerable unsuitable effect on heat transfer rate of nanofluids. 4.2. Helical Coiling or Nanofluidics? The heat transfer ability of each studied techniques is considered in Figure 6. In

Figure 6. Nusselt number ratio versus Reynolds number for flow through HCT-III.

Figure 5. Nusselt number versus Reynolds number and different weight concentration of nanofluid flow inside (a) straight tube, (b) HCT-I, (c) HCT-II, and (d) HCT-III. 13187



Article

this figure, Nusselt number ratio versus Reynolds number of the flows through HCT-III is depicted. When 0.3 wt % of nanofluid is used in the helical coiled tube instead of distilled water, the maximum Nusselt number increment is 37% at Re = 1513, while applying the helical coiled tube instead of a straight one can enhance the Nusselt number up to 3.72 times at Re = 1963 for distilled water flow. These results clearly emphasized that helical coiled tube is a more suitable method to transfer heat than nanofluidics. The similar results have been presented by other researchers.27,28 In addition, when two mentioned techniques are combined together, the Nusselt number enhancement is more significant. In this case, a 341% increment in Nusselt number is observed at Re = 3180. Nusselt number ratio in different states at Re = 2250 is shown in Table 4. From this table, it is clear that the helical

Where NuC,nf and NuS,water are the Nusselt number for nanofluid flow in helical tubes and for distilled water flow in straight tube, respectively. Besides, ΔpC,nf and ΔpS,water represent respectively, the pressure drop for nanofluid flow in helical coils and for distilled water flow in straight tube. The larger the values of the thermal performance factor, the more suitable the enhancement heat transfer technique. The variation of thermal performance factor with Reynolds number for 0.5 wt % of nanofluid flow through helical coiled tubes is illustrated in Figure 7. It can be

Table 4. Nusselt Number Ratio in Different States at Re = 2250 helical coiled tube no.

NuC,water/NuS,water (helical coiling effect)

NuC,0.5%nf/NuC,water (nanofluidics effect)

NuC,0.5%nf/NuS,water (combined effect)

HCT-I HCT-II HCT-III

2.782 3.784 3.526

1.325 1.401 1.391

3.473 5.29 4.871

Figure 7. Variation of thermal performance factor with Reynolds number for 0.5 wt % nanofluid in helical coils.

coiling effect is more powerful than the nanofluidics effect. In addition, when two techniques merge together, the maximum achievable Nusselt number ratio enhancement is observed at 429% for 0.5 wt % nanofluid flow through HCT-II. Nusselt number ratio of different weight concentrations of nanofluid flows inside HCT-II at Re = 3500 is shown in Table 5. As it can be understood from this table, with increasing the

understood from this figure that the thermal performance factor is greater than unity. It means that using both techniques which were studied in this investigation is a good choice in practical application. Moreover, the highest thermal performance factor is observed for flow inside HCT-II which has the biggest pitch spacing and smallest curvature ratio among other helical coils. It means that the heat transfer ability increases as the curvature ratio decreases and pitch spacing increases.24 The main reason to support this trend is intensification of secondary flow. The smaller curvature ratio leads to the more powerful centrifugal forces which in turn causes more severe secondary flow motions. Also, this figure shows that the maximum thermal performance factor (4.24) is obtained for the nanofluid flow inside the HCT-II at Reynolds numbers of 1496.8. It worth mentioning, increasing the CNT concentration and also Reynolds number lead to considerable changes of Prandtl number which is related to physical properties of nanofluid.25 In Figures 5 and 6, the Nusselt number ratio and thermal performance factor are depicted only versus Reynolds number, some nonlinearity and nonuniform trends are observed over empirical data which is due to lack of considering Prandtl number in these figures. In the last section of this article, the influence of Prandtl number on heat transfer rate will be considered. The thermal performance factor for the different weight concentration of nanofluid flows through HCT-I is depicted in Figure 8. As shown in this figure, thermal performance increases as the nanofluid concentration increases. The use of a higher concentration of nanofluids provides better thermal performance at most of the studied Reynolds numbers remarkably. This is a result of a superior efficient of nanofluid disturbance and thus heat transfer caused by the nanofluid compared to the base fluid at the same pumping power.43 4.4. Prediction of Nusselt Number and Pressure Drop. On the basis of the experimental data and using linear

Table 5. Nusselt Number Ratio of Different Weight Concentrations of Nanofluid Flow Inside HCT-II at Re = 3500 weight concentration

NuC,nf/NuC,water

NuC,nf/NuS,water

0.1% 0.3% 0.5%

1.142 1.225 1.240

4.072 4.361 4.416

concentration of nanofluid, the Nusselt number ratio increases. The Patel model (eq 8) which is used to predict the effective thermal conductivity of a CNT nanofluid, considers two paths for heat to flow in a CNT nanofluid: one through the base liquid and the other one through the CNTs. These two paths are assumed to be in parallel to each other.36 When nanofluid concentration increases, the number of these two parallel paths increases. This means that increasing the concentration of MWCNT amplifies the mechanisms responsible for enhanced heat transfer. Therefore, in general, nanofluids with higher weight concentrations have generally higher convective heat transfer coefficients. 4.3. Thermal Performance Evaluation. In order to investigate the combined effect of two different heat transfer enhancement techniques (nanofluidics and helical coiling), the thermal performance factor (η) is defined as the ratio of the Nusselt number ratio to the pressure drop ratio:25 η=

NuC,nf /NuS,water (ΔpC,nf /ΔpS,water )1/6

(15) 13188



Article

3.

4. 5. 6. Figure 8. Variation of thermal performance factor with Reynolds number for different weight concentrations of nanofluids through HCT-I.

■

regression analysis, the Nusselt number correlation is developed for laminar MWCNT/water nanofluid flow in the range of 4.39 ≤ Pr ≤ 6.52 and 116.3 ≤ He ≤ 1473.7. NuC = 1.291He 0.530Pr 0.389φ0.117

R2 = 92.4%

AUTHOR INFORMATION

Corresponding Author

*Tel.: (+98) (511) 8816840. Fax: (+98) (511) 8805108. Email address: [email protected].

(16)

Notes

The authors declare no competing financial interest.

■

The predicted values of the Nusselt number using eq 16 versus experimental values are shown in Figure 9. This figure shows that the predicted Nusselt numbers fall within −20% and +25% of the acquired experimental values.

ACKNOWLEDGMENTS The authors appreciate the financial support from the Ferdowsi University of Mashhad and Iran Nanotechnology Initiative Council (INIC). Also, the first author wishes to thank Dr. Fattaneh Ghaderi Bafti for her valuable comments to improve the technical quality of the paper.

■

Figure 9. Comparison of the experimental values for Nusselt numbers with those predicted by eq 16.

In addition, the least-squares power-law fit on experimental data points yields the following correlation to predict pressure drop of nanofluid flow inside the helical coils, where the correlation coefficient R2 = 97.1%. ΔpC = 2.234He1.39φ0.175

conclusion is true for small concentrations of CNT nanofluid which were examined in the experiments. The maximum achievable Nusselt number ratio enhancement was observed at 429% when 0.5 wt % nanofluid is used inside helical coiled tubes instead of distilled water in a straight tube. According to the empirical data, HCT-II which has the smallest curvature ratio and the largest pitch spacing shows the best performance among other helical coils. The maximum thermal performance factor which is equal to 4.24 was obtained for the nanofluid flow inside the HCT-II. The Nusselt number and pressure drop of nanofluid flow inside helical coiled tube were correlated well with Helical number, Prandtl number, and weight concentration of nanofluid.

(17)

5. CONCLUSION Heat transfer investigation of MWCNT/water nanofluid through helical coiled tubes with different geometries was carried out under constant heat flux and laminar region, and the conclusions based on the experimental results are as follows: 1. Nusselt number of nanofluid is greater than distilled water and is intensified by increasing Reynolds number as well as the weight fraction of CNTs. 2. The helical coiling method is a more suitable technique to enhance heat transfer rate than nanofluidics. This

NOMENCLATURE A = inner surface of tube (m2) b = pitch of coil (m) Cp = specific heat (J/kg·K) d = inside diameter of tube (m) D = diameter of coil (m) De = Dean number f = Fanning friction factor h = average heat transfer coefficient (W/m2·K) He = helical coil number k = thermal conductivity (W/m·K) L = length of tube (m) ṁ = mass flow rate (kg/s) N = number of coil turns Nu = average Nusselt number Pr = Prandtl number r = radius (nm) Re = Reynolds number R2 = correlation coefficient T = temperature (K) t = thickness of wall tube (m) U̅ = average velocity (m/s)

Greek Letters

ΔP = axial pressure drop (Pa) η = thermal performance factor ρ = density (kg/m3) μ = dynamic viscosity (Pa·s) λ = curvature ratio (= D/d) φ = nanoparticle volume fraction (%)

Subscripts

b = bulk 13189



Article

(18) Park, C.; Qunaies, Z.; Watson, K.; Crooks, R.; Smith, J.; Lowther, S.; Connell, J.; Siochi, E.; Harrison, J.; Clair, T. Dispersion of single wall carbon nanotubes by in situ polymerization under sonication. Chem. Phys. Lett. 2002, 364, 303. (19) Assael, M. J.; Chen, C. F.; Metaxa, I.; Wakeham, W. A. Thermal Conductivity of Carbon Nanotube Suspensions in Water. Int. J. Thermophys. 2004, 25, 971. (20) Ding, Y.; Alias, H.; Wen, D.; Williams, R. A. Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). Int. J. Heat Mass Tansfer 2006, 49, 240. (21) Faulkner, D.; Rector, D. R.; Davison, J. J.; Shekarriz, R. Enhanced Heat Transfer through the Use of Nanofluids in Forced Convection. In Proceedings of the ASME Heat Transfer Division; ASME: New York, 2004; Vol. 219. (22) Naphon, P.; Wongwises, S. A. Review of flow and heat transfer characteristics in curved tubes. Renewable Sustainable Energy Rev. 2006, 10, 463. (23) Vashisth, S.; Kumar, V.; Nigam, K. D. P. A review on the potential applications of curved geometries in process industry. Ind. Eng. Chem. Res. 2008, 47, 3291. (24) Kahani, M.; Zeinali Heris, S.; Mousavi, S. M. Effects of curvature ratio and coil pitch spacing on heat transfer performance of Al2O3/ Water Nanofluid laminar Flow through helical coils. J. Disper. Sci. Technol. 2013, DOI: 10.1080/01932691.2013.764485. (25) Kahani, M.; Zeinali Heris, S.; Mousavi, S. M. Comparative study between metal oxide nanopowders on thermal characteristics of nanofluid flow through helical coils. Powder Technol. 2013, 246, 82. (26) Fakoor Pakdaman, M.; Akhavan-Behabadi, A.; Razi, P. An experimental investigation on thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes. Exp. Therm. Fluid Sci. 2012, 40, 103. (27) Akhavan-Behabadi, M. A.; Fakoor Pakdaman, M.; Ghazvini, M. Experimental investigation on the convective heat transfer of nanofluid flow inside vertical helically coiled tubes under uniform wall temperature condition. Int. Commun. Heat Mass. 2012, 39, 556. (28) Akbaridoust, F.; Rakhsha, M.; Abbassi, A.; Saffar-Avval, M. Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model. Int. J. Heat Mass Tansfer 2013, 58, 480. (29) Zhang Z.; Lockwood F. E. Preparation of stable nanotubes dispersions in liquids. US Patent US6783746B1, 2004. (30) Rashmi, W.; IsmailA., F.; Sopyan, I.; Jameel, A. T.; Yusof, F.; Khalid, M.; Mubarak, N. M. Stability and thermal conductivity enhancement of carbon nanotube nanofluid using gum Arabic. J. Exp. Nanosci. 2011, 6, 567. (31) Bandyopadhyaya, R.; Nativ-Roth, E.; Regev, O.; Rozen, R. Y. Stabilization of individual carbon nanotubes in aqueous solutions. Nano Lett. 2002, 2, 25. (32) Liu, M. S.; Lin, M. C. C.; Huang, I. T.; Wang, C. C. Enhancement of thermal conductivity withcarbon nanotube for nanofluids. Int. J. Heat Mass Tansfer 2005, 32, 1202. (33) Phuoc, T. X.; Massoudi, M.; Chen, R. H. Viscosity and thermal conductivity ofnanofluids containing multi-walled carbon nanotubes stabilized by chitosan. Int. J. Thermal Sci. 2011, 50, 12. (34) Ruan, B.; Jacobi, A. M. Heat transfer characteristics of multiwall carbon nanotube suspensions (MWCNT nanofluids) in intertube falling-film flow. Int. J. Heat Mass Tansfer 2012, 55, 3186. (35) Manlapaz, R. L.; Churchill, S. W. Fully developed laminar convection from a helical coil. Chem. Eng. Commun. 1981, 97, 185. (36) Patel, H. E.; Anoop, K. B.; Sundararajan, T.; Das, S. K. Model for thermal conductivity of CNT-nanofluids. Bull. Mater. Sci. 2008, 31, 387. (37) Ebrahimnia-Bajestan E.; Niazmand H. Convective heat transfer of nanofluids flows through an isothermally heated curved pipe. Iran J. Chem. Eng. 2011, 8. (38) Young, H. D. Statistical treatment of experimental data; McGrawHill: New York, 1962. (39) Holman, J. D. Experimental methods for engineers; McGraw-Hill: NewYork, 1986.

C = coiled tube f = base fluid: water nf = nanofluid p = particle S = straight tube w = wall Abbreviation

GA = Gum Arabic HCT = helical coiled tube MWCNT = multiwalled carbon nanotube wt = weight fraction

■

REFERENCES

(1) Wen, D.; Ding, Y. Effective thermal conductivity of aqueous suspensions of carbon nanotubes (carbon nanotube nanofluids). J. Thermophys. Heat Transfer 2004, 18, 481. (2) Assael, M. J.; Metaxa, I.; Arvanitidis, J.; Christofilos, D.; Lioustas, C. Thermal conductivity enhancement in aqueous suspensions of carbon multi-walled and double-walled nanotubes in the presence of two different dispersants. Int. J. Thermophys. 2005, 26, 647. (3) Xiea, H.; Yua, W.; Chena, W. MgO nanofluids: higher thermal conductivity and lower viscosity among ethylene glycol-based nanofluids containing oxide nanoparticles. J. Exp. Nanosci. 2010, 5, 463. (4) Rahman, M. M.; Ö ztop, H. F.; Ahsan, A.; Saidur, R.; Al-Salem, K.; Rahim, A. Laminar Mixed Convection in Inclined Triangular Enclosures Filled with Water Based Cu Nanofluid. Ind. Eng. Chem. Res. 2012, 51, 4090. (5) Nkurikiyimfura, I.; Wanga, Y.; Pan, Z. Effect of chain-like magnetite nanoparticle aggregates on thermal conductivity of magnetic nanofluid in magnetic field. Exp. Therm. Fluid Sci. 2013, 44, 607. (6) Teng, T.; Hung, Y. Estimation and experimental study of the density and specific heat for alumina nanofluid. J. Exp. Nanosci. 2012, DOI: 10.1080/17458080.2012.696219. (7) Hussein, A. M.; Sharma, K. V.; Bakar, R. A.; Kadirgama, K. The effect of cross sectional area of tube on friction factor and heat transfer nanofluid turbulent flow. Int. J. Heat Mass Tansfer 2013, 47, 49. (8) Fan, L.; Hemminger, O.; Yu, Z.; Wang, F. Bubbles in Nanofluids. Ind. Eng. Chem. Res. 2007, 46, 4341. (9) Amrollahia, A.; Rashidia, A. M.; Emami Meibodia, M.; Kashefia, K. Conduction heat transfer characteristics and dispersion behaviour of carbon nanofluids as a function of different parameters. J. Exp. Nanosci. 2009, 4, 347. (10) Urbant, P.; Leshansky, A.; Halupovich, Y. On the forced convective heat transport in a droplet-laden flow in microchannels. Microfluid Nanofluid 2008, 4, 533. (11) Noie, S. H.; Zeinali Heris, S.; Kahani, M.; Nowee, S. M. Heat transfer enhancement using Al2O3/water nanofluid in a two-phase closed thermosyphon. Int. J. Heat Fluid Flow 2009, 30, 700. (12) Ali, I. M. M.; Saidur, R. Nanofluid as a coolant for electronic devices (cooling of electronic devices). Appl. Therm. Eng. 2012, 32, 76. (13) Shanbedi, M.; Zeinali Heris, S.; Baniadam, M.; Amiri, A.; Maghrebi, M. Investigation of heat-transfer characterization of EDAMWCNT/DI-water nanofluid in a two-phase closed thermosyphon. Ind. Eng. Chem. Res. 2012, 51, 1423. (14) Azizi, M.; Hosseini, M.; Zafarnak, S.; Shanbedi, M.; Amiri, A. Experimental analysis of thermal performance in a two-phase closed thermosyphon using graphene/water Nanofluid. Ind. Eng. Chem. Res. 2013, 52, 10015. (15) Tiwari, A. K.; Ghosh, P.; Sarkar, J. Heat transfer and pressure drop characteristics of CeO2/water nanofluid in plate heat exchanger. Appl Therm Eng 2013, 57, 24. (16) Berber, S.; Kwon, Y.; Domanek, T. unusually high thermal conductivity of carbonnanotubes. Phys. Rev. Lett. 2000, 84, 4613. (17) Kim, P.; Shi, L.; Majumdar, A.; McEuen, P. L. Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 2001, 87, 215502/1. 13190



Article

(40) Zeinali Heris, S.; Etemad, S. G.; Nasr Esfahany, M. Experimental investigation of oxide nanofluids laminar flow convective heat transfer. Int. Commun. Heat Mass 2006, 33, 529. (41) Nassan, T. H.; Zeinali Heris, S.; Noie, S. H. A comparison of experimental heat transfer characteristics for Al2O3/water and CuO/ water nanofluids in square cross-section duct. Int. Commun. Heat Mass 2010, 37, 924. (42) Hamed Mosavian, M. T.; Zeinali Heris, S.; Etemad, S. G.; Nasr Esfahany, M. Heat transfer enhancement by application of nanopowder. J. Nanopart. Res. 2010, 12, 2611. (43) Abbasian Arani, A.; Amani, J. Experimental study on the effect of TiO2−water nanofluid on heat transfer and pressure drop. Exp. Therm. Fluid Sci. 2012, 42, 107.

13191


Water Nanofluid or Helical Coiling

Recommend Documents