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Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube
ICHMT-03080; No of Pages 9 International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
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W.H. Azmi a,⁎, K.V. Sharma b, P.K. Sarma c, Rizalman Mamat a, G. Najafi d a
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a r t i c l e
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Available online xxxx
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Keywords: Nanofluid Titanium dioxide Silicon dioxide Friction factor Heat transfer coefficients
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Department of Mechanical Engineering, University Technology Petronas, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia GITAM University, Rishikonda, Visakhapatnam, 530045, India d Tarbiat Modares University, Jalale-E-Aleahmad Highway, Tehran, P.O. Box: 14115-111, Iran b
i n f o
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The heat transfer coefficient and friction factor of TiO2 and SiO2 water based nanofluids flowing in a circular tube under turbulent flow are investigated experimentally under constant heat flux boundary condition. TiO2 and SiO2 nanofluids with an average particle size of 50 nm and 22 nm respectively are used in the working fluid for volume concentrations up to 3.0%. Experiments are conducted at a bulk temperature of 30 °C in the turbulent Reynolds number range of 5000 to 25,000. The enhancements in viscosity and thermal conductivity of TiO2 are greater than SiO2 nanofluid. However, a maximum enhancement of 26% in heat transfer coefficients is obtained with TiO2 nanofluid at 1.0% concentration, while SiO2 nanofluid gave 33% enhancement at 3.0% concentration. The heat transfer coefficients are lower at all other concentrations. The particle concentration at which the nanofluids give maximum heat transfer has been determined and validated with property enhancement ratio. It is observed that the pressure drop is directly proportional to the density of the nanoparticle. © 2014 Published by Elsevier Ltd.
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1. Introduction
34
The heat transfer augmentation has been of significant interest and the methods of obtaining through active and passive methods have been explained by Ahuja [1] and Bergles [2]. In the classification under active type, heat transfer enhancement is associated with external energy on the fluid through forced flow and the use of electrostatic fields. Under passive augmentation, enhancement of heat transfer can be due to artificially roughed surface, extended surface, swirl flow with twisted tape inserts, convoluted or twisted tube, use of additives, etc. Early passive technique such as dispersion of micron sized particles in a base fluid for heat transfer enhancement has been undertaken. However, practical problems arose due to clogging, erosion of pipe lines and high pumping power requirements with the dispersed particles, in spite of the fact that a certain degree of heat transfer augmentation is achieved. Further, agglomeration and resettlement of particles posed a severe maintenance problem.
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Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube☆
1
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (W.H. Azmi), [email protected] (K.V. Sharma), [email protected] (P.K. Sarma), [email protected] (R. Mamat), najafi[email protected] (G. Najafi).
In contrast, recent studies with the nanometer size particles proved effective in achieving better heat transfer enhancement without any substantial increase in pumping power requirement and other associated practical problems. The nanofluids showed better stability and rheological properties, with no significant penalty on pressure drop [3]. The use of nanofluids for possible heat transfer augmentation has drawn the attention of many investigators [4–15]. The experimental determination of thermophysical properties such as viscosity and thermal conductivity of nanofluids has been initiated by Masuda et al. [4]. They determined the effect of dispersing nanosize particles of Al2O3, SiO2 and TiO2 in water. The result indicates 10% and 30% enhancement in the effective thermal conductivity of TiO2 and Al2O3 nanofluids respectively at 4.0% concentration. However, they observed an enhancement of 1.0% in thermal conductivity with SiO2 nanofluid at 1.0% concentration. Turgut et al. [5] determined the thermal conductivity and viscosity of TiO2 nanofluid for volume concentration up to 3.0% in the temperature range of 13 °C and 55 °C with particles of 21 nm diameter. The enhancement in thermal conductivity is 7.4% compared to base fluid at 13 °C. They concluded that the enhancement of nanofluid viscosity is greater than thermal conductivity. Experiments are undertaken by He et al. [6] for the determination of forced convection heat transfer coefficient at various concentrations of TiO2 nanofluid with particles of 15 nm to 95 nm size dispersed in base liquid water. Forced convection heat transfer coefficients for Re b 6500
http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007 0735-1933/© 2014 Published by Elsevier Ltd.
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
Nomenclature
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TiO2 and SiO2 nanofluids supplied in weight concentration were procured from US Research Nanomaterials, Inc. The water based nanofluid contained amorphous SiO2 nanoparticles with an average diameter of 22 nm with a concentration of 25 wt.% (13.1 vol.%). Anatase TiO2 nanoparticles of average diameter 50 nm dispersed in water are supplied at a weight concentration ω = 40 wt. % (φ = 13.6 vol. %). The initial pH of TiO2 and SiO2 nanofluids is 6.5 and 11 respectively. The procured nanofluids are prepared to desired volume concentration of 0.5–3.0 vol.% by dilution process using distilled water. The liquids prepared in this manner are subjected to mechanical homogenization for 2 h and observed for dispersion stability. The present
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2. Sample preparation
P
U
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Subscripts b bulk exp experiment EW ethylene glycol water mixture nf nanofluid p particle r ratio reg regression s surface w water
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Greek symbols α thermal diffusivity, m2/s ΔP pressure drop, Pa φ volume concentration, % ϕ volume fraction, φ = (ϕ/100) μ absolute viscosity, kg/m s μr ratio of nanofluid to water viscosity, (μnf/μw) ρ density, kg/m3 ω weight concentration, %
D
L LPM Nu OD Pr Q q Re T TEM U V
ρV =2
heat transfer coefficient, W/m2 K inner diameter, m thermal conductivity, W/m K thermal conductivity ratio of nanofluid to water, (knf/kw) tube length, m liter per minute Nusselt number, hD k outer diameter, m Prandtl number, μC k heat input, W heat flux, W/m2 Reynolds number, ρVD μ temperature, °C transmission electron microscopy uncertainty average velocity, m/s
E
h ID k kr
85 86
T
f
area, m2 specific heat, J/kg K diameter of nanoparticle, nm tube inner diameter, m electrical conductivity, μS/cm ethylene glycol property enhancement ratio Þ Darcy friction factor, DL ðΔP 2
C
A C dp D EC EG ER
investigations undertaken with different particle sizes indicate heat transfer to increase with nanofluid concentration and Reynolds number. Heat transfer coefficients are determined with SiO2 nanofluid in base liquid water at various concentrations [11–14]. Ferrouillat et al. [11] investigated the effect of inlet temperature on heat transfer coefficients. They undertook experiments under heating and cooling conditions of nanofluid with particles of 22 nm size for three inlet temperatures of 20, 50 and 70 °C in the Reynolds number range of 200 to 10,000. The results indicate 10% to 60% enhancement in heat transfer coefficients compared to the values with water under similar operating conditions. Bontemps et al. [12,13] determined the convective heat transfer coefficient with 22 nm size particles dispersed in water for flow in a circular tube under constant wall temperature and heat flux boundary conditions. Heat transfer enhancements of 30% and 100% were reported by Bontemps et al. [13] with 2.3% and 19.0% volume concentrations respectively. Julia et al. [14] undertook experiments in the Reynolds number range of 3000 to 100,000. A maximum heat transfer coefficient of 300% is reported with 5% concentration for flow in a tube at a Reynolds number of 30,000 with 12 nm particle size at nanofluid inlet temperature of 60 °C. The experimental heat transfer coefficients are determined with various particle sizes and operating temperatures. The studies undertaken by the investigators with TiO2 and SiO2 nanofluids reported an increase in heat transfer coefficient with concentration and Reynolds number. However, Duangthongsuk and Wongwises [15] determined TiO2 nanofluid heat transfer coefficients under turbulent flow with a double pipe heat exchanger for concentration up to 2.0%. They observed an increase in heat transfer coefficient with Reynolds number, for concentration up to 1.0% at the operating temperature of 25 °C. However, the heat transfer coefficients decreased for concentration more than 1.0%, but are observed to be greater than the base liquid water. Similarly, Pak and Cho [10] observed a decrease in heat transfer coefficient with Al2O3 nanofluid when the volume concentration increased to 2.78% at the operating temperature of 25 °C. Most of the earlier studies are limited to the determination of properties and heat transfer coefficient of TiO2 and SiO2 nanofluids at different conditions of flow, concentration and temperature. The studies related to heat transfer enhancement of water based TiO 2 and SiO2 nanofluids at similar operating temperature have not been reported in literature. Most of the authors reported a marginal increase in friction factor. The objective of the present study is to determine and compare under similar operating temperature, the convective heat transfer coefficients and friction factor of TiO2/ water and SiO2/water nanofluids in the turbulent range of Reynolds number for concentrations up to 3.0%. The influence of operating conditions viz., temperature and concentration on enhancement or reduction of heat transfer coefficients for the two nanofluids is determined.
in the volume concentration of 1.2% with 95 nm particles and with 21 nm size particles in the laminar range of Reynolds number have been determined. Sajadi and Kazemi [7] conducted experiments with 30 nm size particles for a maximum concentration of 0.25%, while Arani and Amani [8] undertook experiments up to 2.0% in the Reynolds number range of 8000 to 51000. Kayhani et al. [9] conducted experiments with 15 nm size particles for concentration up to 2.0% in the Reynolds number range of 7000 to 15,000. Pak and Cho [10] undertook experiments with 27 nm size for concentration up to 3.16% under turbulent flow conditions. The
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
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experimental work requires approximately 15 L of the nanofluid per cycle for the conduct of the experiment. The samples are observed to be stable for more than a week and a month respectively for TiO2 and SiO2 nanofluids. The pH of TiO2/water and SiO2/water diluted nanofluids varied between 7.2–7.7 and 8.9–10.1 respectively in the range of concentration tested. The thermo-physical properties of nanofluid such as thermal conductivity and viscosity at each concentration are determined experimentally using a KD2 Pro thermal property analyzer and Brookfield LVDV-III Ultra Rheometer, respectively. The equations for density and specific heat of nanofluid, based on mixture relation used in the analysis, are given as ρn f ¼ φ ρp þ ð1−φÞρw
ð1Þ
ð1−φÞρw þ φρp
:
ð2Þ
165
191 192
The experimental set up consists of a chiller, collecting tank, water pump, flow meter, pressure transducer, control panel, and test section. The test section consists of a copper tube of ID = 16 mm and OD = 19 mm is integrated with thermocouples, ceramic fiber insulation and heaters, the schematic diagram is given as Fig. 1. A stainless steel container of 30 liter capacity is used for storing the working liquid. It is connected to a pump of 0.5 horse power to force the liquid through the test section. The copper tube of 1.5 m length is wrapped with two nichrome heaters of 3.0 kW maximum electric rating for uniform heating. The tube along with heaters is enclosed with ceramic fiber insulation to minimize heat loss to atmosphere. Seven K-type thermocouples are fixed, five on the surface of the tube wall at 0.25, 0.5, 0.75, 1.0 and 1.25 m from the inlet and the other two measures the inlet and outlet temperature of the fluid. A digital flow meter capable of measuring in the range of 5 to 16 LPM connected between the test section and the pump determines the flow rate of the liquid with an accuracy of 0.1 LPM. When the system attains steady state, the temperatures at different locations, electric heat input and the flow rate are noted. A chiller of 1.4 kW capacity connected to the exit of the test section helps in regulating the inlet temperature of the working liquid. The heater is supplied with a constant value of 600 W, while the chiller is set to regulate the fluid temperature at 30 °C. The maximum variation in the liquid temperature is ± 1 °C. A transducer to measure pressure in the range of 0 to 6895 Pa to an accuracy of 0.5 Pa is used to determine the pressure drop across the test section.
t1:1 t1:2 Q1
Table 1 Physical properties of metal oxide nanomaterials.
180 181 182 183 184 185 186 187 188 189 190
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4.1. Dispersion and properties
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167
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3. Forced convection heat transfer apparatus
T
166
170 171
217
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The properties of nanoparticles are listed in Table 1.
168 169
4. Results and discussion
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ð1−φÞðρ C Þw þ φðρC Þp
193 194
O
162 163
Cn f ¼
A data logger is provided to record the temperature of the surface and the fluid every 5 s to determine the state of the experiment. The instrumentation error is estimated in the range of 0.01% to 1.8%. The total length of fluid flow in the tube is approximately 4.0 m which ensures turbulent flow condition at the entry of the test section. The uncertainties in the measuring instruments are given as Appendix 1. Experiments are undertaken with distilled water to determine the pressure drop and heat transfer coefficient at different flow rates. The steady state data of temperatures and pressure drop across the test section are recorded. The Darcy equation and Newton's law of cooling are used in the evaluation of friction factor and heat transfer coefficient respectively. The data of water is compared with the equations in literature to establish the consistency and reliability of the experimental results. Experiments with TiO2 and SiO2 nanofluids are undertaken for volume concentration up to 3.0% for various flow rates to determine heat transfer coefficients and friction factors. It is observed that the temperature on the outer surface of the test section measures value close to ambient. Hence, the heat loss to atmosphere is neglected in the evaluation of heat transfer coefficients. The maximum and minimum error in the experimental data is presented as Appendix 2. The stability and dispersion of nanofluids are ensured through electrical conductivity measurements and TEM images respectively.
F
149 150
3
The stability and dispersion of nanofluid are established before the conduct of the experiment. Liu et al. [17] stated that the electrical conductivity should be lower than 10 μS/cm for distilled water. The measured value for distilled water at room temperature of 28.3 °C is observed to be 6 μS/cm. The dispersion stability of nanofluids can be determined by measuring its electrical conductivity. According to Sarojini et al. [16], the nanofluid is stable, if the electrical conductivity measured before and after the conduct of experiment at each concentration does not change. A close agreement between the measured values of electrical conductivity indicates the non-agglomeration of the nanoparticles, which can be observed from Fig. 2. Fig. 3 shows the TEM photographs of TiO2 and SiO2 nanoparticles bringing out the size, shape and the state of agglomeration in the liquid. The TEM photographs at the same magnification for SiO 2 and TiO2 nanofluids at 3% concentration confirm non-agglomeration of nanoparticles. The viscosity and thermal conductivity of TiO2 and SiO2 nanofluids are determined in the volume concentration range of 0.5–4.0%. Sharma et al. [18] developed regression Eqs. (3) and (4) for the estimation of viscosity and thermal conductivity for water based nanofluids respectively, using the experimental data of various investigators. The equations are valid for concentration ϕ ≤ 4 %, liquid temperature Tnf ≤ 70 °C and
t1:3
Nanoparticle
Thermal conductivity, W/m K
Density, kg/m3
Specific heat, J/kg K
Reference
t1:4 t1:5 t1:6 t1:7 t1:8 t1:9 t1:10
SiO2 Al2O3 TiO2 Fe3O4 (magnetite) ZrO2 ZnO CuO
1.4 36 8.4 80.4 1.7 29 69
2220 3880 4175 5180 5500 5600 6350
745 773 692 670 502 514 535
Vajjha et al. [29] Pak and Cho [10] Pak and Cho [10] Sundar et al. [30] Kothandaraman and Subramanyam [31] Vajjha and Das [32], Hong et al. [33] Fotukian and Nasr Esfahany [34]
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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4
The viscosity of SiO2 nanofluid estimated with Eq. (3) is in good agreement with the experimental data and with that of other investigators [6,10,15,19] as shown in Fig. 4. The variation of thermal conductivity of TiO2 and SiO2 nanofluids with concentration is shown in Fig. 5. The experimental values are in satisfactory agreement with the values estimated with the Eq. (4) and the data from literature [10,15,20].
T
T n f −0:038 dp −0:061 ϕ 11:3 1þ 1þ 1þ 100 70 170
ð3Þ
kn f T n f 0:2777 dp −0:0336 α p 0:01737 ϕ 1:37 kr ¼ ¼ 0:8938 1 þ 1þ 1þ : kw 70 150 αw 100
R
245 246
μn f ¼ μw
R
μr ¼
C
243
particle diameter dp ≤ 170 nm. The equations have the flexibility to estimate the properties of metal and metal oxide nanofluids for spherical shape particles and water. They are given as:
E
241 242
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Fig. 1. Schematic diagram of the experimental setup.
U
N
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248
ð4Þ
250 251 252 253 254 255
4.2. Convective heat transfer coefficient
The heat transfer coefficient is evaluated with the energy balance 256 equation, assuming negligible heat loss to the surroundings. The rele- 257 vant equations used in the analysis are: 258 hexp ¼
Q As ðT s −T b Þ
ð5Þ 260
Nuexp ¼
h exp D : kn f
261
ð6Þ 263
The Reynolds and Prandtl numbers of the nanofluid are determined respectively with Eqs. (7) and (8), the properties referred at the bulk 264 temperature Tb. 265
Ren f ¼
Prn f ¼ Fig. 2. Electrical conductivity of TiO2/water and SiO2/water nanofluids at 30 °C.
249
ρn f VD μn f
μn f Cn f : kn f
ð7Þ 267 268
ð8Þ
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
Fig. 5. Comparison of experimental values of thermal conductivity with Eq. (6) of Sharma et al. [18].
P
(a) TiO2
D
The following equations are available in the literature for the estimation of Nusselt number of single phase fluids. The equation of Notter and 271 Rouse [21] for single phase fluid is given by 272 0:856
R
(b) SiO2
E
C
T
E
Nu ¼ 5 þ 0:015 Re
0:347
:
ð9Þ 274
The equation of Dittus–Boelter [22] applicable for pure fluids for Re N 104 and 0.6 b Pr b 200 is given as 275 Nu ¼ 0:023Re
0:8
Pr
0:4
:
ð10Þ 277
Eqs. (5) and (6) are used in the estimation of average heat transfer coefficient and Nusselt number of water and nanofluids. The 278 Nusselt number of distilled water estimated with Eq. (6) is in good 279 agreement with the values estimated with Eqs. (9) and (10) shown 280
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Fig. 3. TEM images of TiO2 and SiO2 nanofluids at 3 vol.%.
Pr
Fig. 4. Comparison of experimental values of viscosity with Eq. (3) of Sharma et al. [18].
Fig. 6. Comparison of experimental Nusselt number of water with equations in literature.
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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the present values of heat transfer coefficient undertaken at 30 °C are lower than water at the nanofluid concentration of 3.0%. The difference in the value of nanofluid concentration with the present experimental setup and that of Duangthongsuk and Wongwises [15] can be due to different operating temperatures and the particle size of TiO2. The condition for maximum heat transfer is analyzed with the aid of viscosity and thermal conductivity relations developed. Figs. 4 and 5 are shown comparing the viscosity and thermal conductivity of TiO2 and SiO2 nanofluids with Eqs. (3) and (4) respectively. The values of thermal conductivity are in good agreement with Eq. (4). However, the experimental values of TiO2 nanofluid viscosity deviate with values estimated with Eq. (3) as shown in Fig. 5. Hence, an equation applicable to TiO2 nanofluid in the experimental range of viscosity is developed as
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in Fig. 6 ensuring the accuracy and reliability of the experimental setup. The heat transfer coefficients of water and TiO 2 and SiO 2 nanofluids estimated with Eq. (5) are shown plotted in Fig. 7. The experiments are undertaken at a bulk temperature of 30 °C, the TiO 2 and SiO 2 particle sizes being 50 nm and 22 nm respectively. The SiO2 nanofluid heat transfer coefficients increased with concentration up to 3.0%. The values of TiO 2 nanofluid decreased when the concentration is increased to values greater than 1.0%. The heat transfer enhancement with TiO 2 is higher than SiO2 nanofluid at the volume concentration of 1.0%. In contrast, the values of heat transfer augmentation of SiO2 nanofluid at 3.0% concentration are greater than TiO2 nanofluid. A decrease in heat transfer coefficient with TiO2 nanofluid for values greater than 1.0% concentration is observed by Duangthongsuk and Wongwises [15] who have undertaken experiments at a bulk temperature of 25 °C. They observed heat transfer coefficients to increase with concentration up to 1.0%. The heat transfer coefficients at 2% concentration are reported to be 14% lower than water. However,
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Fig. 9. Comparison of present experimental data with Julia et al. [14].
N
282 283
Fig. 7. Variation of heat transfer coefficient with Reynolds number of SiO2 and TiO2 nanofluids.
U
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Fig. 8. Variation of property enhancement ratio with concentration and temperature for SiO2 and TiO2 nanofluids.
μr ¼
μn f ϕ 0:1173 ¼ 2:067 : 100 μw
300 301 302 303 304 305 306 307 308 309 310 311 312 313 314
ð11Þ 316
The ratio of enhancements in viscosity to thermal conductivity defined as Enhancement Ratio (ER) is determined for TiO2 nanofluid with Eqs. (11) and (4) and SiO2 with Eqs. (3) and (4). The variation of enhancement ratio with nanofluid concentration for the two nanofluids at 30 °C and 60 °C is shown in Fig. 8. According to Garg et al. [23], the value of ER should be lower than 5.0 for a nanofluid to behave as a good heat transfer liquid. From experiments, the maximum heat transfer coefficient for TiO2 nanofluid is obtained at 1% concentration and SiO2 is 3% as confirmed with ER values at the operating temperature of 30 °C. This is due to greater values of TiO2 viscosity as compared to SiO2 values. The variation of ER with concentration is shown in Fig. 8 for TiO2 and SiO2 nanofluids at 60 °C. It can be observed that the maximum concentration for heat transfer enhancement has increased from 1% to approximately 6% concentration for TiO2 and 3% to 6% for SiO2, when the temperature is increased from 30 °C to 60 °C. In order to verify the possible heat transfer enhancements up to 6% concentration with SiO2 nanofluid, the experimental data of Julia et al. [14] undertaken at 5% concentration is shown in Fig. 9. It can be observed that the reported heat transfer coefficients are significantly greater than water, thus validating the equations developed for viscosity and thermal conductivity. An equation is obtained with an average deviation of 4.1%, standard deviation of 5.5% and maximum deviation of 17.1% for the estimation of
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
7
nanofluids is greater than the values estimated with the Blasius [26] equation by 23.5%. The effect of density and viscosity ratio of the nanofluids is considered in the development of regression Eq. (16) for friction factor. Eq. (16) developed by Azmi et al. [24] valid for water and oxide nanofluids is in good agreement with the experimental values of TiO2 and SiO2 nanofluids given by f n f ¼ 0:3164 Re
1:3 μn f ρn f ρw μw
hColburn D 1=3 −3:606 ¼ 0:00896 Pr w ð f r =8Þ Re kn f
0:7406
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Nusselt number of water, TiO2/water and SiO2/water nanofluids for concentrations up to 3.0% by Azmi et al. [24] as
NuColburn ¼
ϕ 2:541 0:1 þ : 100
345
4.3. Friction factor
346
The values recorded by the pressure transducer are used in the estimation of Darcy friction factor given by
C
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347
T
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Comparison of experimental values of heat transfer coefficient is in good agreement with the values estimated with Eq. (12).
N C O
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351 352
The experimental values of friction factor for water estimated with Eq. (13) are compared with the values calculated using Petukhov [25] and Blasius [26] equations. The equation of Petukhov [25] valid in the range of 3000 b Re b 5 × 106 is given by −2
f ¼ ð0:79 ln Re −1:64Þ
357 358
:
ð14Þ
U
354 355 356
ð13Þ
R
ΔP !: f ¼ 2 L ρV D 2
350
The friction factor of water and nanofluids estimated by Pak and Cho [10], Xuan and Li [27], Yu et al. [28] and Duangthongsuk and Wongwises [15] with Al2O3, Cu, SiC and TiO2 respectively in the turbulent range is reported to be in agreement with the Blasius [26] equation given by f B ¼ 0:3164=Re
0:25
:
ð15Þ
360 361 Q4 362 363
E
ð12Þ 343
The present data of friction factor for water and TiO2 and SiO2 nanofluids at different volume concentrations are shown in Fig. 10. The experimental data of water is in good agreement with the Eqs. (14) and (15). However, the friction factor of TiO2 and SiO2
in the range of 6800 b Re b 26,500, 5.00 ≤ Pr ≤ 7.24, and 0.5 ≤ ϕ ≤ 3.0 %. It can be observed that friction factor increases with both density and absolute viscosity of the nanofluid. It can be construed based on Eq. (16) that the two nanofluids, SiO2 and TiO2, having similar values of viscosity can have different values of friction factor. The friction factor of nanofluids with low particle density is lower compared to nanofluids prepared with high density particles. Such an observation is useful in the selection of nanofluids where pressure drop is an important parameter. Vajjha et al. [29] developed Eq. (17) with SiO2, Al2O3 and CuO nanofluids using base liquid mixture of water and EG in the ratio of 60:40. The equation also predicts an increase in friction factor with increase in density and viscosity over that of the base fluid. A comparison of Eqs. (16) and (17) indicates the effect of density to be more pronounced in water than in EG water mixtures.
D
340 341
f n f ¼ 0:3164 Re
368 369 370
ð16Þ
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Fig. 10. Variation of TiO2 and SiO2 nanofluid friction factor with Reynolds number.
366 367
−0:25
F
¼
1:3 0:3 μn f ρn f f nf or f r ¼ ρw μw fB 0:3
364 365
−0:25
ρn f ρEW
0:797
μn f μ EW
0:108
:
372 373 374 375 376 377 378 379 380 381 382 383 384 385 386
ð17Þ 388
The friction factors are higher at lower values of Reynolds number. This may be due to additional resistance caused due to slip between the particle and the base liquid. This is pronounced in nanofluids where the particle density is significantly higher than water. It is observed that the friction factor of TiO2 is greater than SiO2 nanofluid.
389 390 391 392
5. Conclusions
393
The viscosity of water based TiO2 nanofluid is observed to be influenced by the shape of the nanoparticle, though not significantly. The nanofluid friction factor increases with concentration and density. The friction coefficient can be estimated with Eq. (16) valid for water and the nanofluids. The forced convective heat transfer coefficients in the turbulent range can be estimated from Eq. (12) applicable for water, TiO2/water and SiO2/water nanofluids up to 3.0% concentration. The enhancement in heat transfer is 26% for 1.0% TiO2 nanofluid at Re = 17,642 while 7% enhancement is observed with SiO2 nanofluid under similar operating conditions. The heat transfer enhancement of SiO2 nanofluid is 25% and 33% at Reynolds number of 7318 and 19,659 respectively at ϕ = 3.0 %. A maximum heat transfer coefficient of 26% at 1.0% volume concentration and 33% at 3.0% volume concentration is observed with TiO2 and SiO2 nanofluids respectively undertaken at nanofluid bulk temperature of 30 °C.
394 395
Acknowledgments
409
The financial support by Universiti Malaysia Pahang under GRS100354 and RDU130391 is gratefully acknowledged. The authors thank Jawaharlal Nehru Technological University Hyderabad and Universiti Teknologi PETRONAS for the academic support rendered in this regard.
410 411
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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412 413 414
8
415
t2:1
t2:2
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Appendix 1. Uncertainties of instruments No.
Name of instrument
Range of instrument
Variable measured
Least division in measuring instrument
t2:4
1
Thermocouple
0–300 °C
Bulk temperature, Tb Tb = (Ti + To)/2
t2:5
2
Thermocouple
0–300 °C
Wall temperature, Tw Tw = (T1 + T2 + T3 + T4 + T5)/5
BC U T ¼ 0:1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi U Tb ¼ 0:12 þ 0:12 ¼ 0:14142 C UT = 0.1 °C rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi U Tw ¼ 5 0:12
t2:6
3
Flow meter
2–30 LPM
Volume flow rate, V
0.1
0–240 V 0–15 A 0–16.2 mV 0–6894.8 Pa (0–1 Psi)
Velocity, V Voltage, V Current, I Voltage, mV Pressure drop, ΔP
0.01 0.01 0.01 –
t2:3
Values measured in experiment
% uncertainty
Min
Max
Min
28.7
Max 31.25
0.49276
0.45255
30
34.18
0.74536
0.65430
5.6
16.1
1.78571
0.62112
110.1 5.45 0.57 332
110.1 5.45 5.74 2503.03
0.00908 0.18348 1.75439 1.75439
0.00908 0.18348 0.17422 0.17422
4 5 6
Voltage Current Pressure transducer
O
t2:7 t2:8 t2:9 t2:10
F
¼ 0:22361
Appendix 2. Uncertainty of physical quantities
t3:2
No.
Heat transfer and friction parameter
t3:3
1
Reynolds number, Re
Maximum uncertainty (%) r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
U Re Re
2
Heat flux, q
E
3
Heat transfer coefficient, h q h ¼ ðT w −T bÞ
Nusselt number, Nu
U Nu Nu
E
4
Friction factor, f ΔP f ¼ 2 ðDL Þ ρV2
Uf f
¼ 0:91220% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi Uh ¼ þ Ukk h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:91220Þ2 þ ð0:1Þ2 ¼ 0:91767% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 U 2ffi U U ΔP ¼ þ ρρ þ V ΔP V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð1:75438Þ2 þ ð0:1Þ2 þ ð1:78571Þ2 ¼ 3:98032%
C
[1] A.S. Ahuja, Augmentation of heat transport in laminar flow of polystyrene suspensions. I. Experiments and results, J. Appl. Phys. 46 (8) (1975) 3408–3416. [2] A.E. Bergles, Techniques to augment heat transfer, in: W.M. Rohsenow, J.P. Hartnett, E.N. Ganic (Eds.), Handbook of Heat Transfer Applications, McGraw-Hill, New York, 1985, pp. 31–380. [3] U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, American Society of Mechanical Engineers (ASME), New York, 1995, pp. 99–105. [4] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra fine particles, Netsu Bussei 4 (4) (1993) 227–233. [5] A. Turgut, I. Tavman, M. Chirtoc, H.P. Schuchmann, C. Sauter, S. Tavman, Thermal conductivity and viscosity measurements of water-based TiO2 nanofluids, Int. J. Thermophys. 30 (2009) 1213–1226. [6] Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang, H. Lu, Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, Int. J. Heat Mass Transf. 50 (11–12) (2007) 2272–2281. [7] A.R. Sajadi, M.H. Kazemi, Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube, Int. Commun. Heat Mass Transfer 38 (10) (2011) 1474–1478. [8] A.A.A. Arani, J. Amani, Experimental study on the effect of TiO2–water nanofluid on heat transfer and pressure drop, Exp. Thermal Fluid Sci. 42 (2012) 107–115. [9] M.H. Kayhani, H. Soltanzadeh, M.M. Heyhat, M. Nazari, F. Kowsary, Experimental study of convective heat transfer and pressure drop of TiO2/water nanofluid, Int. Commun. Heat Mass Transfer 39 (3) (2012) 456–462.
N
420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444
References
U
419
0:89351% ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi q¼ ð0:18371Þ2 þ ð0:89351Þ2
O
418
R
5
R
Nu ¼ hD k
t3:7
¼
C
Uh h
t3:6
U
D
VI q ¼ QA ¼ πDL
t3:5
U
2
P
t3:4
Uρ ρ
2
þ V þ μμ V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:1Þ2 þ ð1:78571Þ2 þ ð0:1Þ2 ¼ 1:79131% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Uq UV ¼ þ UI I q V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:00908Þ2 þ ð0:18348Þ2 ¼ 0:18371% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U Uq 2 Uh Þ ¼ þ ðTðwTw−Tb q −T b Þ h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U ðTw−TbÞ ð0:74536Þ2 þ ð0:49276Þ2 ðT w −T b Þ ¼
Re ¼ ρVD μ
¼
2
T
417
t3:1
R O
416
Minimum uncertainty (%) r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
U Re Re
Uρ 2 ρ
U
2
U
2
þ V þ μμ V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:1Þ2 þ ð0:62112Þ2 þ ð0:1Þ2 ¼ 0:63701% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Uq UV ¼ þ UI I q V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:00908Þ2 þ ð0:18348Þ2 ¼ 0:18371% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U Uq 2 Uh Þ ¼ þ ðTðwTw−Tb q −T b Þ h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U ðTw−TbÞ ð0:65430Þ2 þ ð0:45255Þ2 ðT w −T b Þ ¼ Uh h
U Nu Nu
Uf f
¼
¼
0:79555% ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi q¼ ð0:18371Þ2 þ ð0:79555Þ2
¼ 0:81649% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi Uh ¼ þ Ukk h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:81649Þ2 þ ð0:1Þ2 ¼ 0:82259% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 U 2ffi U U ΔP ¼ þ ρρ þ V ΔP V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:17422Þ2 þ ð0:1Þ2 þ ð0:62112Þ2 ¼ 1:25837%
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O
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9
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
3Q2
W.H. Azmi a,⁎, K.V. Sharma b, P.K. Sarma c, Rizalman Mamat a, G. Najafi d a
8
a r t i c l e
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Available online xxxx
11 12 13 14 15 16
Keywords: Nanofluid Titanium dioxide Silicon dioxide Friction factor Heat transfer coefficients
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Department of Mechanical Engineering, University Technology Petronas, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia GITAM University, Rishikonda, Visakhapatnam, 530045, India d Tarbiat Modares University, Jalale-E-Aleahmad Highway, Tehran, P.O. Box: 14115-111, Iran b
i n f o
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a b s t r a c t
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The heat transfer coefficient and friction factor of TiO2 and SiO2 water based nanofluids flowing in a circular tube under turbulent flow are investigated experimentally under constant heat flux boundary condition. TiO2 and SiO2 nanofluids with an average particle size of 50 nm and 22 nm respectively are used in the working fluid for volume concentrations up to 3.0%. Experiments are conducted at a bulk temperature of 30 °C in the turbulent Reynolds number range of 5000 to 25,000. The enhancements in viscosity and thermal conductivity of TiO2 are greater than SiO2 nanofluid. However, a maximum enhancement of 26% in heat transfer coefficients is obtained with TiO2 nanofluid at 1.0% concentration, while SiO2 nanofluid gave 33% enhancement at 3.0% concentration. The heat transfer coefficients are lower at all other concentrations. The particle concentration at which the nanofluids give maximum heat transfer has been determined and validated with property enhancement ratio. It is observed that the pressure drop is directly proportional to the density of the nanoparticle. © 2014 Published by Elsevier Ltd.
32 30 29
E
31
1. Introduction
34
The heat transfer augmentation has been of significant interest and the methods of obtaining through active and passive methods have been explained by Ahuja [1] and Bergles [2]. In the classification under active type, heat transfer enhancement is associated with external energy on the fluid through forced flow and the use of electrostatic fields. Under passive augmentation, enhancement of heat transfer can be due to artificially roughed surface, extended surface, swirl flow with twisted tape inserts, convoluted or twisted tube, use of additives, etc. Early passive technique such as dispersion of micron sized particles in a base fluid for heat transfer enhancement has been undertaken. However, practical problems arose due to clogging, erosion of pipe lines and high pumping power requirements with the dispersed particles, in spite of the fact that a certain degree of heat transfer augmentation is achieved. Further, agglomeration and resettlement of particles posed a severe maintenance problem.
43 44 45 46 47 48 49
R
N C O
41 42
U
39 40
R
33
37 38
17 18 19 20 21 22 23 24 25 26
C
27 28
35 36
O
4 5 6 7
F
2
Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube☆
1
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (W.H. Azmi), [email protected] (K.V. Sharma), [email protected] (P.K. Sarma), [email protected] (R. Mamat), najafi[email protected] (G. Najafi).
In contrast, recent studies with the nanometer size particles proved effective in achieving better heat transfer enhancement without any substantial increase in pumping power requirement and other associated practical problems. The nanofluids showed better stability and rheological properties, with no significant penalty on pressure drop [3]. The use of nanofluids for possible heat transfer augmentation has drawn the attention of many investigators [4–15]. The experimental determination of thermophysical properties such as viscosity and thermal conductivity of nanofluids has been initiated by Masuda et al. [4]. They determined the effect of dispersing nanosize particles of Al2O3, SiO2 and TiO2 in water. The result indicates 10% and 30% enhancement in the effective thermal conductivity of TiO2 and Al2O3 nanofluids respectively at 4.0% concentration. However, they observed an enhancement of 1.0% in thermal conductivity with SiO2 nanofluid at 1.0% concentration. Turgut et al. [5] determined the thermal conductivity and viscosity of TiO2 nanofluid for volume concentration up to 3.0% in the temperature range of 13 °C and 55 °C with particles of 21 nm diameter. The enhancement in thermal conductivity is 7.4% compared to base fluid at 13 °C. They concluded that the enhancement of nanofluid viscosity is greater than thermal conductivity. Experiments are undertaken by He et al. [6] for the determination of forced convection heat transfer coefficient at various concentrations of TiO2 nanofluid with particles of 15 nm to 95 nm size dispersed in base liquid water. Forced convection heat transfer coefficients for Re b 6500
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Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
Nomenclature
75 76 77 78 79 80 81 82 83 84
136
TiO2 and SiO2 nanofluids supplied in weight concentration were procured from US Research Nanomaterials, Inc. The water based nanofluid contained amorphous SiO2 nanoparticles with an average diameter of 22 nm with a concentration of 25 wt.% (13.1 vol.%). Anatase TiO2 nanoparticles of average diameter 50 nm dispersed in water are supplied at a weight concentration ω = 40 wt. % (φ = 13.6 vol. %). The initial pH of TiO2 and SiO2 nanofluids is 6.5 and 11 respectively. The procured nanofluids are prepared to desired volume concentration of 0.5–3.0 vol.% by dilution process using distilled water. The liquids prepared in this manner are subjected to mechanical homogenization for 2 h and observed for dispersion stability. The present
137
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2. Sample preparation
P
U
N
C
O
Subscripts b bulk exp experiment EW ethylene glycol water mixture nf nanofluid p particle r ratio reg regression s surface w water
R
R
E
Greek symbols α thermal diffusivity, m2/s ΔP pressure drop, Pa φ volume concentration, % ϕ volume fraction, φ = (ϕ/100) μ absolute viscosity, kg/m s μr ratio of nanofluid to water viscosity, (μnf/μw) ρ density, kg/m3 ω weight concentration, %
D
L LPM Nu OD Pr Q q Re T TEM U V
ρV =2
heat transfer coefficient, W/m2 K inner diameter, m thermal conductivity, W/m K thermal conductivity ratio of nanofluid to water, (knf/kw) tube length, m liter per minute Nusselt number, hD k outer diameter, m Prandtl number, μC k heat input, W heat flux, W/m2 Reynolds number, ρVD μ temperature, °C transmission electron microscopy uncertainty average velocity, m/s
E
h ID k kr
85 86
T
f
area, m2 specific heat, J/kg K diameter of nanoparticle, nm tube inner diameter, m electrical conductivity, μS/cm ethylene glycol property enhancement ratio Þ Darcy friction factor, DL ðΔP 2
C
A C dp D EC EG ER
investigations undertaken with different particle sizes indicate heat transfer to increase with nanofluid concentration and Reynolds number. Heat transfer coefficients are determined with SiO2 nanofluid in base liquid water at various concentrations [11–14]. Ferrouillat et al. [11] investigated the effect of inlet temperature on heat transfer coefficients. They undertook experiments under heating and cooling conditions of nanofluid with particles of 22 nm size for three inlet temperatures of 20, 50 and 70 °C in the Reynolds number range of 200 to 10,000. The results indicate 10% to 60% enhancement in heat transfer coefficients compared to the values with water under similar operating conditions. Bontemps et al. [12,13] determined the convective heat transfer coefficient with 22 nm size particles dispersed in water for flow in a circular tube under constant wall temperature and heat flux boundary conditions. Heat transfer enhancements of 30% and 100% were reported by Bontemps et al. [13] with 2.3% and 19.0% volume concentrations respectively. Julia et al. [14] undertook experiments in the Reynolds number range of 3000 to 100,000. A maximum heat transfer coefficient of 300% is reported with 5% concentration for flow in a tube at a Reynolds number of 30,000 with 12 nm particle size at nanofluid inlet temperature of 60 °C. The experimental heat transfer coefficients are determined with various particle sizes and operating temperatures. The studies undertaken by the investigators with TiO2 and SiO2 nanofluids reported an increase in heat transfer coefficient with concentration and Reynolds number. However, Duangthongsuk and Wongwises [15] determined TiO2 nanofluid heat transfer coefficients under turbulent flow with a double pipe heat exchanger for concentration up to 2.0%. They observed an increase in heat transfer coefficient with Reynolds number, for concentration up to 1.0% at the operating temperature of 25 °C. However, the heat transfer coefficients decreased for concentration more than 1.0%, but are observed to be greater than the base liquid water. Similarly, Pak and Cho [10] observed a decrease in heat transfer coefficient with Al2O3 nanofluid when the volume concentration increased to 2.78% at the operating temperature of 25 °C. Most of the earlier studies are limited to the determination of properties and heat transfer coefficient of TiO2 and SiO2 nanofluids at different conditions of flow, concentration and temperature. The studies related to heat transfer enhancement of water based TiO 2 and SiO2 nanofluids at similar operating temperature have not been reported in literature. Most of the authors reported a marginal increase in friction factor. The objective of the present study is to determine and compare under similar operating temperature, the convective heat transfer coefficients and friction factor of TiO2/ water and SiO2/water nanofluids in the turbulent range of Reynolds number for concentrations up to 3.0%. The influence of operating conditions viz., temperature and concentration on enhancement or reduction of heat transfer coefficients for the two nanofluids is determined.
in the volume concentration of 1.2% with 95 nm particles and with 21 nm size particles in the laminar range of Reynolds number have been determined. Sajadi and Kazemi [7] conducted experiments with 30 nm size particles for a maximum concentration of 0.25%, while Arani and Amani [8] undertook experiments up to 2.0% in the Reynolds number range of 8000 to 51000. Kayhani et al. [9] conducted experiments with 15 nm size particles for concentration up to 2.0% in the Reynolds number range of 7000 to 15,000. Pak and Cho [10] undertook experiments with 27 nm size for concentration up to 3.16% under turbulent flow conditions. The
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
151 152 153 154 155 156 157 158 159 160
experimental work requires approximately 15 L of the nanofluid per cycle for the conduct of the experiment. The samples are observed to be stable for more than a week and a month respectively for TiO2 and SiO2 nanofluids. The pH of TiO2/water and SiO2/water diluted nanofluids varied between 7.2–7.7 and 8.9–10.1 respectively in the range of concentration tested. The thermo-physical properties of nanofluid such as thermal conductivity and viscosity at each concentration are determined experimentally using a KD2 Pro thermal property analyzer and Brookfield LVDV-III Ultra Rheometer, respectively. The equations for density and specific heat of nanofluid, based on mixture relation used in the analysis, are given as ρn f ¼ φ ρp þ ð1−φÞρw
ð1Þ
ð1−φÞρw þ φρp
:
ð2Þ
165
191 192
The experimental set up consists of a chiller, collecting tank, water pump, flow meter, pressure transducer, control panel, and test section. The test section consists of a copper tube of ID = 16 mm and OD = 19 mm is integrated with thermocouples, ceramic fiber insulation and heaters, the schematic diagram is given as Fig. 1. A stainless steel container of 30 liter capacity is used for storing the working liquid. It is connected to a pump of 0.5 horse power to force the liquid through the test section. The copper tube of 1.5 m length is wrapped with two nichrome heaters of 3.0 kW maximum electric rating for uniform heating. The tube along with heaters is enclosed with ceramic fiber insulation to minimize heat loss to atmosphere. Seven K-type thermocouples are fixed, five on the surface of the tube wall at 0.25, 0.5, 0.75, 1.0 and 1.25 m from the inlet and the other two measures the inlet and outlet temperature of the fluid. A digital flow meter capable of measuring in the range of 5 to 16 LPM connected between the test section and the pump determines the flow rate of the liquid with an accuracy of 0.1 LPM. When the system attains steady state, the temperatures at different locations, electric heat input and the flow rate are noted. A chiller of 1.4 kW capacity connected to the exit of the test section helps in regulating the inlet temperature of the working liquid. The heater is supplied with a constant value of 600 W, while the chiller is set to regulate the fluid temperature at 30 °C. The maximum variation in the liquid temperature is ± 1 °C. A transducer to measure pressure in the range of 0 to 6895 Pa to an accuracy of 0.5 Pa is used to determine the pressure drop across the test section.
t1:1 t1:2 Q1
Table 1 Physical properties of metal oxide nanomaterials.
180 181 182 183 184 185 186 187 188 189 190
C
E
R
178 179
R
176 177
N C O
174 175
195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216
218
4.1. Dispersion and properties
U
172 173
D
167
E
3. Forced convection heat transfer apparatus
T
166
170 171
217
P
The properties of nanoparticles are listed in Table 1.
168 169
4. Results and discussion
R O
ð1−φÞðρ C Þw þ φðρC Þp
193 194
O
162 163
Cn f ¼
A data logger is provided to record the temperature of the surface and the fluid every 5 s to determine the state of the experiment. The instrumentation error is estimated in the range of 0.01% to 1.8%. The total length of fluid flow in the tube is approximately 4.0 m which ensures turbulent flow condition at the entry of the test section. The uncertainties in the measuring instruments are given as Appendix 1. Experiments are undertaken with distilled water to determine the pressure drop and heat transfer coefficient at different flow rates. The steady state data of temperatures and pressure drop across the test section are recorded. The Darcy equation and Newton's law of cooling are used in the evaluation of friction factor and heat transfer coefficient respectively. The data of water is compared with the equations in literature to establish the consistency and reliability of the experimental results. Experiments with TiO2 and SiO2 nanofluids are undertaken for volume concentration up to 3.0% for various flow rates to determine heat transfer coefficients and friction factors. It is observed that the temperature on the outer surface of the test section measures value close to ambient. Hence, the heat loss to atmosphere is neglected in the evaluation of heat transfer coefficients. The maximum and minimum error in the experimental data is presented as Appendix 2. The stability and dispersion of nanofluids are ensured through electrical conductivity measurements and TEM images respectively.
F
149 150
3
The stability and dispersion of nanofluid are established before the conduct of the experiment. Liu et al. [17] stated that the electrical conductivity should be lower than 10 μS/cm for distilled water. The measured value for distilled water at room temperature of 28.3 °C is observed to be 6 μS/cm. The dispersion stability of nanofluids can be determined by measuring its electrical conductivity. According to Sarojini et al. [16], the nanofluid is stable, if the electrical conductivity measured before and after the conduct of experiment at each concentration does not change. A close agreement between the measured values of electrical conductivity indicates the non-agglomeration of the nanoparticles, which can be observed from Fig. 2. Fig. 3 shows the TEM photographs of TiO2 and SiO2 nanoparticles bringing out the size, shape and the state of agglomeration in the liquid. The TEM photographs at the same magnification for SiO 2 and TiO2 nanofluids at 3% concentration confirm non-agglomeration of nanoparticles. The viscosity and thermal conductivity of TiO2 and SiO2 nanofluids are determined in the volume concentration range of 0.5–4.0%. Sharma et al. [18] developed regression Eqs. (3) and (4) for the estimation of viscosity and thermal conductivity for water based nanofluids respectively, using the experimental data of various investigators. The equations are valid for concentration ϕ ≤ 4 %, liquid temperature Tnf ≤ 70 °C and
t1:3
Nanoparticle
Thermal conductivity, W/m K
Density, kg/m3
Specific heat, J/kg K
Reference
t1:4 t1:5 t1:6 t1:7 t1:8 t1:9 t1:10
SiO2 Al2O3 TiO2 Fe3O4 (magnetite) ZrO2 ZnO CuO
1.4 36 8.4 80.4 1.7 29 69
2220 3880 4175 5180 5500 5600 6350
745 773 692 670 502 514 535
Vajjha et al. [29] Pak and Cho [10] Pak and Cho [10] Sundar et al. [30] Kothandaraman and Subramanyam [31] Vajjha and Das [32], Hong et al. [33] Fotukian and Nasr Esfahany [34]
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
D
P
R O
O
F
4
The viscosity of SiO2 nanofluid estimated with Eq. (3) is in good agreement with the experimental data and with that of other investigators [6,10,15,19] as shown in Fig. 4. The variation of thermal conductivity of TiO2 and SiO2 nanofluids with concentration is shown in Fig. 5. The experimental values are in satisfactory agreement with the values estimated with the Eq. (4) and the data from literature [10,15,20].
T
T n f −0:038 dp −0:061 ϕ 11:3 1þ 1þ 1þ 100 70 170
ð3Þ
kn f T n f 0:2777 dp −0:0336 α p 0:01737 ϕ 1:37 kr ¼ ¼ 0:8938 1 þ 1þ 1þ : kw 70 150 αw 100
R
245 246
μn f ¼ μw
R
μr ¼
C
243
particle diameter dp ≤ 170 nm. The equations have the flexibility to estimate the properties of metal and metal oxide nanofluids for spherical shape particles and water. They are given as:
E
241 242
E
Fig. 1. Schematic diagram of the experimental setup.
U
N
C
O
248
ð4Þ
250 251 252 253 254 255
4.2. Convective heat transfer coefficient
The heat transfer coefficient is evaluated with the energy balance 256 equation, assuming negligible heat loss to the surroundings. The rele- 257 vant equations used in the analysis are: 258 hexp ¼
Q As ðT s −T b Þ
ð5Þ 260
Nuexp ¼
h exp D : kn f
261
ð6Þ 263
The Reynolds and Prandtl numbers of the nanofluid are determined respectively with Eqs. (7) and (8), the properties referred at the bulk 264 temperature Tb. 265
Ren f ¼
Prn f ¼ Fig. 2. Electrical conductivity of TiO2/water and SiO2/water nanofluids at 30 °C.
249
ρn f VD μn f
μn f Cn f : kn f
ð7Þ 267 268
ð8Þ
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
270
5
R O
O
F
W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
Fig. 5. Comparison of experimental values of thermal conductivity with Eq. (6) of Sharma et al. [18].
P
(a) TiO2
D
The following equations are available in the literature for the estimation of Nusselt number of single phase fluids. The equation of Notter and 271 Rouse [21] for single phase fluid is given by 272 0:856
R
(b) SiO2
E
C
T
E
Nu ¼ 5 þ 0:015 Re
0:347
:
ð9Þ 274
The equation of Dittus–Boelter [22] applicable for pure fluids for Re N 104 and 0.6 b Pr b 200 is given as 275 Nu ¼ 0:023Re
0:8
Pr
0:4
:
ð10Þ 277
Eqs. (5) and (6) are used in the estimation of average heat transfer coefficient and Nusselt number of water and nanofluids. The 278 Nusselt number of distilled water estimated with Eq. (6) is in good 279 agreement with the values estimated with Eqs. (9) and (10) shown 280
U
N C O
R
Fig. 3. TEM images of TiO2 and SiO2 nanofluids at 3 vol.%.
Pr
Fig. 4. Comparison of experimental values of viscosity with Eq. (3) of Sharma et al. [18].
Fig. 6. Comparison of experimental Nusselt number of water with equations in literature.
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
295 296 297 298 299
R O
P
D
E
T
C
293 294
E
291 292
R
289 290
R
288
the present values of heat transfer coefficient undertaken at 30 °C are lower than water at the nanofluid concentration of 3.0%. The difference in the value of nanofluid concentration with the present experimental setup and that of Duangthongsuk and Wongwises [15] can be due to different operating temperatures and the particle size of TiO2. The condition for maximum heat transfer is analyzed with the aid of viscosity and thermal conductivity relations developed. Figs. 4 and 5 are shown comparing the viscosity and thermal conductivity of TiO2 and SiO2 nanofluids with Eqs. (3) and (4) respectively. The values of thermal conductivity are in good agreement with Eq. (4). However, the experimental values of TiO2 nanofluid viscosity deviate with values estimated with Eq. (3) as shown in Fig. 5. Hence, an equation applicable to TiO2 nanofluid in the experimental range of viscosity is developed as
O
286 287
in Fig. 6 ensuring the accuracy and reliability of the experimental setup. The heat transfer coefficients of water and TiO 2 and SiO 2 nanofluids estimated with Eq. (5) are shown plotted in Fig. 7. The experiments are undertaken at a bulk temperature of 30 °C, the TiO 2 and SiO 2 particle sizes being 50 nm and 22 nm respectively. The SiO2 nanofluid heat transfer coefficients increased with concentration up to 3.0%. The values of TiO 2 nanofluid decreased when the concentration is increased to values greater than 1.0%. The heat transfer enhancement with TiO 2 is higher than SiO2 nanofluid at the volume concentration of 1.0%. In contrast, the values of heat transfer augmentation of SiO2 nanofluid at 3.0% concentration are greater than TiO2 nanofluid. A decrease in heat transfer coefficient with TiO2 nanofluid for values greater than 1.0% concentration is observed by Duangthongsuk and Wongwises [15] who have undertaken experiments at a bulk temperature of 25 °C. They observed heat transfer coefficients to increase with concentration up to 1.0%. The heat transfer coefficients at 2% concentration are reported to be 14% lower than water. However,
C
284 Q3 285
Fig. 9. Comparison of present experimental data with Julia et al. [14].
N
282 283
Fig. 7. Variation of heat transfer coefficient with Reynolds number of SiO2 and TiO2 nanofluids.
U
281
O
F
6
Fig. 8. Variation of property enhancement ratio with concentration and temperature for SiO2 and TiO2 nanofluids.
μr ¼
μn f ϕ 0:1173 ¼ 2:067 : 100 μw
300 301 302 303 304 305 306 307 308 309 310 311 312 313 314
ð11Þ 316
The ratio of enhancements in viscosity to thermal conductivity defined as Enhancement Ratio (ER) is determined for TiO2 nanofluid with Eqs. (11) and (4) and SiO2 with Eqs. (3) and (4). The variation of enhancement ratio with nanofluid concentration for the two nanofluids at 30 °C and 60 °C is shown in Fig. 8. According to Garg et al. [23], the value of ER should be lower than 5.0 for a nanofluid to behave as a good heat transfer liquid. From experiments, the maximum heat transfer coefficient for TiO2 nanofluid is obtained at 1% concentration and SiO2 is 3% as confirmed with ER values at the operating temperature of 30 °C. This is due to greater values of TiO2 viscosity as compared to SiO2 values. The variation of ER with concentration is shown in Fig. 8 for TiO2 and SiO2 nanofluids at 60 °C. It can be observed that the maximum concentration for heat transfer enhancement has increased from 1% to approximately 6% concentration for TiO2 and 3% to 6% for SiO2, when the temperature is increased from 30 °C to 60 °C. In order to verify the possible heat transfer enhancements up to 6% concentration with SiO2 nanofluid, the experimental data of Julia et al. [14] undertaken at 5% concentration is shown in Fig. 9. It can be observed that the reported heat transfer coefficients are significantly greater than water, thus validating the equations developed for viscosity and thermal conductivity. An equation is obtained with an average deviation of 4.1%, standard deviation of 5.5% and maximum deviation of 17.1% for the estimation of
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339
W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
7
nanofluids is greater than the values estimated with the Blasius [26] equation by 23.5%. The effect of density and viscosity ratio of the nanofluids is considered in the development of regression Eq. (16) for friction factor. Eq. (16) developed by Azmi et al. [24] valid for water and oxide nanofluids is in good agreement with the experimental values of TiO2 and SiO2 nanofluids given by f n f ¼ 0:3164 Re
1:3 μn f ρn f ρw μw
hColburn D 1=3 −3:606 ¼ 0:00896 Pr w ð f r =8Þ Re kn f
0:7406
O
P
Nusselt number of water, TiO2/water and SiO2/water nanofluids for concentrations up to 3.0% by Azmi et al. [24] as
NuColburn ¼
ϕ 2:541 0:1 þ : 100
345
4.3. Friction factor
346
The values recorded by the pressure transducer are used in the estimation of Darcy friction factor given by
C
E
R
347
T
344
Comparison of experimental values of heat transfer coefficient is in good agreement with the values estimated with Eq. (12).
N C O
349
351 352
The experimental values of friction factor for water estimated with Eq. (13) are compared with the values calculated using Petukhov [25] and Blasius [26] equations. The equation of Petukhov [25] valid in the range of 3000 b Re b 5 × 106 is given by −2
f ¼ ð0:79 ln Re −1:64Þ
357 358
:
ð14Þ
U
354 355 356
ð13Þ
R
ΔP !: f ¼ 2 L ρV D 2
350
The friction factor of water and nanofluids estimated by Pak and Cho [10], Xuan and Li [27], Yu et al. [28] and Duangthongsuk and Wongwises [15] with Al2O3, Cu, SiC and TiO2 respectively in the turbulent range is reported to be in agreement with the Blasius [26] equation given by f B ¼ 0:3164=Re
0:25
:
ð15Þ
360 361 Q4 362 363
E
ð12Þ 343
The present data of friction factor for water and TiO2 and SiO2 nanofluids at different volume concentrations are shown in Fig. 10. The experimental data of water is in good agreement with the Eqs. (14) and (15). However, the friction factor of TiO2 and SiO2
in the range of 6800 b Re b 26,500, 5.00 ≤ Pr ≤ 7.24, and 0.5 ≤ ϕ ≤ 3.0 %. It can be observed that friction factor increases with both density and absolute viscosity of the nanofluid. It can be construed based on Eq. (16) that the two nanofluids, SiO2 and TiO2, having similar values of viscosity can have different values of friction factor. The friction factor of nanofluids with low particle density is lower compared to nanofluids prepared with high density particles. Such an observation is useful in the selection of nanofluids where pressure drop is an important parameter. Vajjha et al. [29] developed Eq. (17) with SiO2, Al2O3 and CuO nanofluids using base liquid mixture of water and EG in the ratio of 60:40. The equation also predicts an increase in friction factor with increase in density and viscosity over that of the base fluid. A comparison of Eqs. (16) and (17) indicates the effect of density to be more pronounced in water than in EG water mixtures.
D
340 341
f n f ¼ 0:3164 Re
368 369 370
ð16Þ
R O
Fig. 10. Variation of TiO2 and SiO2 nanofluid friction factor with Reynolds number.
366 367
−0:25
F
¼
1:3 0:3 μn f ρn f f nf or f r ¼ ρw μw fB 0:3
364 365
−0:25
ρn f ρEW
0:797
μn f μ EW
0:108
:
372 373 374 375 376 377 378 379 380 381 382 383 384 385 386
ð17Þ 388
The friction factors are higher at lower values of Reynolds number. This may be due to additional resistance caused due to slip between the particle and the base liquid. This is pronounced in nanofluids where the particle density is significantly higher than water. It is observed that the friction factor of TiO2 is greater than SiO2 nanofluid.
389 390 391 392
5. Conclusions
393
The viscosity of water based TiO2 nanofluid is observed to be influenced by the shape of the nanoparticle, though not significantly. The nanofluid friction factor increases with concentration and density. The friction coefficient can be estimated with Eq. (16) valid for water and the nanofluids. The forced convective heat transfer coefficients in the turbulent range can be estimated from Eq. (12) applicable for water, TiO2/water and SiO2/water nanofluids up to 3.0% concentration. The enhancement in heat transfer is 26% for 1.0% TiO2 nanofluid at Re = 17,642 while 7% enhancement is observed with SiO2 nanofluid under similar operating conditions. The heat transfer enhancement of SiO2 nanofluid is 25% and 33% at Reynolds number of 7318 and 19,659 respectively at ϕ = 3.0 %. A maximum heat transfer coefficient of 26% at 1.0% volume concentration and 33% at 3.0% volume concentration is observed with TiO2 and SiO2 nanofluids respectively undertaken at nanofluid bulk temperature of 30 °C.
394 395
Acknowledgments
409
The financial support by Universiti Malaysia Pahang under GRS100354 and RDU130391 is gratefully acknowledged. The authors thank Jawaharlal Nehru Technological University Hyderabad and Universiti Teknologi PETRONAS for the academic support rendered in this regard.
410 411
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
396 397 398 399 400 401 402 403 404 405 406 407 408
412 413 414
8
415
t2:1
t2:2
W.H. Azmi et al. / International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
Appendix 1. Uncertainties of instruments No.
Name of instrument
Range of instrument
Variable measured
Least division in measuring instrument
t2:4
1
Thermocouple
0–300 °C
Bulk temperature, Tb Tb = (Ti + To)/2
t2:5
2
Thermocouple
0–300 °C
Wall temperature, Tw Tw = (T1 + T2 + T3 + T4 + T5)/5
BC U T ¼ 0:1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi U Tb ¼ 0:12 þ 0:12 ¼ 0:14142 C UT = 0.1 °C rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi U Tw ¼ 5 0:12
t2:6
3
Flow meter
2–30 LPM
Volume flow rate, V
0.1
0–240 V 0–15 A 0–16.2 mV 0–6894.8 Pa (0–1 Psi)
Velocity, V Voltage, V Current, I Voltage, mV Pressure drop, ΔP
0.01 0.01 0.01 –
t2:3
Values measured in experiment
% uncertainty
Min
Max
Min
28.7
Max 31.25
0.49276
0.45255
30
34.18
0.74536
0.65430
5.6
16.1
1.78571
0.62112
110.1 5.45 0.57 332
110.1 5.45 5.74 2503.03
0.00908 0.18348 1.75439 1.75439
0.00908 0.18348 0.17422 0.17422
4 5 6
Voltage Current Pressure transducer
O
t2:7 t2:8 t2:9 t2:10
F
¼ 0:22361
Appendix 2. Uncertainty of physical quantities
t3:2
No.
Heat transfer and friction parameter
t3:3
1
Reynolds number, Re
Maximum uncertainty (%) r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
U Re Re
2
Heat flux, q
E
3
Heat transfer coefficient, h q h ¼ ðT w −T bÞ
Nusselt number, Nu
U Nu Nu
E
4
Friction factor, f ΔP f ¼ 2 ðDL Þ ρV2
Uf f
¼ 0:91220% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi Uh ¼ þ Ukk h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:91220Þ2 þ ð0:1Þ2 ¼ 0:91767% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 U 2ffi U U ΔP ¼ þ ρρ þ V ΔP V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð1:75438Þ2 þ ð0:1Þ2 þ ð1:78571Þ2 ¼ 3:98032%
C
[1] A.S. Ahuja, Augmentation of heat transport in laminar flow of polystyrene suspensions. I. Experiments and results, J. Appl. Phys. 46 (8) (1975) 3408–3416. [2] A.E. Bergles, Techniques to augment heat transfer, in: W.M. Rohsenow, J.P. Hartnett, E.N. Ganic (Eds.), Handbook of Heat Transfer Applications, McGraw-Hill, New York, 1985, pp. 31–380. [3] U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, American Society of Mechanical Engineers (ASME), New York, 1995, pp. 99–105. [4] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra fine particles, Netsu Bussei 4 (4) (1993) 227–233. [5] A. Turgut, I. Tavman, M. Chirtoc, H.P. Schuchmann, C. Sauter, S. Tavman, Thermal conductivity and viscosity measurements of water-based TiO2 nanofluids, Int. J. Thermophys. 30 (2009) 1213–1226. [6] Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang, H. Lu, Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, Int. J. Heat Mass Transf. 50 (11–12) (2007) 2272–2281. [7] A.R. Sajadi, M.H. Kazemi, Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube, Int. Commun. Heat Mass Transfer 38 (10) (2011) 1474–1478. [8] A.A.A. Arani, J. Amani, Experimental study on the effect of TiO2–water nanofluid on heat transfer and pressure drop, Exp. Thermal Fluid Sci. 42 (2012) 107–115. [9] M.H. Kayhani, H. Soltanzadeh, M.M. Heyhat, M. Nazari, F. Kowsary, Experimental study of convective heat transfer and pressure drop of TiO2/water nanofluid, Int. Commun. Heat Mass Transfer 39 (3) (2012) 456–462.
N
420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444
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U
419
0:89351% ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi q¼ ð0:18371Þ2 þ ð0:89351Þ2
O
418
R
5
R
Nu ¼ hD k
t3:7
¼
C
Uh h
t3:6
U
D
VI q ¼ QA ¼ πDL
t3:5
U
2
P
t3:4
Uρ ρ
2
þ V þ μμ V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:1Þ2 þ ð1:78571Þ2 þ ð0:1Þ2 ¼ 1:79131% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Uq UV ¼ þ UI I q V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:00908Þ2 þ ð0:18348Þ2 ¼ 0:18371% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U Uq 2 Uh Þ ¼ þ ðTðwTw−Tb q −T b Þ h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U ðTw−TbÞ ð0:74536Þ2 þ ð0:49276Þ2 ðT w −T b Þ ¼
Re ¼ ρVD μ
¼
2
T
417
t3:1
R O
416
Minimum uncertainty (%) r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
U Re Re
Uρ 2 ρ
U
2
U
2
þ V þ μμ V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:1Þ2 þ ð0:62112Þ2 þ ð0:1Þ2 ¼ 0:63701% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Uq UV ¼ þ UI I q V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:00908Þ2 þ ð0:18348Þ2 ¼ 0:18371% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U Uq 2 Uh Þ ¼ þ ðTðwTw−Tb q −T b Þ h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U ðTw−TbÞ ð0:65430Þ2 þ ð0:45255Þ2 ðT w −T b Þ ¼ Uh h
U Nu Nu
Uf f
¼
¼
0:79555% ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi q¼ ð0:18371Þ2 þ ð0:79555Þ2
¼ 0:81649% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi Uh ¼ þ Ukk h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:81649Þ2 þ ð0:1Þ2 ¼ 0:82259% r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 U 2ffi U U ΔP ¼ þ ρρ þ V ΔP V qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:17422Þ2 þ ð0:1Þ2 þ ð0:62112Þ2 ¼ 1:25837%
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R O
O
F
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U
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9
Please cite this article as: W.H. Azmi, et al., Heat transfer and friction factor of water based TiO2 and SiO2 nanofluids under turbulent flow in a tube, Int. Commun. Heat Mass Transf. (2014), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.10.007
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