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Experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluid in double pipe heat exchanger with and without helical coil inserts
International Communications in Heat and Mass Transfer 50 (2014) 68–76
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Experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluid in double pipe heat exchanger with and without helical coil inserts☆ M. Chandra Sekhara Reddy, Veeredhi Vasudeva Rao ⁎ Department of Mechanical Engineering, Sreenidhi Institute of Science and Technology, Yamnampet, Ghatkesar, Hyderabad 501301, India
a r t i c l e
i n f o
Available online 14 November 2013 Keywords: Heat transfer Friction factor Helical coil inserts TiO2 nanofluid
a b s t r a c t Heat transfer coefficient and friction factor of TiO2 nanofluid flowing in a double pipe heat exchanger with and without helical coil inserts are studied experimentally. The experiments are conducted in the range of Reynolds number from 4000 to 15,000 and in the volume concentration range from 0.0004% to 0.02%. The base fluid is prepared by considering 40% of ethylene glycol and 60% of distilled water. The heat transfer coefficient and friction factor get enhanced by 10.73% and 8.73% for 0.02% volume concentration of nanofluid when compared to base fluid flowing in a tube. Heat transfer coefficient and friction factor further get enhanced by 13.85% and 10.69% respectively for 0.02% nanofluid when compared to base fluid flowing in a tube with helical coil insert of P/d = 2.5. The measured values of heat transfer coefficient and friction factor are compared with the published literature. Based on the experimental data, generalized correlations are proposed for Nusselt number and friction factor. The results are presented in graphical and tabular form. Uncertainty analysis is also carried out and the experimental error is in the range of ±10%. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Heat exchangers are employed in automobiles to dissipate heat rejected by the internal combustion engine to the sink through a suitable liquid called coolant. There are a number of conventional fluids that are suitable to maintain the sink in the desired operating temperature range. Pure water and ethylene glycol in combination with water are being used as coolant during the last couple of centuries. Due to advent of new technologies there are a number of improvements in the field of automobile engineering including enhancements in heat dissipation capabilities, reduction in size and increased power generation. There is a considerable improvement even in heat transfer fluid properties that are responsible for dissipation of heat from the automobile to the environment (surroundings) while passing through the heat exchanger (radiator). The effectiveness of heat exchanger depends on the characteristics and properties of heat transfer fluids. A stage has come now that the limitation of heat transfer fluids is in turn limiting the effectiveness of heat exchangers. To overcome these limitations conventional fluids are now being replaced with nanofluids. There have been many experimental studies by engineers and researchers on converting conventional fluids into nanofluids. In their early attempts micro metallic particles with high thermal conductivity were added to the heat transfer fluids with a hope to improve thermal ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (V. Vasudeva Rao). 0735-1933/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.icheatmasstransfer.2013.11.002
properties. However due to micron size of particles there were several problems like sedimentation and erosion of tubes and pumps while in transit. In the recent past the availability of nanomaterials renewed the interest in the application of nanofluids. The suitability and performance of these conventional fluids can be enhanced by introducing nanoparticles like Al2O3, TiO2 and CuO, by converting them in to nanofluids [1]. Masuda et al. [2], Lee et al. [3], Wang et al. [4], Eastman et al. [5,6], and Das et al. [7] mostly concentrated on the determination of effective thermal conductivity of nanofluids. Heat transfer enhancements in forced convection with different nanofluids flowing in a tube under laminar and turbulent flow conditions have been reported by many researchers in open literature. Pak and Cho [8] experimentally observed enhancements in heat transfer with Al2O3 and TiO2 nanofluids in a tube under turbulent flow condition and proposed Nusselt number correlation. Similar observations were made by Xuan and Li [9] with Cu nanofluid and proposed correlations for Nusselt number as a function of particle diameter. Wen and Ding [10] experimentally observed heat transfer enhancement with Al2O3 nanofluid in laminar entry region. Heris et al. [11] conducted experiments on Al2O3/water nanofluid in the range of Reynolds number from 700 to 2050 and observed heat transfer enhancement with increase of Peclet number and volume concentration. Numerical analysis has been conducted to fully understand the heat transfer capabilities of these nanofluids. Maiga et al. [12] observed the heat transfer enhancement in water/Al2O3 and ethylene glycol/Al2O3 nanofluid in the laminar flow through their numerical analysis. Palm et al. [13] also reported results of numerical analysis of laminar flow heat transfer of
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
Nomenclature A C D d f h k L m˙ Nu Pr P Q Re T v
Area, m2 Specific heat, J/kg K Inner diameter of the tube, m Diameter of the helical coil, m Friction factor Heat transfer coefficient, W/m2K Thermal conductivity, W/mK Length of the tube, m Mass flow rate, kg/s Nusselt number, hD/k Prandtl number, μ C/k Helical pitch, m Heat flow, Watts Reynolds number, 4 m/πDμ Temperature, °C Velocity, m/s
Greek symbols δ Uncertainty ΔT Temperature difference Δp Pressure drop φ Volume concentration of nanoparticles, % μ Dynamic viscosity, kg/m2s ρ Density, kg/m3
Subscripts bf Base fluid C cold Exp Experimental h hot i Inlet nf Nanofluid o Outlet p Particle Reg Regression
69
transfer of 1.5% volume concentration of Al2O3/water nanofluid in a tube with twisted tape inserts of 2.93 twist ratio and found 31.29% enhancement in the heat transfer at Reynolds number of 2039. Saeedinia et al. [20] experimentally found 45% enhancement in heat transfer for 0.3% volume concentration of CuO/base oil nanofluid in a tube with wire coil inserts under laminar flow conditions. Fully developed laminar flow of 0.1% of Al2O3 nanofluid in a tube with wire coil inserts has been analyzed by Chandrasekar et al. [21]. They have experimentally observed 21.53% heat transfer enhancement with wire coil insert with a pitch of 3 and developed Nusselt number correlation. Sundar and Singh [22] emphasized on the available Nusselt number correlations for nanofluid in a tube with different types of inserts. Many researchers have considered water based nanofluids for their heat transfer studies in a tube with inserts. The applicability of water based nanofluids is limited in the cold countries like Alaska, Canada, Northern Europe and Russia, due to freezing of water at 0 °C. To avoid freezing of water ethylene glycol is added in suitable proportions. A mixture of water and ethylene glycol is a commonly used coolant in car radiators. Generally, ethylene glycol and water are mixed in the ratio of 40:60%. Namburu et al. [23] first time prepared 60:40% EG/W mixture based CuO nanofluid and conducted studies on viscosity. Vajjha and Das [24] studied thermal conductivity of 60:40% EG/W based Al2O3, CuO and ZnO nanofluids and they observed that for same volume concentration and temperature range CuO nanofluid has a high thermal conductivity compared to Al2O3 and ZnO nanofluids with volume concentrations up to 10%. Naik and Sundar [25] considered propylene glycol and water mixture in the ratio of 70:30 as a base fluid for the preparation of CuO nanofluid and found better thermal conductivity and viscosity compared to base fluid. Namburu et al. [26] obtained numerically the heat transfer enhancement with CuO, Al2O3, and SiO2 nanofluids and compared with the base liquid, under turbulent flow conditions. The data on the mixture of ethylene glycol and water based nanofluid flowing in a tube with inserts is not available in the literature. Therefore, the focus of the present work is on the estimation of heat transfer coefficient and friction factor of ethylene glycol and water mixture based TiO2 nanofluid flowing in double pipe heat exchanger with helical coil inserts experimentally. The heat transfer experiments are conducted in the Reynolds number range from 4000 to 15,000. Based on the experimental data generalized correlations are proposed for Nusselt number and friction factor. 2. Nanofluid preparation and its properties
Al2O3/ethylene glycol and Al2O3/water nanofluids in a tube. Roy et al. [14] observed heat transfer enhancement by considering wall shear stress to increase with volume concentration and Reynolds number. Putra et al. [15] reported natural convection heat transfer with Al2O3/ water and CuO/water nanofluids. Thus in all cases nanofluids exhibited higher heat transfer capability compared to water in both laminar and turbulent flow conditions in all experimental and numerical studies. Further, heat transfer enhancement using nanofluids is possible through passive methods such as creation of turbulence in the flow field by inserting some kind of inserts in a tube. Sundar and Sharma [16] conducted experiments to determine heat transfer coefficient and friction factor with Al2O3 nanofluid flowing in a tube with different types of twisted tape inserts. They observed 30.30% enhancement in heat transfer with 0.5% volume concentration of Al2O3 at 22,000 Reynolds number. Further enhancement of 42.17% in heat transfer is observed with same concentration of Al2O3 using twisted tape inserts of twist ratio H/D = 5. Sundar and Sharma [17] observed further heat transfer enhancement of 80.19% with 0.5% volume concentration of Al2O3 nanofluid in a tube with longitudinal strip insert of aspect ratio AR = 1 at a Reynolds number of 22,000. Chandrasekar et al. [18] investigated the heat transfer from a circular tube when Al2O3/water nanofluid flows through circular tube with wire coil inserts and found enhancement of heat transfer up to 15.91%. Pathipakka and Sivashanmugam [19] numerically investigated heat
Nanofluid is prepared by dispersing TiO2 nanoparticles with an average particle size of 21 nm supplied by Sigma-Aldrich Chemicals Ltd. USA [27] in the mixture of ethylene glycol and water in the ratio of 40:60 by weight. The amount of nanoparticles required for different volume concentrations is estimated from the equation given below,
2 φ 6 ¼ 4 Weight 100 4260
Weight 4260 TiO 2
TiO2
þ
3
Weight 4260 Base fluid
7 5:
ð1Þ
Properties of nanofluid like thermal conductivity, viscosity, density and specific heat are estimated using the equations available in the literature. Solid–liquid homogeneous models for density and specific heat of nanofluid are given below: φ φ ρ þ ρ ρnf ¼ 1− 100 bf 100 p
ð2Þ
φ φ C þ C : C nf ¼ 1− 100 bf 100 p
ð3Þ
70
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
Fig. 1. Schematic diagram of the experimental setup.
Absolute viscosity of nanofluid is estimated from Einstein's [28] model which is given below: 5 φ : μ nf ¼ μ bf 1 þ 2 100
ð4Þ
Maxwell's model [29] which is used to estimate thermal conductivity of nanofluid is given below: 2 3 φ kp −kbf kp þ 2kbf þ 2 6 7 100 knf ¼ kbf 4 ð5Þ 5: φ kp −kbf kp þ 2kbf − 100 3. Experimental investigation 3.1. Experimental setup and procedure The schematic and photographic representation of the experimental setup used is shown in Figs. 1 and 2 respectively. It consists of a test
section, two reservoirs and two pumps. The test section is a double pipe heat exchanger of length 1.5 m. The inner tube is made from copper material with an outer diameter of 0.00953 m and an inner diameter of 0.00813 m, while the outer tube is made from PVC with an outer diameter of 0.0339 m and an inner diameter of 0.0278 m. The nanofluid is circulated through the inner tube and hot fluid is circulated through the annular space by using two pumps with an accuracy of ± 0.1 l/s. The outer tube is wound with asbestos rope insulation for minimizing the heat loss to atmosphere. The inlet and outlet temperatures of nanofluid and hot fluid are measured with J-type thermocouples with an accuracy of ±0.1 °C once the system attains the steady state conditions. The mass flow rate of nanofluid and hot fluid were also recorded. Nanofluids with different volume concentrations are prepared adding required quantity of nanoparticles to EG/W base fluid. Each time 15 l of nanofluid with desired volume concentration is prepared for heat transfer and friction factor tests. To ensure uniform dispersion of nanoparticles in the base fluid 0.5 ml of oleic acid and C-TAB (Cetyl Trimethyl Ammonium Bromide) equal to 1/10th weight of TiO2 nanoparticles were added. The solution was stirred with mechanical stirring
Fig. 2. Photograph of an experimental setup.
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
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Gnielinski [30] correlation for single phase fluid: f ðRe−1000ÞPr 2 Nu ¼ 0:5 2 1 þ 12:7 2f Pr 3 −1 −2
f ¼ ð1:58 ln ðReÞ−3:82Þ
ð12Þ 6
; 2300bReb5 10 ; 0:5bPrb2000:
Tam and Ghajar [31] correlation for single phase fluid: 0:8
Nu ¼ 0:023 Re Fig. 3. Photograph of wire coil inserts.
3≤
for about 8 h to achieve stable nanofluid. Friction factor of nanofluid is measured in terms of pressure drop. A U-tube manometer is employed to measure the pressure drop of nanofluid along the length of the test section. The U-tube manometer is attached to the 4 mm holes at both the ends of the inner tube as shown in Fig. 1. Mercury is used as manometric fluid to determine the pressure drop along the test section. Further, heat transfer experiments were conducted with nanofluid flowing in an inner tube with helical coil inserts. Helical coil inserts with P/d = 1 and 2.5 were specially made which is shown in Fig. 3 as a photographic view. The diameter of the helical wire is 0.002 m and the length is 1.5 m; helical wire coil inserts were inserted into the tube from one end of the test section. Once the experimental setup is ready, the storage tank is filled with the nanofluid. The Reynolds number is calculated based on the equivalent diameter when helical inserts are used. Initial experiments on heat transfer and friction factor are conducted with base fluid which is a mixture of ethylene glycol and water in the ratio of 40:60% by weight as a working fluid. Later nanofluids with different volume concentrations are introduced into the system. Heat transfer and friction factor experiments were conducted subsequently for nanofluid flowing in the tube with and without helical coil inserts. 3.2. Measurement of heat transfer coefficient
Q h ¼ mh C h T h;i −T ho
ð6Þ
Q c ¼ mc C c T c;0 −T c;i
ð7Þ
Q average
0:385
−0:0054 0:14 L μb D μw
L μ ≤192; 7000≤Re≤49; 000; 4≤Pr ≤34; 1:1≤ b ≤1:7: D μw
ð13Þ
Duangthongsuk and Wongwises [32] correlation for TiO2 nanofluid: 0:707
0:385
0:074
Nu ¼ 0:074Re Pr φ 3000bReb18; 000; 0bφb2:0%:
ð14Þ
Sajadi and Kazemi [33] correlation for TiO2 nanofluid 0:71
0:35
Nu ¼ 0:067Re Pr þ 0:0005Re 5000bReb30; 000; 0bφb0:25%:
ð15Þ
3.3. Measurement of friction factor Experimental friction factor is determined from the measurements of pressure drop along the length of test section and using the following equation ΔP !: f Exp ¼ L ρv2 D 2
ð16Þ
Blasius [34] equation:
Rate of heat flow from hot fluid to the cold fluid is estimated based on the measurements of inlet and outlet temperatures along with the mass flow rates of hot and cold fluids using the following set of equations:
Q þ Qc : ¼ h 2
Pr
ð8Þ
−0:25
f ¼ 0:3164Re
:
ð17Þ
A systematic error analysis is made to estimate possible errors associated with the Reynolds number, heat transfer coefficient, Nusselt number and friction factor following the procedure detailed by Beckwith et al. [36] which is shown below. 4 m˙ Reynolds number, Re ¼ πDμ δRe ¼ Re
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi δμ δ m˙ ¼ ð0:00001Þ2 þ ð0:1Þ2 ¼ 0:1%: þ μ m˙
ð18Þ
Q
average Heat transfer coefficient, hExp ¼ AðΔT Þ
LMTD
The heat loss to the environment (surroundings) from the hot fluid is of the order of ± 2.5%. Experimental heat transfer coefficient for nanofluid in a tube with and without inserts is calculated based on the Newton's law of cooling and the expression is given below: hExp ¼
Q average AðΔT ÞLMTD
ðΔT ÞLMTD
NuExp ¼
T h;i −T c;o − T h;o −T c;i ! ¼ T h;i −T c;o ln T h;o −T c;i
hExp D : k
ð9Þ
ð10Þ
ð11Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi δðΔT ÞLMTD 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi δq 2 δh ¼ þ ¼ ð0:2Þ2 þ ð−0:09Þ2 ¼ 0:22%: h q ðΔT ÞLMTD
ð19Þ
Nusselt number, Nu ¼ hD k δNu ¼ Nu
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi δh 2 δ ¼ ð0:22Þ2 þ ð0:1Þ2 ¼ 0:25%: þ k h k
Δp 2 ðDL Þ ρv2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2ffi δf δΔp 2 δρ 2 2δv ¼ þ f p ρ v qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð0:0003Þ þ ð0:1Þ þ ð2 0:00001Þ2 ¼ 0:1%:
ð20Þ
Friction factor, f ¼
ð21Þ
72
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Fig. 4. Comparison of experimental Nusselt number of 40:60% EG/W with the data from Gnielinski [30] and Tam and Ghajar [31].
Fig. 6. Nusselt number ratio as a function of Reynolds Number for TiO2 nanofluids with different volume concentrations.
As a part of calibration, experimental setup is validated by circulating base fluid through the test section and the experimental heat transfer coefficient and Nusselt number are estimated using Eqs. (9) and (11). The data generated is shown in Fig. 4 along with the data of Gnielinski [30] and Eq. (9) of Tam and Ghajar [31]. In the measured Reynolds number range, a maximum of 2.5% deviation is observed between the present experimental data and theoretical values. Close agreement with the published literature ensures reliability of the experimental test setup and the measured data. The same Eqs. (9) and (11) are used to estimate the experimental heat transfer coefficient and Nusselt number of different volume concentrations of TiO2 nanofluid. The Nusselt number estimated from Eq. (11) incorporating thermal conductivity of nanofluid is shown in Fig. 5 along with base fluid data.
Nusselt number ratio for different volume concentrations of nanofluid is shown in Fig. 6. It indicates that Nusselt number increases with increase of Reynolds number and volume concentration. The enhancement in Nusselt number for 0.02% volume concentration of TiO2 nanofluid is 7.85% and 10.73% compared to base fluid at Reynolds number from 4000 to 15,000. The enhancement in heat transfer is attributed to attractive properties of nanofluid in terms of high thermal conductivity and lower specific heat compared to the base fluid. As nanofluid contains suspended nanoparticles, they take less heat to attain a particular temperature when compared to the ethylene glycol/water mixture alone. The heat transfer enhancement in the TiO2 nanofluid is also attributed to particle Brownian motion and hence the heat transport capability of TiO2 nanoparticles will increase further. TiO2 nanoparticles present large surface area over the coarse grains and this large surface area of nanoparticles enhances the heat transfer rate of nanofluid. Experimental Nusselt number of TiO2 with different volume concentrations of nanofluid is shown in Fig. 7 and Fig. 8 with the data obtained from Sajadi and Kazemi [33] and Kayhani et al. [35]. The present
Fig. 5. Comparison of experimental Nusselt number of TiO2 nanofluid for different volume concentrations with the base fluid.
Fig. 7. Comparison of present experimental Nusselt number with the data of Sajadi and Kazemi [33].
4. Results and discussion 4.1. Nusselt number of nanofluid in a tube
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Table 1 Percentage improvement in heat transfer coefficient.
Fig. 8. Comparison of present experimental Nusselt number with the data of Kayhani et al. [35].
investigation showed similar trends of increase in Nusselt number with increase in Reynolds number and volume concentration. 4.2. Nusselt number of nanofluid in a tube with helical coil inserts Further experiments are conducted to determine heat transfer coefficient with nanofluid flowing in a tube with helical coil inserts and the Nusselt number is estimated using Eq. (11). The results are shown in Fig. 9 along with the result of nanofluid without inserts. Table 1 shows typical improvement in the measured heat transfer coefficient in terms of Nusselt number (non dimensional heat transfer coefficient) at Reynolds numbers 4000 and 15,000 respectively. The enhancement in Nusselt number of base fluid in the presence of helical wire insert with P/d = 2.5 is of the order of 9.89% and 13.85% compared to the same base fluid flowing in a plain tube without any inserts. The heat
Fig. 9. Experimental Nusselt number of base fluid and TiO2 nanofluid with different volume concentrations in plain tube with and without helical coil inserts.
Reynolds no (Re)
P/d = 0 TiO2 nanofluid with 0.02% volume concentration
P/d = 2.5 Base fluid (EG and water mixture in the ratio of 40:60% by weight)
TiO2 nanofluid with 0.02% volume concentration
4000 15,000
7.85 10.73
9.89 13.85
16.11 17.71
transfer coefficient improved further with the use of 0.02% volume concentration nanofluid for the same set of test conditions from 16.11% for Reynolds number 4000 to 17.71% for Reynolds number 15,000 compared to base fluid with inserts. It is observed that with the use of helical insert enhancement in convective heat transfer coefficient is achieved in both base fluid and TiO2 nanofluid. The helices generated in the inner tube create turbulence and swirl in the fluid and cause effective mixing of fluid. The nanoparticles in the vicinity of inner wall of the tube will carry heat energy and transmit the same to the adjacent fluid layers of cold fluid at a faster rate. The helices also increase the retention time of flow in the test section as the fluid has to move in a helical path, consequently increasing the flow path length. This could be another reason which is responsible for enhancement in the performance of heat transfer in nanofluid. The pitch length also affects the heat transfer and more heat transfer is observed with helical inserts of shorter pitch length. This is due to intensification of swirl which promotes convective heat transfer in the TiO2 nanofluid. Experimental work with ethylene glycol based TiO2 nanofluid with helical inserts is not reported so far in the literature. New correlations are developed based on the present experimental data. A regression equation is presented to predict the Nusselt number with an average deviation of 4.33% and standard deviation of 5.396% and is given below. P 0:037 1þ d 4000bReb15000; 0bφb0:02%; 24:45bPrb32:85 0bP=db2:5 ðφ ¼ 0; P=d ¼ 0 for plain tubeÞ: 0:8
NuReg ¼ 0:007523 Re
Pr
0:5
7:6
ð1 þ φÞ
ð22Þ
The present experimental data of Nusselt number and estimated values from Eq. (22) are shown in Fig. 10 which ensures the validity of the regression equation.
Fig. 10. Comparison between experimental and proposed regression values of Nusselt number.
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Fig. 11. Comparison of experimental friction factor of 40:60% EG/W with Eq. (17) of Blasius [34].
4.3. Friction factor for nanofluid flowing in a plain tube Experimental friction factor of base fluid estimated from Eq. (16) and the data obtained from Eq. (17) of Blasius [34] is shown in Fig. 11. There is not much of a deviation between the measured and theoretical values. Experiments are conducted to determine friction factor with different volume concentrations of TiO2 nanofluid and are shown in Fig. 12 along with the base fluid friction factor data. It is observed that friction factor increases with increase of volume concentration and Reynolds number. The enhancement in friction factor for 0.02% volume concentration of TiO2 nanofluid is about 7.67% and 8.73% compared to base fluid at the Reynolds numbers 4000 and 15,000 respectively. This is caused due to the addition of nanoparticles to the base fluid. However, it is expected that it may not affect the pump performance because of very low volume concentrations considered in the present work. 4.4. Friction factor for nanofluid flowing in a tube with helical coil inserts Further experiments are conducted on friction factor with helical wire inserts inside a tube and the experimental results are shown in
Fig. 13. Experimental friction factor of TiO2 nanofluid in a tube with helical coil inserts.
Fig. 13 and Table 2. From the figure one can observe that friction factor increases with increase of helical twist ratio, volume concentration and Reynolds number. Table 2 shows increase in the measured friction factor at Reynolds numbers 4000 and 15,000 respectively. The enhancement in the friction factor of base fluid in the presence of helical wire insert with P/d = 2.5 is of the order of 8.35% and 10.69% compared to the same base fluid flowing in a plain tube without any inserts. The friction factor increased further, when TiO2 nanofluids are used with 0.02% volume concentration for the same test conditions, from 13.39% for Reynolds number 4000 to 16.58% for Reynolds number 15,000 compared to the base fluid with inserts. This is caused due to the flow obstruction which takes place with helical coil inserts. But, the magnitude of nanofluid friction factor with helical coil inserts is negligible. It is expected that, it may not cause severe penalty on the pumping power of nanofluid into the test section. The correlation for friction factor is developed with an average deviation of 1.86% and standard deviation of 2.2% and is given by P 0:041 1þ d 4000bReb15000; 0bφb0:02%; 24:45bPrb32:85 0bP=db2:5 ðφ ¼ 0; P=d ¼ 0 for plain tubeÞ: −0:2377
f Reg ¼ 0:3250 Re
2:723
ð1 þ φÞ
ð23Þ
The graph between the experimental friction factor and the values estimated from Eq. (23) is shown in Fig. 14 to validate the regression equation. Eqs. (22) and (23) developed for Nusselt number and for friction factor are valid for both base fluid and TiO2 nanofluid in a plain tube and tube with helical inserts.
Table 2 Percentage increase in friction factor.
Fig. 12. Experimental friction factor of TiO2 nanofluid and corresponding base fluid.
Reynolds no (Re)
P/d = 0 TiO2 nanofluid with 0.02% volume concentration
P/d = 2.5 Base fluid (EG and water mixture in the ratio of 40:60% by weight)
TiO2 nanofluid with 0.02% volume concentration
4000 15,000
7.67 8.73
8.35 10.69
13.39 16.58
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References
Fig. 14. Comparison between experimental and proposed regression values.
5. Conclusions The present study is focused on the investigation of heat transfer and friction factor of ethylene glycol/water based TiO2 nanofluid flowing in a circular tube with and without helical coil inserts. The following are the observations from the experimental investigation. 1. In TiO2 nanofluid with 0.02% concentration there is an enhancement of heat transfer from 7.85% to 10.73% when the Reynolds number is varied in the range from 4000 to 15,000 compared to base fluid. 2. There is further enhancement of heat transfer in the presence of helical coil inserts. It is observed that in the presence of helical coil inserts with P/d ratio of 2.5 there is an enhancement from 7.85% to 16.11% at 4000 Reynolds number. The enhancement in heat transfer further increased to 17.71% when Reynolds number increased to 15,000. As can be seen from Table 1 the heat transfer enhancement is also due to the contribution of helical coil inserts. Hence, there is a combined effect of coil inserts as well as the presence of nanoparticles. Similar explanation holds good even for friction factor, as per the data shown in Table 2. 3. The use of helical coil inserts is advantageous to enhance heat transfer on one hand and on the other hand it introduces undesirable pressure drop in the circuit. Much better performance in terms of heat transfer is observed with TiO2 nanofluid over the conventional base fluid. 4. Nusselt number and friction factor correlations from present investigation are given below. 0:8
NuReg ¼ 0:007523 Re
−0:2377
f Reg ¼ 0:3250 Re
Pr
0:5
7:6
ð1 þ φÞ
2:723
ð1 þ φÞ
P 0:037 1þ d
P 0:041 1þ : d
Acknowledgments The authors would like to thank the management of Sreenidhi Institute of Science and Technology, Hyderabad for the support and encouragement given for this research work. The authors would like to acknowledge AICTE for the financial support through RPS project on “Energy optimization in heat transfer equipment” file no#8023/RID/ BOR/RPS/83/5/3.
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Thompson, Anomalously increase effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78 (6) (2001) 718–720. [7] S.K. Das, N. Putra, P. Thiesen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, J. Heat Transf. 125 (2003) 567–574. [8] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer 11 (1998) 151–170. [9] Y. Xuan, Q. Li, Investigation on convective heat transfer and flow features of nanofluids, J. Heat Transf. 125 (2003) 151–155. [10] D. Wen, Y. Ding, Experimental investigation into convective heat transfer of nanofluid at the entrance region under laminar flow conditions, Int. J. Heat Mass Transf. 47 (24) (2004) 5181–5188. [11] S.Z. Heris, M.N. Esfahany, S.Gh. Etemad, Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube, Int. J. Heat Fluid Flow 28 (2007) 203–210. [12] S.E.B. Maiga, S.J. Palm, C.T. Nguyen, G. Roy, N. Galanis, Heat transfer enhancement by using nanofluids in forced convection flows, Int. J. Heat Fluid Flow 26 (2005) 530–546. [13] S.J. Palm, G. Roy, C.T. Nguyen, Heat transfer enhancement in radial flow cooling system-using nanofluid, Proc. ICHMT Int. Symp. Adv. Comput. Heat Transfer Norway (2004) 04–121. [14] G. Roy, C.T. Nguyen, P.R. Lajoie, Numerical investigation of laminar flow and heat transfer in a radial flow cooling system with the use of nanofluids, Superlattice. Microst. 35 (3) (2004) 497–511. [15] N. Putra, W. Roetzel, S.K. Das, Natural convection of nanofluids, Heat Mass Transf. 39 (8) (2003) 775–784. [16] L.S. Sundar, K.V. Sharma, Turbulent heat transfer and friction factor of Al2O3 nanofluid in circular tube with twisted tape inserts, Int. J. Heat Mass Transf. 53 (2010) 1409–1416. [17] L.S. Sundar, K.V. Sharma, Heat transfer enhancements of low volume concentration Al2O3 nanofluid and with longitudinal strip inserts in a circular tube, Int. J. Heat Mass Transf. 53 (19–20) (2010) 4280–4286. [18] M. Chandrasekar, S. Suresh, A. Chandra Bose, Experimental studies on heat transfer and friction factor characteristics of Al2O3/water nanofluid in a circular pipe under laminar flow with wire coil inserts, Exp. Thermal Fluid Sci. 34 (2) (2010) 122–130. [19] G. Pathipakka, P. Sivashanmugam, Heat transfer behaviour of nanofluids in a uniformly heated circular tube fitted with helical inserts in laminar flow, Superlattice. Microst. 47 (2) (2010) 349–360. [20] M. Saeedinia, M.A.A. Behabadi, M. Nasr, Experimental study on heat transfer and pressure drop of nanofluid flow in a horizontal coiled wire inserted tube under constant heat flux, Exp. Thermal Fluid Sci. 36 (2012) 158–168. [21] M. Chandrasekar, S. Suresh, A. Chandra Bose, Experimental studies on heat transfer and friction factor characteristics of Al2O3/water nanofluid in a circular pipe under transition flow with wire coil inserts, Heat Transfer Eng. 32 (6) (2011) 485–496. [22] L.S. Sundar, M.K. Singh, Convective heat transfer and friction factor correlations of nanofluid in a tube and with inserts: a review, Renew. Sust. Energ. Rev. 20 (2013) 23–35. [23] P.K. Namburu, D.P. Kulkarni, D. Misra, D.K. Das, Viscosity of copper oxide nanoparticles dispersed in ethylene glycol and water mixture, Exp. Thermal Fluid Sci. 32 (2007) 397–402. [24] R.S. Vajjha, D.K. Das, Experimental determination of thermal conductivity of three nanofluids and development of new correlations, Int. J. Heat Mass Transf. 52 (2009) 4675–4682. [25] M.T. Naik, L.S. Sundar, Investigation into thermophysical properties of glycol based CuO nanofluid for heat transfer applications, World Acad. Sci. Eng. Technol. 59 (2011) 440–446. [26] P.K. Namburu, D.K. Das, K.M. Tanguturi, R.K. Vajjha, Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties, Int. J. Therm. Sci. 48 (2) (2009) 290–302. [27] www.sigma-aldrich.com. [28] A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Publications, New York, 1956. [29] J.C. Maxwell, On Electricity and Magnetism, Oxford University Press, Oxford, 1881. [30] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359–368. [31] L.M. Tam, A.F. Ghajar, Transitional heat transfer in plain horizontal tubes, Heat Transfer Eng. 27 (5) (2006) 23–38. [32] W. Duangthongsuk, S. Wongwises, Heat transfer enhancement and pressure drop characteristics of TiO2–water nanofluid in a double-tube counter flow heat exchanger, Int. J. Heat Mass Transf. 52 (7–8) (2009) 2059–2067.
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[33] 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 (2011) 1474–1478. [34] H. Blasius, Grenzschichten in Flussigkeiten mit kleiner Reibung (German), Z. Math. Phys. 56 (1908) 1–37.
[35] 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 (2012) 456–462. [36] T.G. Beckwith, R.D. Marangoni, L.H. Lienhard, Mechanical Measurements, Fifth ed. Addison–Wesley Publishing Company, New York, 1990. 45–112.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluid in double pipe heat exchanger with and without helical coil inserts☆ M. Chandra Sekhara Reddy, Veeredhi Vasudeva Rao ⁎ Department of Mechanical Engineering, Sreenidhi Institute of Science and Technology, Yamnampet, Ghatkesar, Hyderabad 501301, India
a r t i c l e
i n f o
Available online 14 November 2013 Keywords: Heat transfer Friction factor Helical coil inserts TiO2 nanofluid
a b s t r a c t Heat transfer coefficient and friction factor of TiO2 nanofluid flowing in a double pipe heat exchanger with and without helical coil inserts are studied experimentally. The experiments are conducted in the range of Reynolds number from 4000 to 15,000 and in the volume concentration range from 0.0004% to 0.02%. The base fluid is prepared by considering 40% of ethylene glycol and 60% of distilled water. The heat transfer coefficient and friction factor get enhanced by 10.73% and 8.73% for 0.02% volume concentration of nanofluid when compared to base fluid flowing in a tube. Heat transfer coefficient and friction factor further get enhanced by 13.85% and 10.69% respectively for 0.02% nanofluid when compared to base fluid flowing in a tube with helical coil insert of P/d = 2.5. The measured values of heat transfer coefficient and friction factor are compared with the published literature. Based on the experimental data, generalized correlations are proposed for Nusselt number and friction factor. The results are presented in graphical and tabular form. Uncertainty analysis is also carried out and the experimental error is in the range of ±10%. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Heat exchangers are employed in automobiles to dissipate heat rejected by the internal combustion engine to the sink through a suitable liquid called coolant. There are a number of conventional fluids that are suitable to maintain the sink in the desired operating temperature range. Pure water and ethylene glycol in combination with water are being used as coolant during the last couple of centuries. Due to advent of new technologies there are a number of improvements in the field of automobile engineering including enhancements in heat dissipation capabilities, reduction in size and increased power generation. There is a considerable improvement even in heat transfer fluid properties that are responsible for dissipation of heat from the automobile to the environment (surroundings) while passing through the heat exchanger (radiator). The effectiveness of heat exchanger depends on the characteristics and properties of heat transfer fluids. A stage has come now that the limitation of heat transfer fluids is in turn limiting the effectiveness of heat exchangers. To overcome these limitations conventional fluids are now being replaced with nanofluids. There have been many experimental studies by engineers and researchers on converting conventional fluids into nanofluids. In their early attempts micro metallic particles with high thermal conductivity were added to the heat transfer fluids with a hope to improve thermal ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (V. Vasudeva Rao). 0735-1933/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.icheatmasstransfer.2013.11.002
properties. However due to micron size of particles there were several problems like sedimentation and erosion of tubes and pumps while in transit. In the recent past the availability of nanomaterials renewed the interest in the application of nanofluids. The suitability and performance of these conventional fluids can be enhanced by introducing nanoparticles like Al2O3, TiO2 and CuO, by converting them in to nanofluids [1]. Masuda et al. [2], Lee et al. [3], Wang et al. [4], Eastman et al. [5,6], and Das et al. [7] mostly concentrated on the determination of effective thermal conductivity of nanofluids. Heat transfer enhancements in forced convection with different nanofluids flowing in a tube under laminar and turbulent flow conditions have been reported by many researchers in open literature. Pak and Cho [8] experimentally observed enhancements in heat transfer with Al2O3 and TiO2 nanofluids in a tube under turbulent flow condition and proposed Nusselt number correlation. Similar observations were made by Xuan and Li [9] with Cu nanofluid and proposed correlations for Nusselt number as a function of particle diameter. Wen and Ding [10] experimentally observed heat transfer enhancement with Al2O3 nanofluid in laminar entry region. Heris et al. [11] conducted experiments on Al2O3/water nanofluid in the range of Reynolds number from 700 to 2050 and observed heat transfer enhancement with increase of Peclet number and volume concentration. Numerical analysis has been conducted to fully understand the heat transfer capabilities of these nanofluids. Maiga et al. [12] observed the heat transfer enhancement in water/Al2O3 and ethylene glycol/Al2O3 nanofluid in the laminar flow through their numerical analysis. Palm et al. [13] also reported results of numerical analysis of laminar flow heat transfer of
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
Nomenclature A C D d f h k L m˙ Nu Pr P Q Re T v
Area, m2 Specific heat, J/kg K Inner diameter of the tube, m Diameter of the helical coil, m Friction factor Heat transfer coefficient, W/m2K Thermal conductivity, W/mK Length of the tube, m Mass flow rate, kg/s Nusselt number, hD/k Prandtl number, μ C/k Helical pitch, m Heat flow, Watts Reynolds number, 4 m/πDμ Temperature, °C Velocity, m/s
Greek symbols δ Uncertainty ΔT Temperature difference Δp Pressure drop φ Volume concentration of nanoparticles, % μ Dynamic viscosity, kg/m2s ρ Density, kg/m3
Subscripts bf Base fluid C cold Exp Experimental h hot i Inlet nf Nanofluid o Outlet p Particle Reg Regression
69
transfer of 1.5% volume concentration of Al2O3/water nanofluid in a tube with twisted tape inserts of 2.93 twist ratio and found 31.29% enhancement in the heat transfer at Reynolds number of 2039. Saeedinia et al. [20] experimentally found 45% enhancement in heat transfer for 0.3% volume concentration of CuO/base oil nanofluid in a tube with wire coil inserts under laminar flow conditions. Fully developed laminar flow of 0.1% of Al2O3 nanofluid in a tube with wire coil inserts has been analyzed by Chandrasekar et al. [21]. They have experimentally observed 21.53% heat transfer enhancement with wire coil insert with a pitch of 3 and developed Nusselt number correlation. Sundar and Singh [22] emphasized on the available Nusselt number correlations for nanofluid in a tube with different types of inserts. Many researchers have considered water based nanofluids for their heat transfer studies in a tube with inserts. The applicability of water based nanofluids is limited in the cold countries like Alaska, Canada, Northern Europe and Russia, due to freezing of water at 0 °C. To avoid freezing of water ethylene glycol is added in suitable proportions. A mixture of water and ethylene glycol is a commonly used coolant in car radiators. Generally, ethylene glycol and water are mixed in the ratio of 40:60%. Namburu et al. [23] first time prepared 60:40% EG/W mixture based CuO nanofluid and conducted studies on viscosity. Vajjha and Das [24] studied thermal conductivity of 60:40% EG/W based Al2O3, CuO and ZnO nanofluids and they observed that for same volume concentration and temperature range CuO nanofluid has a high thermal conductivity compared to Al2O3 and ZnO nanofluids with volume concentrations up to 10%. Naik and Sundar [25] considered propylene glycol and water mixture in the ratio of 70:30 as a base fluid for the preparation of CuO nanofluid and found better thermal conductivity and viscosity compared to base fluid. Namburu et al. [26] obtained numerically the heat transfer enhancement with CuO, Al2O3, and SiO2 nanofluids and compared with the base liquid, under turbulent flow conditions. The data on the mixture of ethylene glycol and water based nanofluid flowing in a tube with inserts is not available in the literature. Therefore, the focus of the present work is on the estimation of heat transfer coefficient and friction factor of ethylene glycol and water mixture based TiO2 nanofluid flowing in double pipe heat exchanger with helical coil inserts experimentally. The heat transfer experiments are conducted in the Reynolds number range from 4000 to 15,000. Based on the experimental data generalized correlations are proposed for Nusselt number and friction factor. 2. Nanofluid preparation and its properties
Al2O3/ethylene glycol and Al2O3/water nanofluids in a tube. Roy et al. [14] observed heat transfer enhancement by considering wall shear stress to increase with volume concentration and Reynolds number. Putra et al. [15] reported natural convection heat transfer with Al2O3/ water and CuO/water nanofluids. Thus in all cases nanofluids exhibited higher heat transfer capability compared to water in both laminar and turbulent flow conditions in all experimental and numerical studies. Further, heat transfer enhancement using nanofluids is possible through passive methods such as creation of turbulence in the flow field by inserting some kind of inserts in a tube. Sundar and Sharma [16] conducted experiments to determine heat transfer coefficient and friction factor with Al2O3 nanofluid flowing in a tube with different types of twisted tape inserts. They observed 30.30% enhancement in heat transfer with 0.5% volume concentration of Al2O3 at 22,000 Reynolds number. Further enhancement of 42.17% in heat transfer is observed with same concentration of Al2O3 using twisted tape inserts of twist ratio H/D = 5. Sundar and Sharma [17] observed further heat transfer enhancement of 80.19% with 0.5% volume concentration of Al2O3 nanofluid in a tube with longitudinal strip insert of aspect ratio AR = 1 at a Reynolds number of 22,000. Chandrasekar et al. [18] investigated the heat transfer from a circular tube when Al2O3/water nanofluid flows through circular tube with wire coil inserts and found enhancement of heat transfer up to 15.91%. Pathipakka and Sivashanmugam [19] numerically investigated heat
Nanofluid is prepared by dispersing TiO2 nanoparticles with an average particle size of 21 nm supplied by Sigma-Aldrich Chemicals Ltd. USA [27] in the mixture of ethylene glycol and water in the ratio of 40:60 by weight. The amount of nanoparticles required for different volume concentrations is estimated from the equation given below,
2 φ 6 ¼ 4 Weight 100 4260
Weight 4260 TiO 2
TiO2
þ
3
Weight 4260 Base fluid
7 5:
ð1Þ
Properties of nanofluid like thermal conductivity, viscosity, density and specific heat are estimated using the equations available in the literature. Solid–liquid homogeneous models for density and specific heat of nanofluid are given below: φ φ ρ þ ρ ρnf ¼ 1− 100 bf 100 p
ð2Þ
φ φ C þ C : C nf ¼ 1− 100 bf 100 p
ð3Þ
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Fig. 1. Schematic diagram of the experimental setup.
Absolute viscosity of nanofluid is estimated from Einstein's [28] model which is given below: 5 φ : μ nf ¼ μ bf 1 þ 2 100
ð4Þ
Maxwell's model [29] which is used to estimate thermal conductivity of nanofluid is given below: 2 3 φ kp −kbf kp þ 2kbf þ 2 6 7 100 knf ¼ kbf 4 ð5Þ 5: φ kp −kbf kp þ 2kbf − 100 3. Experimental investigation 3.1. Experimental setup and procedure The schematic and photographic representation of the experimental setup used is shown in Figs. 1 and 2 respectively. It consists of a test
section, two reservoirs and two pumps. The test section is a double pipe heat exchanger of length 1.5 m. The inner tube is made from copper material with an outer diameter of 0.00953 m and an inner diameter of 0.00813 m, while the outer tube is made from PVC with an outer diameter of 0.0339 m and an inner diameter of 0.0278 m. The nanofluid is circulated through the inner tube and hot fluid is circulated through the annular space by using two pumps with an accuracy of ± 0.1 l/s. The outer tube is wound with asbestos rope insulation for minimizing the heat loss to atmosphere. The inlet and outlet temperatures of nanofluid and hot fluid are measured with J-type thermocouples with an accuracy of ±0.1 °C once the system attains the steady state conditions. The mass flow rate of nanofluid and hot fluid were also recorded. Nanofluids with different volume concentrations are prepared adding required quantity of nanoparticles to EG/W base fluid. Each time 15 l of nanofluid with desired volume concentration is prepared for heat transfer and friction factor tests. To ensure uniform dispersion of nanoparticles in the base fluid 0.5 ml of oleic acid and C-TAB (Cetyl Trimethyl Ammonium Bromide) equal to 1/10th weight of TiO2 nanoparticles were added. The solution was stirred with mechanical stirring
Fig. 2. Photograph of an experimental setup.
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
71
Gnielinski [30] correlation for single phase fluid: f ðRe−1000ÞPr 2 Nu ¼ 0:5 2 1 þ 12:7 2f Pr 3 −1 −2
f ¼ ð1:58 ln ðReÞ−3:82Þ
ð12Þ 6
; 2300bReb5 10 ; 0:5bPrb2000:
Tam and Ghajar [31] correlation for single phase fluid: 0:8
Nu ¼ 0:023 Re Fig. 3. Photograph of wire coil inserts.
3≤
for about 8 h to achieve stable nanofluid. Friction factor of nanofluid is measured in terms of pressure drop. A U-tube manometer is employed to measure the pressure drop of nanofluid along the length of the test section. The U-tube manometer is attached to the 4 mm holes at both the ends of the inner tube as shown in Fig. 1. Mercury is used as manometric fluid to determine the pressure drop along the test section. Further, heat transfer experiments were conducted with nanofluid flowing in an inner tube with helical coil inserts. Helical coil inserts with P/d = 1 and 2.5 were specially made which is shown in Fig. 3 as a photographic view. The diameter of the helical wire is 0.002 m and the length is 1.5 m; helical wire coil inserts were inserted into the tube from one end of the test section. Once the experimental setup is ready, the storage tank is filled with the nanofluid. The Reynolds number is calculated based on the equivalent diameter when helical inserts are used. Initial experiments on heat transfer and friction factor are conducted with base fluid which is a mixture of ethylene glycol and water in the ratio of 40:60% by weight as a working fluid. Later nanofluids with different volume concentrations are introduced into the system. Heat transfer and friction factor experiments were conducted subsequently for nanofluid flowing in the tube with and without helical coil inserts. 3.2. Measurement of heat transfer coefficient
Q h ¼ mh C h T h;i −T ho
ð6Þ
Q c ¼ mc C c T c;0 −T c;i
ð7Þ
Q average
0:385
−0:0054 0:14 L μb D μw
L μ ≤192; 7000≤Re≤49; 000; 4≤Pr ≤34; 1:1≤ b ≤1:7: D μw
ð13Þ
Duangthongsuk and Wongwises [32] correlation for TiO2 nanofluid: 0:707
0:385
0:074
Nu ¼ 0:074Re Pr φ 3000bReb18; 000; 0bφb2:0%:
ð14Þ
Sajadi and Kazemi [33] correlation for TiO2 nanofluid 0:71
0:35
Nu ¼ 0:067Re Pr þ 0:0005Re 5000bReb30; 000; 0bφb0:25%:
ð15Þ
3.3. Measurement of friction factor Experimental friction factor is determined from the measurements of pressure drop along the length of test section and using the following equation ΔP !: f Exp ¼ L ρv2 D 2
ð16Þ
Blasius [34] equation:
Rate of heat flow from hot fluid to the cold fluid is estimated based on the measurements of inlet and outlet temperatures along with the mass flow rates of hot and cold fluids using the following set of equations:
Q þ Qc : ¼ h 2
Pr
ð8Þ
−0:25
f ¼ 0:3164Re
:
ð17Þ
A systematic error analysis is made to estimate possible errors associated with the Reynolds number, heat transfer coefficient, Nusselt number and friction factor following the procedure detailed by Beckwith et al. [36] which is shown below. 4 m˙ Reynolds number, Re ¼ πDμ δRe ¼ Re
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi δμ δ m˙ ¼ ð0:00001Þ2 þ ð0:1Þ2 ¼ 0:1%: þ μ m˙
ð18Þ
Q
average Heat transfer coefficient, hExp ¼ AðΔT Þ
LMTD
The heat loss to the environment (surroundings) from the hot fluid is of the order of ± 2.5%. Experimental heat transfer coefficient for nanofluid in a tube with and without inserts is calculated based on the Newton's law of cooling and the expression is given below: hExp ¼
Q average AðΔT ÞLMTD
ðΔT ÞLMTD
NuExp ¼
T h;i −T c;o − T h;o −T c;i ! ¼ T h;i −T c;o ln T h;o −T c;i
hExp D : k
ð9Þ
ð10Þ
ð11Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi δðΔT ÞLMTD 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi δq 2 δh ¼ þ ¼ ð0:2Þ2 þ ð−0:09Þ2 ¼ 0:22%: h q ðΔT ÞLMTD
ð19Þ
Nusselt number, Nu ¼ hD k δNu ¼ Nu
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi δh 2 δ ¼ ð0:22Þ2 þ ð0:1Þ2 ¼ 0:25%: þ k h k
Δp 2 ðDL Þ ρv2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2ffi δf δΔp 2 δρ 2 2δv ¼ þ f p ρ v qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð0:0003Þ þ ð0:1Þ þ ð2 0:00001Þ2 ¼ 0:1%:
ð20Þ
Friction factor, f ¼
ð21Þ
72
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
Fig. 4. Comparison of experimental Nusselt number of 40:60% EG/W with the data from Gnielinski [30] and Tam and Ghajar [31].
Fig. 6. Nusselt number ratio as a function of Reynolds Number for TiO2 nanofluids with different volume concentrations.
As a part of calibration, experimental setup is validated by circulating base fluid through the test section and the experimental heat transfer coefficient and Nusselt number are estimated using Eqs. (9) and (11). The data generated is shown in Fig. 4 along with the data of Gnielinski [30] and Eq. (9) of Tam and Ghajar [31]. In the measured Reynolds number range, a maximum of 2.5% deviation is observed between the present experimental data and theoretical values. Close agreement with the published literature ensures reliability of the experimental test setup and the measured data. The same Eqs. (9) and (11) are used to estimate the experimental heat transfer coefficient and Nusselt number of different volume concentrations of TiO2 nanofluid. The Nusselt number estimated from Eq. (11) incorporating thermal conductivity of nanofluid is shown in Fig. 5 along with base fluid data.
Nusselt number ratio for different volume concentrations of nanofluid is shown in Fig. 6. It indicates that Nusselt number increases with increase of Reynolds number and volume concentration. The enhancement in Nusselt number for 0.02% volume concentration of TiO2 nanofluid is 7.85% and 10.73% compared to base fluid at Reynolds number from 4000 to 15,000. The enhancement in heat transfer is attributed to attractive properties of nanofluid in terms of high thermal conductivity and lower specific heat compared to the base fluid. As nanofluid contains suspended nanoparticles, they take less heat to attain a particular temperature when compared to the ethylene glycol/water mixture alone. The heat transfer enhancement in the TiO2 nanofluid is also attributed to particle Brownian motion and hence the heat transport capability of TiO2 nanoparticles will increase further. TiO2 nanoparticles present large surface area over the coarse grains and this large surface area of nanoparticles enhances the heat transfer rate of nanofluid. Experimental Nusselt number of TiO2 with different volume concentrations of nanofluid is shown in Fig. 7 and Fig. 8 with the data obtained from Sajadi and Kazemi [33] and Kayhani et al. [35]. The present
Fig. 5. Comparison of experimental Nusselt number of TiO2 nanofluid for different volume concentrations with the base fluid.
Fig. 7. Comparison of present experimental Nusselt number with the data of Sajadi and Kazemi [33].
4. Results and discussion 4.1. Nusselt number of nanofluid in a tube
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
73
Table 1 Percentage improvement in heat transfer coefficient.
Fig. 8. Comparison of present experimental Nusselt number with the data of Kayhani et al. [35].
investigation showed similar trends of increase in Nusselt number with increase in Reynolds number and volume concentration. 4.2. Nusselt number of nanofluid in a tube with helical coil inserts Further experiments are conducted to determine heat transfer coefficient with nanofluid flowing in a tube with helical coil inserts and the Nusselt number is estimated using Eq. (11). The results are shown in Fig. 9 along with the result of nanofluid without inserts. Table 1 shows typical improvement in the measured heat transfer coefficient in terms of Nusselt number (non dimensional heat transfer coefficient) at Reynolds numbers 4000 and 15,000 respectively. The enhancement in Nusselt number of base fluid in the presence of helical wire insert with P/d = 2.5 is of the order of 9.89% and 13.85% compared to the same base fluid flowing in a plain tube without any inserts. The heat
Fig. 9. Experimental Nusselt number of base fluid and TiO2 nanofluid with different volume concentrations in plain tube with and without helical coil inserts.
Reynolds no (Re)
P/d = 0 TiO2 nanofluid with 0.02% volume concentration
P/d = 2.5 Base fluid (EG and water mixture in the ratio of 40:60% by weight)
TiO2 nanofluid with 0.02% volume concentration
4000 15,000
7.85 10.73
9.89 13.85
16.11 17.71
transfer coefficient improved further with the use of 0.02% volume concentration nanofluid for the same set of test conditions from 16.11% for Reynolds number 4000 to 17.71% for Reynolds number 15,000 compared to base fluid with inserts. It is observed that with the use of helical insert enhancement in convective heat transfer coefficient is achieved in both base fluid and TiO2 nanofluid. The helices generated in the inner tube create turbulence and swirl in the fluid and cause effective mixing of fluid. The nanoparticles in the vicinity of inner wall of the tube will carry heat energy and transmit the same to the adjacent fluid layers of cold fluid at a faster rate. The helices also increase the retention time of flow in the test section as the fluid has to move in a helical path, consequently increasing the flow path length. This could be another reason which is responsible for enhancement in the performance of heat transfer in nanofluid. The pitch length also affects the heat transfer and more heat transfer is observed with helical inserts of shorter pitch length. This is due to intensification of swirl which promotes convective heat transfer in the TiO2 nanofluid. Experimental work with ethylene glycol based TiO2 nanofluid with helical inserts is not reported so far in the literature. New correlations are developed based on the present experimental data. A regression equation is presented to predict the Nusselt number with an average deviation of 4.33% and standard deviation of 5.396% and is given below. P 0:037 1þ d 4000bReb15000; 0bφb0:02%; 24:45bPrb32:85 0bP=db2:5 ðφ ¼ 0; P=d ¼ 0 for plain tubeÞ: 0:8
NuReg ¼ 0:007523 Re
Pr
0:5
7:6
ð1 þ φÞ
ð22Þ
The present experimental data of Nusselt number and estimated values from Eq. (22) are shown in Fig. 10 which ensures the validity of the regression equation.
Fig. 10. Comparison between experimental and proposed regression values of Nusselt number.
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Fig. 11. Comparison of experimental friction factor of 40:60% EG/W with Eq. (17) of Blasius [34].
4.3. Friction factor for nanofluid flowing in a plain tube Experimental friction factor of base fluid estimated from Eq. (16) and the data obtained from Eq. (17) of Blasius [34] is shown in Fig. 11. There is not much of a deviation between the measured and theoretical values. Experiments are conducted to determine friction factor with different volume concentrations of TiO2 nanofluid and are shown in Fig. 12 along with the base fluid friction factor data. It is observed that friction factor increases with increase of volume concentration and Reynolds number. The enhancement in friction factor for 0.02% volume concentration of TiO2 nanofluid is about 7.67% and 8.73% compared to base fluid at the Reynolds numbers 4000 and 15,000 respectively. This is caused due to the addition of nanoparticles to the base fluid. However, it is expected that it may not affect the pump performance because of very low volume concentrations considered in the present work. 4.4. Friction factor for nanofluid flowing in a tube with helical coil inserts Further experiments are conducted on friction factor with helical wire inserts inside a tube and the experimental results are shown in
Fig. 13. Experimental friction factor of TiO2 nanofluid in a tube with helical coil inserts.
Fig. 13 and Table 2. From the figure one can observe that friction factor increases with increase of helical twist ratio, volume concentration and Reynolds number. Table 2 shows increase in the measured friction factor at Reynolds numbers 4000 and 15,000 respectively. The enhancement in the friction factor of base fluid in the presence of helical wire insert with P/d = 2.5 is of the order of 8.35% and 10.69% compared to the same base fluid flowing in a plain tube without any inserts. The friction factor increased further, when TiO2 nanofluids are used with 0.02% volume concentration for the same test conditions, from 13.39% for Reynolds number 4000 to 16.58% for Reynolds number 15,000 compared to the base fluid with inserts. This is caused due to the flow obstruction which takes place with helical coil inserts. But, the magnitude of nanofluid friction factor with helical coil inserts is negligible. It is expected that, it may not cause severe penalty on the pumping power of nanofluid into the test section. The correlation for friction factor is developed with an average deviation of 1.86% and standard deviation of 2.2% and is given by P 0:041 1þ d 4000bReb15000; 0bφb0:02%; 24:45bPrb32:85 0bP=db2:5 ðφ ¼ 0; P=d ¼ 0 for plain tubeÞ: −0:2377
f Reg ¼ 0:3250 Re
2:723
ð1 þ φÞ
ð23Þ
The graph between the experimental friction factor and the values estimated from Eq. (23) is shown in Fig. 14 to validate the regression equation. Eqs. (22) and (23) developed for Nusselt number and for friction factor are valid for both base fluid and TiO2 nanofluid in a plain tube and tube with helical inserts.
Table 2 Percentage increase in friction factor.
Fig. 12. Experimental friction factor of TiO2 nanofluid and corresponding base fluid.
Reynolds no (Re)
P/d = 0 TiO2 nanofluid with 0.02% volume concentration
P/d = 2.5 Base fluid (EG and water mixture in the ratio of 40:60% by weight)
TiO2 nanofluid with 0.02% volume concentration
4000 15,000
7.67 8.73
8.35 10.69
13.39 16.58
M. Chandra Sekhara Reddy, V. Vasudeva Rao / International Communications in Heat and Mass Transfer 50 (2014) 68–76
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References
Fig. 14. Comparison between experimental and proposed regression values.
5. Conclusions The present study is focused on the investigation of heat transfer and friction factor of ethylene glycol/water based TiO2 nanofluid flowing in a circular tube with and without helical coil inserts. The following are the observations from the experimental investigation. 1. In TiO2 nanofluid with 0.02% concentration there is an enhancement of heat transfer from 7.85% to 10.73% when the Reynolds number is varied in the range from 4000 to 15,000 compared to base fluid. 2. There is further enhancement of heat transfer in the presence of helical coil inserts. It is observed that in the presence of helical coil inserts with P/d ratio of 2.5 there is an enhancement from 7.85% to 16.11% at 4000 Reynolds number. The enhancement in heat transfer further increased to 17.71% when Reynolds number increased to 15,000. As can be seen from Table 1 the heat transfer enhancement is also due to the contribution of helical coil inserts. Hence, there is a combined effect of coil inserts as well as the presence of nanoparticles. Similar explanation holds good even for friction factor, as per the data shown in Table 2. 3. The use of helical coil inserts is advantageous to enhance heat transfer on one hand and on the other hand it introduces undesirable pressure drop in the circuit. Much better performance in terms of heat transfer is observed with TiO2 nanofluid over the conventional base fluid. 4. Nusselt number and friction factor correlations from present investigation are given below. 0:8
NuReg ¼ 0:007523 Re
−0:2377
f Reg ¼ 0:3250 Re
Pr
0:5
7:6
ð1 þ φÞ
2:723
ð1 þ φÞ
P 0:037 1þ d
P 0:041 1þ : d
Acknowledgments The authors would like to thank the management of Sreenidhi Institute of Science and Technology, Hyderabad for the support and encouragement given for this research work. The authors would like to acknowledge AICTE for the financial support through RPS project on “Energy optimization in heat transfer equipment” file no#8023/RID/ BOR/RPS/83/5/3.
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