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Effect of full length twisted tape inserts on heat transfer and friction factor enhancement with Fe3O4 magnetic nanofluid inside a plain tube: An experimental study
International Journal of Heat and Mass Transfer 55 (2012) 2761–2768
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Effect of full length twisted tape inserts on heat transfer and friction factor enhancement with Fe3O4 magnetic nanofluid inside a plain tube: An experimental study L. Syam Sundar a,⇑, N.T. Ravi Kumar b, M.T. Naik b, K.V. Sharma a,b a b
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Center for Energy Studies, J.N.T.U. College of Engineering, Kukatpally, Hyderabad 500085, India
a r t i c l e
i n f o
Article history: Received 27 April 2011 Received in revised form 24 January 2012 Accepted 24 January 2012 Available online 3 March 2012 Keywords: Fe3O4 nanofluid Forced convection Twisted tape insert Heat transfer enhancement
a b s t r a c t Turbulent convective heat transfer and friction factor characteristics of magnetic Fe3O4 nanofluid flowing through a uniformly heated horizontal circular tube with and without twisted tape inserts are estimated experimentally. Experiments are conducted in the particle volume concentration range of 0 < u < 0.6%, twisted tape inserts of twist ratio in the range of 0 < H/D < 15and Reynolds number range of 3000 < Re < 22000. Heat transfer and friction factor enhancement of 0.6% volume concentration of Fe3O4 nanofluid in a plain tube with twisted tape insert of twist ratio H/D = 5 is 51.88% and 1.231 times compared to water flowing in a plain tube under same Reynolds number. Generalized regression equation is presented for the estimation of Nusselt number and friction factor for both water and Fe3O4 nanofluid in a plain tube and with twisted tape inserts under turbulent flow condition. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Nanofluid is a fluid containing nanometer-sized particles, called nanoparticles. These fluids are engineered colloidal suspensions of nanoparticles in a base fluid have been explained by Buongiorno [1]. The nanoparticles used in nanofluids are typically made of metals, oxides, carbides or carbon nanotubes and the common base fluids include water and ethylene glycol. Nanofluids have novel properties that make them potentially useful in many applications in heat transfer, including microelectronics, fuel cells, pharmaceutical processes and hybrid-powered engines that have been explained by Das et al. [2]. Nanofluids exhibit enhanced thermal conductivity and the convective heat transfer coefficient compared to the base fluid by Kakaç and Pramuanjaroenkij [3]. Thermal conductivity of Fe3O4 nanofluid is explained by many researchers. Parekh and Lee [4] have observed 30% enhancements in thermal conductivity with 4.7% volume concentration in the temperature range of 25-65 °C with Fe3O4 nanofluid of 9.9 nm particle size. Fertman et al. [5] have investigated the temperature range of 20–80 °C and volume concentration range of 0.01–0.2% of thermal conductivity of hydrocarbon-based magnetic fluids containing colloidal Fe3O4 particles coated with oleic acid. Philip et al. [6] have been observed thermal conductivity enhancement of ⇑ Corresponding author. E-mail address: [email protected] (L. Syam Sundar). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2012.02.040
Fe3O4 nanofluid up to 300% with volume concentration of 6.3% and particle size of 6.7 nm under the influence of an applied magnetic field. Yu et al. [7] have found 34.0% enhancement in thermal conductivity for 1.0% volume fraction with an average particle size of 155 nm in the temperature range from 10 to 60 °C using the kerosene based Fe3O4 nanofluids and oleic acid. Convective heat transfer enhancement with different kinds of nanofluid in a plain tube is explained by many researchers. Wen and Ding [8] have conducted the experiments in the Reynolds number range of 700 and 2050 in plain tube with Al2O3 nanoparticles and found significant heat transfer enhancement. Heris et al. [9] under isothermal wall boundary condition and observed that enhancement of heat transfer takes place with increase of Peclet number and volume concentration. Xuan and Li [10] have preformed the Cu nanofluid in circular tube under turbulent flow conditions and regression equation is presented. Pak and Cho [11] conducted the experiments with Al2O3 and TiO2 nanofluids in plain tube in turbulent region and also developed the regression equation. Convective heat transfer enhancement of single phase fluid with twisted tape inserts in a plain tube is explained by many researchers. Smithberg and Landis [12], Lopina and Bergles [13], Manglik and Bergles [14], Sarma et al. [15], Kishore [16] and Lecjaks et al. [17] have found the significant heat transfer enhancement of single phase fluid with twisted tape inserts in a plain tube. Convective heat transfer enhancement of Al2O3 nanofluid in a plain tube with inserts is explained by many researchers. Sharma
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Nomenclature C D h H H/D k L _ m Nu P Pr Q Re T V
specific heat, J/kg K inner diameter of the tube, m convective heat transfer coefficient, W/m2 K pitch for 180 degrees rotation, m dimensionless twist ratio thermal conductivity, W/m K length of the tube, m mass flow rate, kg/s Nusselt number, hD/k power, watts Prandtl Number, lC/k heat flow, W Reynolds number, p4Dm_l temperature, K velocity, m/s
et al. [18], Sundar and Sharma [19] for the first time presented the empirical correlation for the estimation of Nusselt number and friction factor in transition and turbulent flow condition using water and different volume concentration of Al2O3 nanofluid in plain tube and with twisted tape inserts. Chandrasekar et al. [20] have observed the 15.91% convective heat transfer enhancement with Al2O3/water nanofluid in plain tube with wire coiled inserts under laminar flow. Chandrasekar et al. [21] have conducted the experiments of Al2O3/water nanofluid in plain with wire coiled inserts under Reynolds number range of 2500 to 5000. Pathipakka and Sivashanmugam [22] numerically investigated the convective heat transfer of Al2O3/water nanofluid in a tube with twisted tape inserts of H/D = 2.93 and found 31.29% enhancement at Re = 2039 with 1.5% volume concentration. Most of the experimental work is undertaken for the estimation of heat transfer coefficient of Al2O3 and Cu nanofluids in plain tube and some researchers have concentrated for the estimation of heat transfer of coefficient of Al2O3 nanofluid in plain tube with twisted and wire coiled inserts. Thermal conductivity of magnetic Fe3O4 nanofluid literature is available, experimental turbulent convective heat transfer and friction factor of Fe3O4 magnetic nanofluid for tube flow and with twisted tape inserts data is not available. The advantage with this fluid is separation of magnetic nanoparticles (Fe3O4) from the base fluid is possible, which is not possible with non magnetic (Al2O3, Cu and TiO2) type nanoparticles. The present investigation is carried out to estimate turbulent forced convective heat transfer and friction factor at different volume concentrations of Fe3O4 nanofluid in a plain tube and with twisted tape inserts under turbulent flow conditions. Based on the experimental data generalized regression equations are developed for Nusselt number and friction factor. 2. Nanofluid preparation and properties Average diameter of Fe3O4 nanoparticle is 36 nm procured from Sigma Aldrich Chemicals Ltd., USA is dispersed in distilled water (base fluid). The physical properties of distilled water and magnetite nanoparticles are listed in Table 1. The properties of distilled water are obtained from ASHRAE hand book [23]. Since the density difference between magnetite Fe3O4 nanoparticles and distilled water is large, the particles are to be prevented from sedimentation in water. Two kinds of techniques have been suggested by Masuda et al. [24]. One is to use the force of electrostatic repulsion between particle surfaces, and the other is with the use of surfactants. Since
Greek symbols dynamic viscosity, kg/m s density, kg/m3 volume concentration of nanoparticles, % d thickness of strip, m DP pressure drop across the tube, Pa
l q u
Subscripts bf base fluid Exp Experiment nf nanofluid p nanoparticle Reg regression w water
the first method is found to cause significant changes in the thermophysical properties of dispersed fluid, the second technique is used in the present study. When the metallic oxide nanoparticles comes in contact with water, a hydroxyl radical, OH is formed at the surface of the metallic oxide particle. The overall behavior of the particle water interaction depends on whether the water is acidic or alkalic. For example, the particle surface in acidic water (i.e., having excess hydrogen ions) has a positive charge, since a hydrogen ion from the acidic water is combined with a hydroxyl radical at the surface of the metallic particle. Eqs. (1) and (2) show the reaction with acidic in water in general, respectively:
H2 SO4 () Hþ þ HSO4
ðIonisationÞ
M OH þ Hþ ) Mþ OH2
ð1Þ ð2Þ
where ‘M’ indicates a metal cation. In summary, iron particles exhibit basic properties in the presence of strong acids. The reaction of the compound with hydrogen ions is given by Masuda et al. [24] as
Fe3 O4 þ Hþ ¼ Fe4þ Fe3 O4 þ OH ¼ FeðOHÞ5
ð3Þ or FeO3
ð4Þ
However, at a certain value of pH, the mixture reaches an equipotential (or equivalence) point, at which the numbers of positive ions, Mþ OH2 are exactly the same as the number of negatively charged ions. In other words, if the pH of a dispersed fluid is near the equipotential value, agglomeration of particles will take place. The equipotential point depends strongly on the type of metallic oxide particle. From several experiments, it is found that Fe3O4 nanoparticles are well dispersed at pH value of 3. At this value, an electric double layer is formed at the surface of the nanoparticle and subsequently, these particles are suspended in water without forming a cluster due to the repulsive force between them. In preparing dispersed fluids for a desired volume concentration, the required amount of particles are weighed with a precision balance, mixed with a carrier fluid, and the pH value of the dispersed fluid adjusted with an extremely small amount of sulfuric acid H2SO4. After sonification for approximately 2 h, the dispersion of the nanoparticles is established by visual observation for nanoparticle sedimentation. The uniform dispersion is established by measuring the densities of nanofluid at different locations in the container. The volume concentration is evaluated from the following relation in percentage
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Mean Diameter Specific surface, m2/g Density, kg/m3 Thermal conductivity, W/m K Specific heat, kJ/kg K Kinematic viscosity, m2/sec
S. no. Substance 1 2
uv ¼
Fe3O4 nanoparticle 36 nm Water –
60 –
5180 995.7
Volume of Fe3 O4 100 Volume of Fe3 O4 þ Volume of water
W Fe
uv ¼
3 O4
3 O4
qFe3 O4
þ
ð5Þ
qFe3 O4
W Fe
80.4 0.609
Wwater
100
ð6Þ
qwater
where ðqFeO4 ) is density of Fe3O4, (qwater) is density of water and uv is the volume concentration. The density and specific heat of nanofluid is measured with the conventional mixture laws given by Pak and Cho [11]
qnanofluid ¼ ð1 uÞqwater þ uqFe3 O4
ð7Þ
Cnanofluid ¼ ð1 uÞCwater þ uC Fe3 O4
ð8Þ
Wasp [25] model is considered for the estimation of thermal conductivity
knanofluid ¼ kwater
kFe3 O4 þ 2kwater 2/ðkwater kFe3 O4 Þ kFe3 O4 þ 2kwater þ 2kFe3 O4 ðkwater kFe3 O4 Þ
ð9Þ
Brickman [26] presented viscosity correlation as it applies to concentrated particle suspension
lnanofluid ¼ lwater
1
!
ð1 þ uÞ2:5
ð10Þ
3. Experimental set up and procedure An experimental set up is designed and fabricated to study the flow and convective heat transfer feature of the Fe3O4 nanofluid flowing in a tube with twisted tape inserts. As shown schematically in Fig. 1a, the experimental system mainly consists of storage tank, pump, pipe line, test section, cooler, fluid collection tank, data acquisition system and personal computer. The storage tank of 30 l capacity is manufactured of stainless steel to store the nanofluid and to monitor the dispersion behavior and stability of the nanofluid. The cooler of 2 kW cooling capacity is used to keep a constant temperature of the nanofluid at the inlet of the test section. The nanofluid is forced through the test section with an aid of an A.C. pump (Crompton Greaves Ltd, India) with a maximum capacity of 16 liters/sec, the suction side connected to a storage tank. The flow rate of the nanofluid is controlled with bypass valve arrangement, required quantity of fluid is allowed into the test section through totalizer and the remaining fluid is sent back to the storage tank. With help of totalizer mass flow rate of nanofluid flowing into the test section is recorded. The test section is a straight copper tube of the inner diameter of 0.014 m and the length of 1.7 m. The copper tube is heated uniformly by wrapping with two nichrome heaters of 20 gauge, having a resistance of 53.5 X per meter length and 1000 W maximum rating and subject the entire test section to constant heat flux boundary condition. The gap between the test section and the casing is filled with glass wool insulation in order to minimize the heat loss from the test section to the ambient. The hydrodynamic entry section is long enough to accomplish fully developed flow at the entrance of the
670 4.179
– 0.801
heat transfer test section. Five K-type thermocouples are mounted on the surface of the tube at distances of 0.1875, 0.375, 0.75, 1.125, 1.312 m to measure the surface temperatures of the tube and two K-type thermocouples are located inlet and exit of the test section to measure the working fluid (water, Fe3O4 nanofluid) inlet and outlet temperatures. The thermocouples have 0.1°C resolution and are calibrated before fixing them at the specified locations. U-tube manometer with Carbon tetrachloride (CCl4) as manometer liquid is provided for determining the pressure drop across the test section. Experiments are then conducted with water and different volume concentrations of Fe3O4 nanofluid to estimate the convective heat transfer and friction factor for flow in a tube with twisted tape inserts. The storage tank is filled with the working fluid. The inlet valve of the test section is opened and the pump is put on. The heater is adjusted for a desired input with the help of a variable transformer. When steady state conditions are attained, the temperatures at various locations and the input power to the heater are recorded. The flow is adjusted to conduct experiments in the Reynolds number range of 3000 to 22000. Heat transfer coefficients and friction factors at 0.02%, 0.1%, 0.3% and 0.6% volume concentration are estimated. During experimental runs, the tube wall temperatures, inlet and outlet temperatures of the Fe3O4 nanofluid, mass flow rates and electric power inputs as well as the pressure drop are measured. The twisted tapes are made in the laboratory from 1 mm thick and 0.013 m width of aluminum strip as shown in the Fig. 1b and dimensions of twisted tape inserts is shown in Table. 2. The two ends of a strip were inserted into the lathe, one at the headstock end and the other at the tail stock end by special devices made in the laboratory. The strip was then subjected to twist by turning the chuck manually. Three twist ratios of H/D = 5, 10 and 15 were made. Twisted tapes are tightly fitted into the tube and the tape fin effect is neglected.
4. Results and discussion 4.1. Experimental Nusselt number of nanofluid in plain tube The deviation in the electrical input to heater estimated with Eq. (11) and that absorbed by the working fluid estimated from Eq. (12) is less than 2.0%. This indicates the negligible amount heat loss that takes place from the test section to atmosphere.
P¼VI
ðHeat supplied to the test sectionÞ
Q ¼ m C ðT0 Ti Þ ðHeat absorbed by the fluidÞ
ð11Þ ð12Þ
Newton’s law of cooling Eq. (13) is used for the estimation of experimental heat transfer coefficient and Eq. (14) is used for the estimation of experimental Nusselt number.
hEXP ¼
Q AðT wall T mean Þ
ð13Þ
o where A ¼ pDL, Twall ¼ T1 þT2 þT53 þT4 þT5 , Tmean ¼ Ti þT 2
NuExp ¼
hExp D k
ð14Þ
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Fig. 1a. Schematic diagram of the experimental setup.
Fig. 1b. Full-length twisted tape insert inside a tube.
The following correlations give the single phase fluid Nusselt number (a) Gnielinski’s [27] correlation for single phase fluid
Nu ¼
f 2
ðRe 1000ÞPr 0:5 ðPr2=3 1Þ 1 þ 12:7 2f
imental set up is in good condition and it may be used for measuring the convective heat transfer of Fe3O4 nanofluid. Experimental Nusselt number of Fe3O4 nanofluid estimated from the Eq. (14) in
ð15Þ
where f ¼ ð1:58 ln Re 3:82Þ2 , 2300 < Re < 5 106 , 0:5 < Pr < 2000 (b) Notter–Rouse [28] correlation for single phase fluid
Nu ¼ 5 þ 0:015Re0:856 Pr0:347
ð16Þ
As shown in Fig. 2, the good coincidence between the experimental Nusselt number of water obtained from Eq. (14) and the values obtained from Eq. (15) of Gnielinski [27] and Eq. (16) of Notter– Rouse [28] under turbulent flow condition. This indicates the exper-
Table 2 Dimensions of twisted tape inserts. S. no.
1 2
Parameter
H (Width) D (Diameter)
Twist ratio, H/D, m 5
10
15
0.065 0.013
0.13 0.013
0.195 0.013
Fig. 2. Experimental Nusselt number of water is in comparison with the correlations of Gnelinski [27] and Notter–Rouse [28].
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plain tube is shown in Fig. 3 along with the data of water. It indicated that the convective heat transfer coefficient of the nanofluid increases with the increase of Reynolds number and volume concentration compared to base fluid (water). It may be point out that proper selection of the nanoparticle volume concentration and pair of solid particles and base liquid is important for applying nanoparticles to heat transfer enhancement. In some cases, the viscosity of the dispersed fluid increases with increasing the particle volume concentration and becomes much higher than that of the base liquid, so that higher volume concentration of the solid particles may suppress heat transfer enhancement of the suspension. Heat transfer enhancement with 0.6% volume concentration of Fe3O4 nanofluid is 20.99% at 3000 Reynolds number and 30.96% at 22000 Reynolds number compared to water under same Reynolds number. The various effects of thermal conductivities under static and dynamic conditions, energy transfer by nanoparticles dispersion, particle migration due to viscosity gradient, Brownian motion of the particles on remarkable enhancement of the convective heat transfer coefficient of water-based Fe3O4 nanofluid flowing through a plain tube. The similar trend is observed by Pak and Cho [11] with Al2O3 and TiO2 nanofluid and Xuan and Li [10] with Cu nanofluid.
shown in Fig. 4 along with the values obtained from Eq. (17) of Sarma et al. [15]. From the figure both the experimental values and the values obtained from Sarma et al. [15] are in good agreement. The similar procedure is adopted to conduct the experiments for Fe3O4 nanofluid with twisted tape inserts and Eq. (14) is used for the estimation of experimental Nusselt number. Three twist ratios like H/D = 5, 10 and 15 were considered. Experimental Nusselt number of different volume concentrations of Fe3O4 nanofluid in circular tube with and with out twisted tape inserts are represented in the Fig. 5 along with the values of water. It can be observed from figure, that higher heat transfer rates are obtained for nanofluid with twisted tape inserts compared to the nanofluid in plain tube. The tape creates the turbulence inside the flow and effective mixing of the fluid will take place. Heat transfer enhancement of 0.6% nanofluid flowing in a plain tube with twisted tape insert of H/D = 5 is 16.06% at 3000 Reynolds number and 18.49% at 22000 Reynolds number under same volume concentration of nanofluid flowing in a tube.
4.2. Experimental Nusselt number of nanofluid in plain tube with twisted tape inserts
3000 < Re < 22000;
Experiments are further conducted in order to estimate the heat transfer coefficient of Fe3O4 nanofluid flowing in a plain tube with twisted tape inserts, because that is the main objective of the present work. No experimental data and regression equation is available for Fe3O4 nanofluid in plain tube with twisted tape inserts. Sarma et al. [15], single-phase fluid in plain tube with twisted tape inserts
log10
Nu Pr1=3 ½1 þ D=H2
0 < u < 0:6%;
ð18Þ
3:19 < Pr < 6:50;
0 < H=D < 15 The present data is correlated for the estimation of Nusselt number for both water and Fe3O4 nanofluid with and without twisted tape inserts and regression Eq. (18) is developed with an average deviation (AD) of 6.72% and standard deviation (SD) of 7.56%. Comparison between the experimental Nusselt number and proposed regression Nusselt number Eq. (18) is represented in Fig. 6. 4.3. Experimental friction factor of nanofluid in plain tube The experimental friction factor is obtained from the relation
¼ 0:974 0:783log10 ½Re
DP f ¼ 2 qV L
þ 0:35flog10 ½Reg2 0:0273flog10 ½Reg3
0:028 H NuReg ¼ 0:0223Re0:8 Pr0:5 ð1 þ uÞ0:54 1 þ D
D
ð17Þ
90 < Re < 1; 30; 000; 4 < Pr < 460; 2:5 < H=D < 10
ð19Þ
2
Blasius [29], using one-seventh power velocity distribution, developed an expression for the determination of friction factor valid in the range 3000 < Re < 105 for pure fluids as
Experimental Nusselt number of water estimated from Eq. (14) in plain tube with different twist ratios of twisted tape inserts is
Fig. 3. Experimental Nusselt number of water and different volume concentrations of Fe3O4 nanofluid.
Fig. 4. Experimental Nusselt number of water in plain tube with twisted tape inserts is in comparison with the Eq. (12) of Sarma et al. [15] and experimental data of Kishore [16] and Lacjakas [17].
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Fig. 5. Experimental Nusselt number of water and Fe3O4 nanofluid in plain tube with and without twisted tape inserts.
Fig. 7. Experimental friction factor of water is in comparison with the values obtained from Eq. (14).
Fig. 6. Experimental Nusselt number is in comparison with the developed regression equation.
Fig. 8. Experimental friction factor of water and different volume concentrations of Fe3O4 nanofluid.
f ¼ 4 0:0079=Re0:25
ð20Þ
Experimental friction factor of water obtained from Eq. (19) is shown in Fig. 7 along with the values obtained from Eq. (20) of Blasius [29] and it found that good agreement. The friction factor of Fe3O4 nanofluid obtained from Eq. (19) shown in Fig. 8 along with friction factor of water. Friction factor of Fe3O4 nanofluid is high compared to the friction factor of water, but it is negligible. The reason for enhancement in friction factor is solid nanoparticles present in the base fluid. 4.4. Experimental friction factor of nanofluid in plain tube with twisted tape inserts Experimental friction factor of water in plain tube with twisted tape inserts obtained from Eq. (19) shown in Fig. 9 along with the values obtained from Eq. (21) of Sarma et al. [15]. It is observed that the values are in close agreement. Sundar and Sharma. [19], single-phase fluid in plain tube with twisted tape inserts
f ½1 þ D=H3:378
¼ 0:474 0:3log10 ½Re þ 0:065flog10 ½Reg2 4:66 103 flog10 ½Reg3
400 < Re < 1; 30; 000; 4 < Pr < 460;
ð21Þ
2:5 < H=D < 10
Experimental friction factor of different volume concentrations of Fe3O4 nanofluid in plain tube with twisted tape inserts estimated from Eq. (19) is shown in Fig. 10. It is observed that with twisted tape inserts in the flow friction factor enhances, but it is negligible. The present experimental data is fit to a regression Eq. (22) for the estimation of friction factor for both water and Fe3O4 nanofluid with and without twisted tape inserts with an average deviation (AD) of 4.07% and standard deviation (SD) of 4.90%. Comparison between the experimental Nusselt number and proposed regression Nusselt number Eq. (22) is represented in the Fig. 11.
0:017 H fReg ¼ 0:3490Re0:25: ð1 þ uÞ0:21 1 þ D
ð22Þ
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Fig. 9. Experimental friction factor of water in plain tube with twisted tape inserts is in comparison with the equation of Sarma et al. [15] and experimental data of Kishore [16] and Lecjakas et al. [17].
Fig. 11. Experimental friction factor is in comparison with the developed regression equation.
twisted tape insert, H/D = 5 is 43.37% and 51.88% compared to water flowing in a plain tube without inserts at Reynolds number 3000 and 22,000, respectively. The enhancement of friction factor in a plain tube with 0.6% volume concentration of Fe3O4 nanofluid when compared to water is 1.09 times and 1.10 times for Reynolds number of 3000 and 22,000 respectively. Under 0.6% volume concentration of Fe3O4 nanofluid in plain tube with twisted tape insert, H/D = 5 is 1.092 times and 1.122 times at Reynolds number 3000 and 22,000, respectively compared to same volume concentration of fluid in plain tube. The friction factor enhancement of 0.6% nanofluid with twisted tape insert, H/D = 5 is 1.179 times and 1.231 times compared to water flowing in a plain tube without inserts at Reynolds number 3000 and 22,000, respectively. Eq. (18) and Eq. (22) is used for the estimation of heat transfer coefficient and friction factor of water, different volume concentrations of Fe3O4 nanofluid in plain tube with and without inserts.
Appendix A. Appendix Fig. 10. Experimental friction factor of water and Fe3O4 nanofluid in plain tube with and without twisted tape inserts.
3000 < Re < 22000; 0 < H=D < 15
0 < u < 0:6%;
3:19 < Pr < 6:50; ð23Þ
5. Conclusions The Nusselt number estimated with Eq. (15) of Gnielinski’s [27] valid for single phase fluid predicts values which are lower by 13.4% for 0.6% for Fe3O4 nanofluid under similar operating conditions. The enhancement of heat transfer coefficient in a plain tube with 0.6% volume concentration of Fe3O4 nanofluid is 20.99% and 30.96% for Reynolds number of 3000 and 22,000, respectively compared to water. Further heat transfer enhancement is observed with twisted tape inserts into plain tube. Under 0.6% volume concentration of Fe3O4 nanofluid in plain tube with twisted tape insert, H/D = 5 is 16.06% and 18.49% at Reynolds number 3000 and 22,000, respectively compared to the same volume concentration of fluid flowing in plain tube without insert. In the similar way, the heat transfer enhancement of 0.6% nanofluid in plain tube with
A.1. Uncertainty Analysis A systematic error analysis is made to estimate the errors associated in the experimental analysis following the procedure detailed by Beckwith et al. [30]. The uncertainties in the values estimated with different instruments are given in Table 3. The maximum possible error for the parameters involved in the analysis are estimated and summarized in Table 4. (a) Heat flux, q
q¼
P ; A
q¼
V I ; pDL
q¼
V 2 =R pDL
Table 3 Uncertainties of parameters and variables. S. no.
Variable name
Uncertainty error,%
1 2 3 4 5
Reynolds number, Re Heat Flux, q Heat transfer coefficient, W/m2 K Nusselt number, Nu Friction factor, f
0.10 0.20 0.2203 0.24196 0.10
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Table 4 Uncertainties of instruments and properties. S. no.
Name of instrument
Range of instrument
1 2 3 4 5 6 7 8
Thermocouple Thermocouple Voltage Current Resistance U-tube manometer Totalizer Properties
0.1 °C 0–120 °C Wall Temperature, Tw 0–120 °C Bulk Temperature, Tb 0.1 °C 0–220 V Voltage, V 0.1 V 0–20 I Current, I 0.01 I 0–53.3 R Resistance, R 0.1 R 0–50 cm Height of the CCl4 1 mm 0–999999 l Mass flow rate, m 1l Thermal conductivity, density, specific heat, viscosity
Uq ¼ q
Variable measured
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2U V UR þ ¼ ð2 0:04545Þ2 þ ð0:1876Þ2 V R
¼ 0:1983% (b) Reynolds number, Re
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Ul U Re U m_ _ pDl; Re ¼ 4m= þ ¼ _ Re l m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:00001Þ2 þ ð0:1Þ2 ¼ 0:1% (c) Heat transfer coefficient
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U T W T b 2 q Uh Uq h¼ ; þ ¼ Tw Tb h q TW Tb qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð0:1983Þ þ ð0:09604Þ ¼ 0:220% (d) Nusselt number, Nu
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 hD U Nu Uh UK Nu ¼ þ ; ¼ K Nu h K qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:2203Þ2 þ ð0:1Þ2 ¼ 0:24196% (e) Friction factor, f
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 Uq Uf U DP 2U V þ þ ¼ f DP q V D 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:002610Þ2 þ ð0:1Þ2 þ ð2 0:00001Þ2 ¼ 0:100%
Dp f ¼ 2 ; qV L
References [1] J. Buongiorno, Convective transport in nanofluids, J. Heat Transfer 128 (3) (2006) 240–250. [2] S.K. Das, S.U.S. Choi, W. Yu, T. Pradeep, Nanofluids: Science and Technology, Wiley-InterScience (2007) 397. [3] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer 52 (2009) 3187–3196. [4] K. Parekh, H.S. Lee, Magnetic field induced enhancement in thermal conductivity of magnetite nanofluid, Journal of Applied Physics 107 (2010) 09A310. [5] V.E. Fertman, L.E. Golovicher, N.P. Matusevich, Thermal conductivity of magnetite magnetic fluids, J. Magnet. Magnet. Mater. 65 (1987) 211–214. [6] J. Philip, P.D. Shima, B. Raj, Enhancement of thermal conductivity in magnetite based nanofluid due to chainlike structures, Appl. Phys. Lett. 91 (2007) 203108–203108-3. [7] W. Yu, H. Xie, L. Chen, Y. Li, Enhancement of thermal conductivity of kerosenebased Fe3O4 nanofluids prepared via phase-transfer method, Coll. Surf. A: Physicochem. Eng. Aspects 355 (2010) 109–113.
Least division in measuring instrument
Min. and max. values measured in experiment
Uncertainty, %
45.66–72.96 31.25–42.9 0–220 0–20 0–53.3 2.0–38.3 cm 1–16 l
0.13706 0.23310 0.04545 0.05 0.1876 0.002610 0.00001 0.1
[8] D. Wen, Y. Ding, Experimental investigation into convective heat transfer of nanofluid at the entrance region under laminar flow conditions, Int. J. Heat Mass Transfer 47 (24) (2004) 5181–5188. [9] 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. [10] Y. Xuan, Q. Li, Investigation on convective heat transfer and flow features of nanofluids, J. Heat Transfer 125 (2003) 151–155. [11] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Expt. Heat Transfer 11 (1998) 151– 170. [12] E. Smithberg, F. Landis, Friction and forced convective heat transfer characteristics in tube with twisted-tape swirl generators, J. Heat Transfer 86 (1964) 39–49. [13] R.F. Lopina, A.E. Bergles, Heat transfer and pressure drop in tape-generated swirl flow of single phase water, J. Heat Transfer 91 (1969) 434–442. [14] R.M. Manglik, A.E. Bergles, Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes: part II-transition and turbulent flows, J. Heat Transfer 115 (1993) 890–896. [15] P.K. Sarma, P.S. Kishore, V. Dharma Rao, T. Subrahmanyam, A combined approach to predict coefficients and convective heat transfer characteristics in a tube with twisted tape inserts for a wide range of Re and Pr, Int. J. Thermal Sci. 44 (2005) 393–398. [16] P.S. Kishore, Experimental and theoretical studies of convective momentum and heat transfer in tubes with twisted tape inserts, Ph.D. Thesis, Andhra University, India, 2001. [17] Z. Lecjaks, I. Machac, J. Sir, Heat transfer to a Newtonian liquid flowing through a tube with an internal helical element, Int. Chem. Eng. 27 (1987) 210–217. [18] K.V. Sharma, L.S. Sundar, P.K. Sarma, Estimation of heat transfer coefficient and friction factor in the transition flow with low volume concentration of Al2O3 nanofluid flowing in a circular tube and with twisted tape insert, Int. Commun. Heat Mass Transfer 36 (2009) 503–507. [19] 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 Transfer 53 (2010) 1409–1416. [20] 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, Expt. Thermal Fluid Sci. 34 (2) (2010) 122–130. [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] G. Pathipakka, P. Sivashanmugam, Heat transfer behaviour of nanofluids in a uniformly heated circular tube fitted with helical inserts in laminar flow, Superlatt. Microstruct. 47 (2) (2010) 349–360. [23] ASHRAE Hand Book – Fundamentals, 2009, pp. 25–37. [24] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Altration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of c-Al2O3, SiO2 and TiO2 ultra-fine particles), Netsu Bussei 4 (4) (1993) 227–233 (in Japanese). [25] F.J. Wasp, Solid-liquid slurry pipeline transportation, Trans., Tech., 1977. [26] H.C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys. 20 (1952) 571–581. [27] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359–368. [28] R.H. Notter, M.W. Rouse, A solution to the Graetz problem – III. Fully developed region heat transfer rates, Chem. Eng. Sci. 27 (1972) (1972) 2073– 2093. [29] H. Blasius, Grenzschichten in Flussigkeiten mit kleiner Reibung (German), Z. Math. Phys. 56 (1908) 1–37. [30] T.G. Beckwith, R.D. Marangoni, L.H. Lienhard, Mechanical measurements, 5th ed., Addison-Wesley Publishing Company, New York, 1990, pp. 45–112.
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effect of full length twisted tape inserts on heat transfer and friction factor enhancement with Fe3O4 magnetic nanofluid inside a plain tube: An experimental study L. Syam Sundar a,⇑, N.T. Ravi Kumar b, M.T. Naik b, K.V. Sharma a,b a b
Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia Center for Energy Studies, J.N.T.U. College of Engineering, Kukatpally, Hyderabad 500085, India
a r t i c l e
i n f o
Article history: Received 27 April 2011 Received in revised form 24 January 2012 Accepted 24 January 2012 Available online 3 March 2012 Keywords: Fe3O4 nanofluid Forced convection Twisted tape insert Heat transfer enhancement
a b s t r a c t Turbulent convective heat transfer and friction factor characteristics of magnetic Fe3O4 nanofluid flowing through a uniformly heated horizontal circular tube with and without twisted tape inserts are estimated experimentally. Experiments are conducted in the particle volume concentration range of 0 < u < 0.6%, twisted tape inserts of twist ratio in the range of 0 < H/D < 15and Reynolds number range of 3000 < Re < 22000. Heat transfer and friction factor enhancement of 0.6% volume concentration of Fe3O4 nanofluid in a plain tube with twisted tape insert of twist ratio H/D = 5 is 51.88% and 1.231 times compared to water flowing in a plain tube under same Reynolds number. Generalized regression equation is presented for the estimation of Nusselt number and friction factor for both water and Fe3O4 nanofluid in a plain tube and with twisted tape inserts under turbulent flow condition. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Nanofluid is a fluid containing nanometer-sized particles, called nanoparticles. These fluids are engineered colloidal suspensions of nanoparticles in a base fluid have been explained by Buongiorno [1]. The nanoparticles used in nanofluids are typically made of metals, oxides, carbides or carbon nanotubes and the common base fluids include water and ethylene glycol. Nanofluids have novel properties that make them potentially useful in many applications in heat transfer, including microelectronics, fuel cells, pharmaceutical processes and hybrid-powered engines that have been explained by Das et al. [2]. Nanofluids exhibit enhanced thermal conductivity and the convective heat transfer coefficient compared to the base fluid by Kakaç and Pramuanjaroenkij [3]. Thermal conductivity of Fe3O4 nanofluid is explained by many researchers. Parekh and Lee [4] have observed 30% enhancements in thermal conductivity with 4.7% volume concentration in the temperature range of 25-65 °C with Fe3O4 nanofluid of 9.9 nm particle size. Fertman et al. [5] have investigated the temperature range of 20–80 °C and volume concentration range of 0.01–0.2% of thermal conductivity of hydrocarbon-based magnetic fluids containing colloidal Fe3O4 particles coated with oleic acid. Philip et al. [6] have been observed thermal conductivity enhancement of ⇑ Corresponding author. E-mail address: [email protected] (L. Syam Sundar). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2012.02.040
Fe3O4 nanofluid up to 300% with volume concentration of 6.3% and particle size of 6.7 nm under the influence of an applied magnetic field. Yu et al. [7] have found 34.0% enhancement in thermal conductivity for 1.0% volume fraction with an average particle size of 155 nm in the temperature range from 10 to 60 °C using the kerosene based Fe3O4 nanofluids and oleic acid. Convective heat transfer enhancement with different kinds of nanofluid in a plain tube is explained by many researchers. Wen and Ding [8] have conducted the experiments in the Reynolds number range of 700 and 2050 in plain tube with Al2O3 nanoparticles and found significant heat transfer enhancement. Heris et al. [9] under isothermal wall boundary condition and observed that enhancement of heat transfer takes place with increase of Peclet number and volume concentration. Xuan and Li [10] have preformed the Cu nanofluid in circular tube under turbulent flow conditions and regression equation is presented. Pak and Cho [11] conducted the experiments with Al2O3 and TiO2 nanofluids in plain tube in turbulent region and also developed the regression equation. Convective heat transfer enhancement of single phase fluid with twisted tape inserts in a plain tube is explained by many researchers. Smithberg and Landis [12], Lopina and Bergles [13], Manglik and Bergles [14], Sarma et al. [15], Kishore [16] and Lecjaks et al. [17] have found the significant heat transfer enhancement of single phase fluid with twisted tape inserts in a plain tube. Convective heat transfer enhancement of Al2O3 nanofluid in a plain tube with inserts is explained by many researchers. Sharma
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Nomenclature C D h H H/D k L _ m Nu P Pr Q Re T V
specific heat, J/kg K inner diameter of the tube, m convective heat transfer coefficient, W/m2 K pitch for 180 degrees rotation, m dimensionless twist ratio thermal conductivity, W/m K length of the tube, m mass flow rate, kg/s Nusselt number, hD/k power, watts Prandtl Number, lC/k heat flow, W Reynolds number, p4Dm_l temperature, K velocity, m/s
et al. [18], Sundar and Sharma [19] for the first time presented the empirical correlation for the estimation of Nusselt number and friction factor in transition and turbulent flow condition using water and different volume concentration of Al2O3 nanofluid in plain tube and with twisted tape inserts. Chandrasekar et al. [20] have observed the 15.91% convective heat transfer enhancement with Al2O3/water nanofluid in plain tube with wire coiled inserts under laminar flow. Chandrasekar et al. [21] have conducted the experiments of Al2O3/water nanofluid in plain with wire coiled inserts under Reynolds number range of 2500 to 5000. Pathipakka and Sivashanmugam [22] numerically investigated the convective heat transfer of Al2O3/water nanofluid in a tube with twisted tape inserts of H/D = 2.93 and found 31.29% enhancement at Re = 2039 with 1.5% volume concentration. Most of the experimental work is undertaken for the estimation of heat transfer coefficient of Al2O3 and Cu nanofluids in plain tube and some researchers have concentrated for the estimation of heat transfer of coefficient of Al2O3 nanofluid in plain tube with twisted and wire coiled inserts. Thermal conductivity of magnetic Fe3O4 nanofluid literature is available, experimental turbulent convective heat transfer and friction factor of Fe3O4 magnetic nanofluid for tube flow and with twisted tape inserts data is not available. The advantage with this fluid is separation of magnetic nanoparticles (Fe3O4) from the base fluid is possible, which is not possible with non magnetic (Al2O3, Cu and TiO2) type nanoparticles. The present investigation is carried out to estimate turbulent forced convective heat transfer and friction factor at different volume concentrations of Fe3O4 nanofluid in a plain tube and with twisted tape inserts under turbulent flow conditions. Based on the experimental data generalized regression equations are developed for Nusselt number and friction factor. 2. Nanofluid preparation and properties Average diameter of Fe3O4 nanoparticle is 36 nm procured from Sigma Aldrich Chemicals Ltd., USA is dispersed in distilled water (base fluid). The physical properties of distilled water and magnetite nanoparticles are listed in Table 1. The properties of distilled water are obtained from ASHRAE hand book [23]. Since the density difference between magnetite Fe3O4 nanoparticles and distilled water is large, the particles are to be prevented from sedimentation in water. Two kinds of techniques have been suggested by Masuda et al. [24]. One is to use the force of electrostatic repulsion between particle surfaces, and the other is with the use of surfactants. Since
Greek symbols dynamic viscosity, kg/m s density, kg/m3 volume concentration of nanoparticles, % d thickness of strip, m DP pressure drop across the tube, Pa
l q u
Subscripts bf base fluid Exp Experiment nf nanofluid p nanoparticle Reg regression w water
the first method is found to cause significant changes in the thermophysical properties of dispersed fluid, the second technique is used in the present study. When the metallic oxide nanoparticles comes in contact with water, a hydroxyl radical, OH is formed at the surface of the metallic oxide particle. The overall behavior of the particle water interaction depends on whether the water is acidic or alkalic. For example, the particle surface in acidic water (i.e., having excess hydrogen ions) has a positive charge, since a hydrogen ion from the acidic water is combined with a hydroxyl radical at the surface of the metallic particle. Eqs. (1) and (2) show the reaction with acidic in water in general, respectively:
H2 SO4 () Hþ þ HSO4
ðIonisationÞ
M OH þ Hþ ) Mþ OH2
ð1Þ ð2Þ
where ‘M’ indicates a metal cation. In summary, iron particles exhibit basic properties in the presence of strong acids. The reaction of the compound with hydrogen ions is given by Masuda et al. [24] as
Fe3 O4 þ Hþ ¼ Fe4þ Fe3 O4 þ OH ¼ FeðOHÞ5
ð3Þ or FeO3
ð4Þ
However, at a certain value of pH, the mixture reaches an equipotential (or equivalence) point, at which the numbers of positive ions, Mþ OH2 are exactly the same as the number of negatively charged ions. In other words, if the pH of a dispersed fluid is near the equipotential value, agglomeration of particles will take place. The equipotential point depends strongly on the type of metallic oxide particle. From several experiments, it is found that Fe3O4 nanoparticles are well dispersed at pH value of 3. At this value, an electric double layer is formed at the surface of the nanoparticle and subsequently, these particles are suspended in water without forming a cluster due to the repulsive force between them. In preparing dispersed fluids for a desired volume concentration, the required amount of particles are weighed with a precision balance, mixed with a carrier fluid, and the pH value of the dispersed fluid adjusted with an extremely small amount of sulfuric acid H2SO4. After sonification for approximately 2 h, the dispersion of the nanoparticles is established by visual observation for nanoparticle sedimentation. The uniform dispersion is established by measuring the densities of nanofluid at different locations in the container. The volume concentration is evaluated from the following relation in percentage
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Mean Diameter Specific surface, m2/g Density, kg/m3 Thermal conductivity, W/m K Specific heat, kJ/kg K Kinematic viscosity, m2/sec
S. no. Substance 1 2
uv ¼
Fe3O4 nanoparticle 36 nm Water –
60 –
5180 995.7
Volume of Fe3 O4 100 Volume of Fe3 O4 þ Volume of water
W Fe
uv ¼
3 O4
3 O4
qFe3 O4
þ
ð5Þ
qFe3 O4
W Fe
80.4 0.609
Wwater
100
ð6Þ
qwater
where ðqFeO4 ) is density of Fe3O4, (qwater) is density of water and uv is the volume concentration. The density and specific heat of nanofluid is measured with the conventional mixture laws given by Pak and Cho [11]
qnanofluid ¼ ð1 uÞqwater þ uqFe3 O4
ð7Þ
Cnanofluid ¼ ð1 uÞCwater þ uC Fe3 O4
ð8Þ
Wasp [25] model is considered for the estimation of thermal conductivity
knanofluid ¼ kwater
kFe3 O4 þ 2kwater 2/ðkwater kFe3 O4 Þ kFe3 O4 þ 2kwater þ 2kFe3 O4 ðkwater kFe3 O4 Þ
ð9Þ
Brickman [26] presented viscosity correlation as it applies to concentrated particle suspension
lnanofluid ¼ lwater
1
!
ð1 þ uÞ2:5
ð10Þ
3. Experimental set up and procedure An experimental set up is designed and fabricated to study the flow and convective heat transfer feature of the Fe3O4 nanofluid flowing in a tube with twisted tape inserts. As shown schematically in Fig. 1a, the experimental system mainly consists of storage tank, pump, pipe line, test section, cooler, fluid collection tank, data acquisition system and personal computer. The storage tank of 30 l capacity is manufactured of stainless steel to store the nanofluid and to monitor the dispersion behavior and stability of the nanofluid. The cooler of 2 kW cooling capacity is used to keep a constant temperature of the nanofluid at the inlet of the test section. The nanofluid is forced through the test section with an aid of an A.C. pump (Crompton Greaves Ltd, India) with a maximum capacity of 16 liters/sec, the suction side connected to a storage tank. The flow rate of the nanofluid is controlled with bypass valve arrangement, required quantity of fluid is allowed into the test section through totalizer and the remaining fluid is sent back to the storage tank. With help of totalizer mass flow rate of nanofluid flowing into the test section is recorded. The test section is a straight copper tube of the inner diameter of 0.014 m and the length of 1.7 m. The copper tube is heated uniformly by wrapping with two nichrome heaters of 20 gauge, having a resistance of 53.5 X per meter length and 1000 W maximum rating and subject the entire test section to constant heat flux boundary condition. The gap between the test section and the casing is filled with glass wool insulation in order to minimize the heat loss from the test section to the ambient. The hydrodynamic entry section is long enough to accomplish fully developed flow at the entrance of the
670 4.179
– 0.801
heat transfer test section. Five K-type thermocouples are mounted on the surface of the tube at distances of 0.1875, 0.375, 0.75, 1.125, 1.312 m to measure the surface temperatures of the tube and two K-type thermocouples are located inlet and exit of the test section to measure the working fluid (water, Fe3O4 nanofluid) inlet and outlet temperatures. The thermocouples have 0.1°C resolution and are calibrated before fixing them at the specified locations. U-tube manometer with Carbon tetrachloride (CCl4) as manometer liquid is provided for determining the pressure drop across the test section. Experiments are then conducted with water and different volume concentrations of Fe3O4 nanofluid to estimate the convective heat transfer and friction factor for flow in a tube with twisted tape inserts. The storage tank is filled with the working fluid. The inlet valve of the test section is opened and the pump is put on. The heater is adjusted for a desired input with the help of a variable transformer. When steady state conditions are attained, the temperatures at various locations and the input power to the heater are recorded. The flow is adjusted to conduct experiments in the Reynolds number range of 3000 to 22000. Heat transfer coefficients and friction factors at 0.02%, 0.1%, 0.3% and 0.6% volume concentration are estimated. During experimental runs, the tube wall temperatures, inlet and outlet temperatures of the Fe3O4 nanofluid, mass flow rates and electric power inputs as well as the pressure drop are measured. The twisted tapes are made in the laboratory from 1 mm thick and 0.013 m width of aluminum strip as shown in the Fig. 1b and dimensions of twisted tape inserts is shown in Table. 2. The two ends of a strip were inserted into the lathe, one at the headstock end and the other at the tail stock end by special devices made in the laboratory. The strip was then subjected to twist by turning the chuck manually. Three twist ratios of H/D = 5, 10 and 15 were made. Twisted tapes are tightly fitted into the tube and the tape fin effect is neglected.
4. Results and discussion 4.1. Experimental Nusselt number of nanofluid in plain tube The deviation in the electrical input to heater estimated with Eq. (11) and that absorbed by the working fluid estimated from Eq. (12) is less than 2.0%. This indicates the negligible amount heat loss that takes place from the test section to atmosphere.
P¼VI
ðHeat supplied to the test sectionÞ
Q ¼ m C ðT0 Ti Þ ðHeat absorbed by the fluidÞ
ð11Þ ð12Þ
Newton’s law of cooling Eq. (13) is used for the estimation of experimental heat transfer coefficient and Eq. (14) is used for the estimation of experimental Nusselt number.
hEXP ¼
Q AðT wall T mean Þ
ð13Þ
o where A ¼ pDL, Twall ¼ T1 þT2 þT53 þT4 þT5 , Tmean ¼ Ti þT 2
NuExp ¼
hExp D k
ð14Þ
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Fig. 1a. Schematic diagram of the experimental setup.
Fig. 1b. Full-length twisted tape insert inside a tube.
The following correlations give the single phase fluid Nusselt number (a) Gnielinski’s [27] correlation for single phase fluid
Nu ¼
f 2
ðRe 1000ÞPr 0:5 ðPr2=3 1Þ 1 þ 12:7 2f
imental set up is in good condition and it may be used for measuring the convective heat transfer of Fe3O4 nanofluid. Experimental Nusselt number of Fe3O4 nanofluid estimated from the Eq. (14) in
ð15Þ
where f ¼ ð1:58 ln Re 3:82Þ2 , 2300 < Re < 5 106 , 0:5 < Pr < 2000 (b) Notter–Rouse [28] correlation for single phase fluid
Nu ¼ 5 þ 0:015Re0:856 Pr0:347
ð16Þ
As shown in Fig. 2, the good coincidence between the experimental Nusselt number of water obtained from Eq. (14) and the values obtained from Eq. (15) of Gnielinski [27] and Eq. (16) of Notter– Rouse [28] under turbulent flow condition. This indicates the exper-
Table 2 Dimensions of twisted tape inserts. S. no.
1 2
Parameter
H (Width) D (Diameter)
Twist ratio, H/D, m 5
10
15
0.065 0.013
0.13 0.013
0.195 0.013
Fig. 2. Experimental Nusselt number of water is in comparison with the correlations of Gnelinski [27] and Notter–Rouse [28].
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plain tube is shown in Fig. 3 along with the data of water. It indicated that the convective heat transfer coefficient of the nanofluid increases with the increase of Reynolds number and volume concentration compared to base fluid (water). It may be point out that proper selection of the nanoparticle volume concentration and pair of solid particles and base liquid is important for applying nanoparticles to heat transfer enhancement. In some cases, the viscosity of the dispersed fluid increases with increasing the particle volume concentration and becomes much higher than that of the base liquid, so that higher volume concentration of the solid particles may suppress heat transfer enhancement of the suspension. Heat transfer enhancement with 0.6% volume concentration of Fe3O4 nanofluid is 20.99% at 3000 Reynolds number and 30.96% at 22000 Reynolds number compared to water under same Reynolds number. The various effects of thermal conductivities under static and dynamic conditions, energy transfer by nanoparticles dispersion, particle migration due to viscosity gradient, Brownian motion of the particles on remarkable enhancement of the convective heat transfer coefficient of water-based Fe3O4 nanofluid flowing through a plain tube. The similar trend is observed by Pak and Cho [11] with Al2O3 and TiO2 nanofluid and Xuan and Li [10] with Cu nanofluid.
shown in Fig. 4 along with the values obtained from Eq. (17) of Sarma et al. [15]. From the figure both the experimental values and the values obtained from Sarma et al. [15] are in good agreement. The similar procedure is adopted to conduct the experiments for Fe3O4 nanofluid with twisted tape inserts and Eq. (14) is used for the estimation of experimental Nusselt number. Three twist ratios like H/D = 5, 10 and 15 were considered. Experimental Nusselt number of different volume concentrations of Fe3O4 nanofluid in circular tube with and with out twisted tape inserts are represented in the Fig. 5 along with the values of water. It can be observed from figure, that higher heat transfer rates are obtained for nanofluid with twisted tape inserts compared to the nanofluid in plain tube. The tape creates the turbulence inside the flow and effective mixing of the fluid will take place. Heat transfer enhancement of 0.6% nanofluid flowing in a plain tube with twisted tape insert of H/D = 5 is 16.06% at 3000 Reynolds number and 18.49% at 22000 Reynolds number under same volume concentration of nanofluid flowing in a tube.
4.2. Experimental Nusselt number of nanofluid in plain tube with twisted tape inserts
3000 < Re < 22000;
Experiments are further conducted in order to estimate the heat transfer coefficient of Fe3O4 nanofluid flowing in a plain tube with twisted tape inserts, because that is the main objective of the present work. No experimental data and regression equation is available for Fe3O4 nanofluid in plain tube with twisted tape inserts. Sarma et al. [15], single-phase fluid in plain tube with twisted tape inserts
log10
Nu Pr1=3 ½1 þ D=H2
0 < u < 0:6%;
ð18Þ
3:19 < Pr < 6:50;
0 < H=D < 15 The present data is correlated for the estimation of Nusselt number for both water and Fe3O4 nanofluid with and without twisted tape inserts and regression Eq. (18) is developed with an average deviation (AD) of 6.72% and standard deviation (SD) of 7.56%. Comparison between the experimental Nusselt number and proposed regression Nusselt number Eq. (18) is represented in Fig. 6. 4.3. Experimental friction factor of nanofluid in plain tube The experimental friction factor is obtained from the relation
¼ 0:974 0:783log10 ½Re
DP f ¼ 2 qV L
þ 0:35flog10 ½Reg2 0:0273flog10 ½Reg3
0:028 H NuReg ¼ 0:0223Re0:8 Pr0:5 ð1 þ uÞ0:54 1 þ D
D
ð17Þ
90 < Re < 1; 30; 000; 4 < Pr < 460; 2:5 < H=D < 10
ð19Þ
2
Blasius [29], using one-seventh power velocity distribution, developed an expression for the determination of friction factor valid in the range 3000 < Re < 105 for pure fluids as
Experimental Nusselt number of water estimated from Eq. (14) in plain tube with different twist ratios of twisted tape inserts is
Fig. 3. Experimental Nusselt number of water and different volume concentrations of Fe3O4 nanofluid.
Fig. 4. Experimental Nusselt number of water in plain tube with twisted tape inserts is in comparison with the Eq. (12) of Sarma et al. [15] and experimental data of Kishore [16] and Lacjakas [17].
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Fig. 5. Experimental Nusselt number of water and Fe3O4 nanofluid in plain tube with and without twisted tape inserts.
Fig. 7. Experimental friction factor of water is in comparison with the values obtained from Eq. (14).
Fig. 6. Experimental Nusselt number is in comparison with the developed regression equation.
Fig. 8. Experimental friction factor of water and different volume concentrations of Fe3O4 nanofluid.
f ¼ 4 0:0079=Re0:25
ð20Þ
Experimental friction factor of water obtained from Eq. (19) is shown in Fig. 7 along with the values obtained from Eq. (20) of Blasius [29] and it found that good agreement. The friction factor of Fe3O4 nanofluid obtained from Eq. (19) shown in Fig. 8 along with friction factor of water. Friction factor of Fe3O4 nanofluid is high compared to the friction factor of water, but it is negligible. The reason for enhancement in friction factor is solid nanoparticles present in the base fluid. 4.4. Experimental friction factor of nanofluid in plain tube with twisted tape inserts Experimental friction factor of water in plain tube with twisted tape inserts obtained from Eq. (19) shown in Fig. 9 along with the values obtained from Eq. (21) of Sarma et al. [15]. It is observed that the values are in close agreement. Sundar and Sharma. [19], single-phase fluid in plain tube with twisted tape inserts
f ½1 þ D=H3:378
¼ 0:474 0:3log10 ½Re þ 0:065flog10 ½Reg2 4:66 103 flog10 ½Reg3
400 < Re < 1; 30; 000; 4 < Pr < 460;
ð21Þ
2:5 < H=D < 10
Experimental friction factor of different volume concentrations of Fe3O4 nanofluid in plain tube with twisted tape inserts estimated from Eq. (19) is shown in Fig. 10. It is observed that with twisted tape inserts in the flow friction factor enhances, but it is negligible. The present experimental data is fit to a regression Eq. (22) for the estimation of friction factor for both water and Fe3O4 nanofluid with and without twisted tape inserts with an average deviation (AD) of 4.07% and standard deviation (SD) of 4.90%. Comparison between the experimental Nusselt number and proposed regression Nusselt number Eq. (22) is represented in the Fig. 11.
0:017 H fReg ¼ 0:3490Re0:25: ð1 þ uÞ0:21 1 þ D
ð22Þ
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Fig. 9. Experimental friction factor of water in plain tube with twisted tape inserts is in comparison with the equation of Sarma et al. [15] and experimental data of Kishore [16] and Lecjakas et al. [17].
Fig. 11. Experimental friction factor is in comparison with the developed regression equation.
twisted tape insert, H/D = 5 is 43.37% and 51.88% compared to water flowing in a plain tube without inserts at Reynolds number 3000 and 22,000, respectively. The enhancement of friction factor in a plain tube with 0.6% volume concentration of Fe3O4 nanofluid when compared to water is 1.09 times and 1.10 times for Reynolds number of 3000 and 22,000 respectively. Under 0.6% volume concentration of Fe3O4 nanofluid in plain tube with twisted tape insert, H/D = 5 is 1.092 times and 1.122 times at Reynolds number 3000 and 22,000, respectively compared to same volume concentration of fluid in plain tube. The friction factor enhancement of 0.6% nanofluid with twisted tape insert, H/D = 5 is 1.179 times and 1.231 times compared to water flowing in a plain tube without inserts at Reynolds number 3000 and 22,000, respectively. Eq. (18) and Eq. (22) is used for the estimation of heat transfer coefficient and friction factor of water, different volume concentrations of Fe3O4 nanofluid in plain tube with and without inserts.
Appendix A. Appendix Fig. 10. Experimental friction factor of water and Fe3O4 nanofluid in plain tube with and without twisted tape inserts.
3000 < Re < 22000; 0 < H=D < 15
0 < u < 0:6%;
3:19 < Pr < 6:50; ð23Þ
5. Conclusions The Nusselt number estimated with Eq. (15) of Gnielinski’s [27] valid for single phase fluid predicts values which are lower by 13.4% for 0.6% for Fe3O4 nanofluid under similar operating conditions. The enhancement of heat transfer coefficient in a plain tube with 0.6% volume concentration of Fe3O4 nanofluid is 20.99% and 30.96% for Reynolds number of 3000 and 22,000, respectively compared to water. Further heat transfer enhancement is observed with twisted tape inserts into plain tube. Under 0.6% volume concentration of Fe3O4 nanofluid in plain tube with twisted tape insert, H/D = 5 is 16.06% and 18.49% at Reynolds number 3000 and 22,000, respectively compared to the same volume concentration of fluid flowing in plain tube without insert. In the similar way, the heat transfer enhancement of 0.6% nanofluid in plain tube with
A.1. Uncertainty Analysis A systematic error analysis is made to estimate the errors associated in the experimental analysis following the procedure detailed by Beckwith et al. [30]. The uncertainties in the values estimated with different instruments are given in Table 3. The maximum possible error for the parameters involved in the analysis are estimated and summarized in Table 4. (a) Heat flux, q
q¼
P ; A
q¼
V I ; pDL
q¼
V 2 =R pDL
Table 3 Uncertainties of parameters and variables. S. no.
Variable name
Uncertainty error,%
1 2 3 4 5
Reynolds number, Re Heat Flux, q Heat transfer coefficient, W/m2 K Nusselt number, Nu Friction factor, f
0.10 0.20 0.2203 0.24196 0.10
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Table 4 Uncertainties of instruments and properties. S. no.
Name of instrument
Range of instrument
1 2 3 4 5 6 7 8
Thermocouple Thermocouple Voltage Current Resistance U-tube manometer Totalizer Properties
0.1 °C 0–120 °C Wall Temperature, Tw 0–120 °C Bulk Temperature, Tb 0.1 °C 0–220 V Voltage, V 0.1 V 0–20 I Current, I 0.01 I 0–53.3 R Resistance, R 0.1 R 0–50 cm Height of the CCl4 1 mm 0–999999 l Mass flow rate, m 1l Thermal conductivity, density, specific heat, viscosity
Uq ¼ q
Variable measured
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2U V UR þ ¼ ð2 0:04545Þ2 þ ð0:1876Þ2 V R
¼ 0:1983% (b) Reynolds number, Re
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Ul U Re U m_ _ pDl; Re ¼ 4m= þ ¼ _ Re l m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:00001Þ2 þ ð0:1Þ2 ¼ 0:1% (c) Heat transfer coefficient
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U T W T b 2 q Uh Uq h¼ ; þ ¼ Tw Tb h q TW Tb qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð0:1983Þ þ ð0:09604Þ ¼ 0:220% (d) Nusselt number, Nu
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 hD U Nu Uh UK Nu ¼ þ ; ¼ K Nu h K qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ð0:2203Þ2 þ ð0:1Þ2 ¼ 0:24196% (e) Friction factor, f
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 Uq Uf U DP 2U V þ þ ¼ f DP q V D 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:002610Þ2 þ ð0:1Þ2 þ ð2 0:00001Þ2 ¼ 0:100%
Dp f ¼ 2 ; qV L
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Least division in measuring instrument
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0.13706 0.23310 0.04545 0.05 0.1876 0.002610 0.00001 0.1
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