J Therm Anal Calorim DOI 10.1007/s10973-017-6791-5

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids in a circular tube under constant heat flux boundary condition Erfan Dabiri1

•

Farhad Bahrami1 • Soroush Mohammadzadeh1

Received: 7 April 2017 / Accepted: 28 October 2017  Akade´miai Kiado´, Budapest, Hungary 2017

Abstract The main purpose of this research is to investigate the effect of using SiC/water and MgO/water nanofluids on convection heat transfer in a circular tube with constant heat flux boundary condition. Thermophysical properties of these nanofluids, such as viscosity, density, and thermal conductivity, have also been measured and reported. SiC nanoparticles with 50 nm diameters at 0.04–0.2% volume concentrations and MgO nanoparticles with a size of 40 nm and volume concentration ranging from 0.02 to 0.12% are used to make the nanofluids. This study is done in a vertically oriented straight stainless steel tube under turbulent flow condition. Results of heat analysis showed that both Gnielinski and Hausen correlations underpredict the experimental data. Two models have been developed to predict heat parameters of nanofluids based on Gnielinski and Hausen correlations using experimental data. Modified correlations can precisely estimate Nusselt number and heat transfer coefficient of nanofluids in the range of nanoparticles studied with maximum errors of less than 1%. The average increase in Nusselt number for SiC/ water and MgO/water nanofluids in the entire range of Reynolds number and volume percent used in this work is 8.88 and 5.71%, respectively, compared to distilled water under similar conditions. Keywords SiC  MgO  Nanofluids  Thermophysical property  Turbulent flow  Heat transfer

& Erfan Dabiri [email protected] 1

Department of Gas Engineering, Petroleum University of Technology, P. O. Box 63431, Ahwaz, Iran

List of A a, b, c CP D d h I k L m m_ Nu S Pr Q q_ Re T u V x fi

symbols Tube cross-sectional area (m2) Constant (dimensionless) Specific heat capacity (kJ kg-1 K-1) Diameter (m) Nanoparticle diameter (nm) Heat transfer coefficient (W m-2 K-1) Electrical current (A) Thermal conductivity (W m-1 K-1) Length (m) Mass (kg) Mass flow rate (kg s-1) Nusselt number (dimensionless) Tube perimeter (m) Prandtl number (dimensionless) Thermal power (W) Heat flux (W m-2) Reynolds number (dimensionless) Temperature (K) Mean fluid velocity (m s-1) Volume (m3) or voltage (v) Axial direction (m) Friction factor (dimensionless)

Greek letters Dimensionless thickness of laminar sublayer dþ V [ Nanoparticle volume fraction in nanofluid l Dynamic viscosity (kg m-1 s-1) m Kinematic viscosity (m2 s-1) q Density (kg m-3) Subscripts b Bulk bf Base fluid

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in nf out s w wnf

Inlet condition Nanofluid Outlet condition Solid particle Wall Nanofluid at water temperature

Abbreviations CNT Carbon nanotube Exp Experimental EG Ethylene glycol MW Multiwalled NP Nanoparticle W Water

Introduction Heat transfer plays a prominent role in industrial equipment. Recently, researchers have attempted to modernize these facilities in order to increase the heat transfer rate while reducing the size of equipment. For this purpose, different methods, such as changing flow geometry, boundary conditions, and improving thermophysical properties of fluids, have been applied by researchers over the years. In heat transfer equipment, traditional working fluids, such as water, ethylene glycol, and engine oil, have the disadvantage of low thermal conductivity. Increasing thermal conductivity of fluids with the addition of millimeter or micron-sized particles had been noted since years ago, but utilizing solids with these magnitudes caused lots of problems including excessive pressure drop of the flow in the channel, clogging, and sedimentation [1]. Choi [2] introduced the definition of nanofluid in fluid heat transfer in 1995, as a suspension of solid nanoparticles (1–100 nm) in common fluids. After that, many interests have been addressed toward nanofluids including metal (Cu and Ag) [3, 4], non-metal (CNT, graphene and SiC) [5–7] and metal oxide (Al2O3, Fe2O3, ZnO, SiO2, and CuO) [8–10] particles. Ceramic nanoparticles have also found to have high chemical and physical stability and outstanding oxidation and corrosion durability [11]. Generally, ceramics have low thermal conductivity except for nitrides and carbides [12]. Increase in viscosity of base fluid due to the addition of nanoparticles will cause some problems, such as increasing pressure drop and power consumption, and reducing heat performance of equipment [13]. Therefore, more attentions should be paid on the viscosity variation of nanofluids with their nanoparticle concentrations. Toghraie et al. [14] experimentally investigated the effect of temperature and solid volume concentration on viscosity of Fe3O4/water nanofluid. They reported significantly decrease in viscosity

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of the nanofluid with increasing temperature and enhancement of the viscosity with an increase in the nanoparticle concentration. Effect of temperature and nanoparticle volume fraction has also been studied in alumina/engine oil nanofluid [15]. Hybrid nanofluids have recently attracted some attentions, and their viscosities have been investigated, as what Esfe et al. [16] have done on MWCNTs-ZnO/SAE40 nanolubricant. In another work, a precise pattern have been developed for estimating the viscosity of TiO2/water nanofluid with respect to the temperature and nanoparticle mass fraction by artificial neural network using experimental data [17]. According to the literature, various factors, such as concentration, size and kind of nanoparticles, temperature, and the base fluid, affect thermal conductivities of nanofluids [18]. Xie et al. [19] prepared a nanofluid by dispersing of 25 nm SiC nanoparticles in water. They observed 15.8% enhancement in the thermal conductivity when particle loading was 4.2 vol% and in the case of 600 nm cylindrical SiC nanoparticles, the increase was 22.9%. Singh et al. [20] investigated the thermal conductivity and viscosity of SiC (170 nm)/water nanofluid for concentrations ranging from 1 to 7 vol%. Viscosity of nanofluids ranged from 2 to 3 cP for nominal nanoparticle loadings 4–7 vol% in the room temperature. Enhancement in thermal conductivity of nanofluid with 7 vol% particle loadings under ambient conditions was approximately 28% higher than that of water. Lee et al. [21] reported 102 and 7.2% enhancement, respectively, in the viscosity and thermal conductivity of SiC/water nanofluid for 3 vol% of SiC nanoparticle. Timofeeva et al. [23] investigated the effect of nanoparticle size on thermal conductivity of SiC/water nanofluid and an increase in thermal conductivity obtained by raising the size of nanoparticles. However, in another study, Manna et al. [24] found the inverse dependence of conductivity and particle size. They also reported that adding 0.1 vol% SiC nanoparticles to the water would lead to 12% increase in thermal conductivity of the fluid. An investigation has also been conducted on the effect of nanoparticle diameter on thermal conductivity and viscosity of aqueous nanofluid of Fe. An increase in nanoparticle size has led to reduction of the viscosity and enhancement of the thermal conductivity [22]. Esfahani and Toghraie [25] measured thermal conductivity of SiO2/water–EG and reported 45.5% enhancement in thermal conductivity of 5% volume concentration of the nanofluid. Some authors have investigated on thermal conductivity of hybrid nanofluids, such as Zadkhast et al. [26] and Toghraie et al. [27] who measured thermal conductivity of MWCNT-CuO/water and ZnO–TiO2/EG nanofluids, respectively. Prediction of thermal conductivity of Al2O3/EG, Al2O3/water–EG and MgO/EG nanofluids

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids…

have also been conducted by neural network modeling using experimental data [28–30]. Optimum viscosity and thermal conductivity of the aqueous nanofluid of Al2O3 have been investigated and obtained at maximum temperature [31]. Heat transfer behavior of nanofluids as working fluid was investigated in tubes (with and without inserts), heat exchangers, heat pipes, minichannels, and ducts. Yu et al. [32] conducted experiments on 3.7% volume concentration of SiC/water nanofluid flowing inside a circular tube with turbulent flow regime. They obtained 50–60% increase in the heat transfer coefficient compared to water as working fluid in constant Reynolds number. In a similar study by Celata et al. [33], effects of Reynolds number and uniform heat flux on heat convection performance of SiC/water nanofluid in a circular tube have been investigated in both laminar and turbulent flow regimes. Esfe et al. [34] studied thermophysical properties and turbulent heat transfer behavior of MgO/water nanofluid in a circular pipe at low concentrations (less than 1 vol%). They reported maximum enhancement of heat transfer coefficient around 35.93% for 1.0% volume fraction of the nanofluid in the turbulent flow condition. In another study, Esfe and Saedodin [35] investigated the effect of nanoparticles’ diameter (20, 40, 50 and 60 nm) on heat transfer behavior of MgO/water nanofluid inside a double-tube heat exchanger. Zhang et al. [36] experimentally studied heat transfer behaviors of SiC/water nanofluid in a multiport minichannel flat tube in the volume concentrations ranging from 0.001 to 1%. They found 30.3 and 81.7% increase in laminar and turbulent flow regimes, respectively. Kim et al. [37] used 0.01 and 0.1 vol% of SiC/water nanofluid as the working fluid inside a heat pipe. They did not observe any improvement in thermal performance of the heat pipe using SiC/water nanofluid compared to water as the working fluid. Ghanbarpour et al. [38] indicated that the maximum heat removal capacity of the heat pipe increased by 29% with using SiC nanoparticle at 1.0% mass concentration the nanofluid. In another work, numerical investigation on laminar forced convection of CuO/water nanofluid inside a triangle duct has been conducted and an increase in the heat performance and pressure drop have been concluded by the presence of nanoparticles [39]. Convection heat transfer of CuO/water nanofluid flowing inside a sinusoidal channel with a porous medium has also been studied

numerically [40]. Akbari et al. [41] numerically analyzed laminar and turbulent heat performance of Al2O3/water nanofluid flowing inside a tube containing twisted tape in different aspect ratios. Force convection of a non-Newtonian nanofluid in a microtube has also been studied numerically by Sajadifar et al. [42]. In summarizing the above literature review, although SiC and MgO have higher thermal conductivities in comparison with many nanoparticles, limited numbers of researches have been conducted on the effect of these particles on convective heat transfer performance in a circular tube. Therefore, the present work focuses on SiC/ water and MgO/water nanofluids. In this study, firstly, thermophysical characteristics (viscosity, density, and thermal conductivity) of SiC/water and MgO/water nanofluids have been measured experimentally as a function of particle concentration. Then, the effect of SiC and MgO nanoparticles on the turbulent convection heat transfer of fluid flow in a circular tube has investigated.

Materials and methods Materials Silicon carbide (SiC) and magnesium oxide (MgO) nanoparticles have been obtained from the Tecnan (Navarra, Spain). Thermophysical properties of these nanoparticles are shown in Table 1. Analytical methods Viscosities of solutions have been measured by a SVMTM series viscometer (SVMTM 2001, Anton Paar, Austria) which is capable of measuring the kinematic viscosity in the range of 0.2–30,000 mm2 s-1. Density measurements have been taken by one of the most accurate density meters in the market (Model DMA 4500 M, Anton Paar, Austria) with the accuracy of 0.00005 g cm-3. An analytical balance (ABT 100-5 M, Kern Corporation) with a measurement range of 10 mg–200 g and a maximum error of 0.1 mg has been used in massing of nanoparticles. A halfindustrial ultrasonic vibrator (UIP500hd, Hielscher, Germany) is used for dispersing nanoparticles in distilled water. Thermal conductivities of fluids have been measured

Table 1 Thermophysical properties of SiC and MgO nanoparticles Nanosized particle

Mean diameter/nm

Specific surface area/m2 g-1

Density/kg m-3

Specific heat/ J kg-1 K-1

Thermal conductivity/ W m-1 K-1

SiC

50

90

3220

800

148

MgO

40

40

3580

877

48

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E. Dabiri et al.

by KD2 Thermal Analyzer (Decagon Devices, USA) with ± 0.01 W m-1 K-1 accuracy based on the transient hot wire method. ABB flow meter (2600T, ABB, Switzerland) has been used for non-contact flow measurements of low viscosity liquids. Heater’s power is provided electrically by a DC power supply, and a personal computer has been used for data acquisition. Experimental setup and procedure Aghajani et al. [43] have experimentally analyzed heat performance of liquid/solid fluidized bed in vertical pipes. For the purpose of the present work, application of their setup has been changed to enable us conducting experiments on convection heat performance of fluids in a tube (Fig. 1). The main parts of the apparatus are flow loop, heat source unit, cooling reservoir, pump, measuring and controlling unit. The test section is a vertically oriented straight stainless steel tube (type 316) with 300 mm length, 23.8 mm inner diameter, and 25.4 mm outer diameter (see Fig. 2). Hundred and sixty millimeter of the tube length is heated electrically by a DC power supply which is capable of delivering a maximum power of 500 W. Thick thermal isolated coverings around the heater establishes a constant heat flux condition. The average wall temperature distribution is measured by four K-type thermocouples which are fixed at the end of the test section. Bulk temperature measurements of nanofluids are taken by two further K-type thermocouples inserted at the inlet and outlet section of the tube. Temperature of the cooling reservoir is also precisely controlled by another thermocouple. The

precision error in temperatures is considered to be the least count determined by the thermocouples and found to be within ± 0.01 C. The flow meter has been calibrated for different solutions using a bucket and stopwatch technique. During experiments, nanofluid flow rate, voltage, current of the DC power supply, and temperature readings from the seven thermocouples have been recorded by a data requisition system. The experimental procedure for running the whole setup is as follows: Firstly, the reservoir tank is filled with distilled water, and then the pump and cooling and heating systems are started. After about 50–60 min, the system reaches to steady-state condition. All measurements have been taken after the system reaches to steady-state conditions. During experimental runs, inlet and outlet temperatures of the fluid, the tube wall temperature at different positions and the flow rate have been monitored. To investigate the heat transfer in a wide range of Reynolds number, experiments have been conducted at 16 flow rates for all concentrations of nanofluids. Each measurement has been repeated at least two times to ensure measurements to be precise enough. After starting up with the water, experiments have been carried out at different concentrations of SiC/water and MgO/water nanofluids to find convection heat transfer parameters. Measuring heat transfer coefficient By neglecting the heat loss to atmosphere and considering the system to be insulated, energy supplied by heating and energy absorbed by the flowing liquid should be balanced.

T T Test heater

Sampling point

q·

Cooling water

T V

Insulation T

Holding tank Flow meter

PC Data acquisition

Drain

Pump

Fig. 1 Schematic diagram of the test apparatus for heat transfer experiments [43]

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Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids… Fig. 2 Schematic of the test section [43]

200

100 mm

100 mm

160 mm

Subminiature thermocouple

Heated section

Capillary

4 mm

10 mm

23.8 mm

Thermocouples

Equations 1 and 2 refer to supplied and absorbed energy, respectively. The difference between values obtained from these equations is less than 2.5%. The experimental local convective heat transfer coefficient (h) and corresponding Nusselt number (Nu) are calculated by Eqs. 3 and 4.

where q is density of fluid/kg m-3, S and A are the perimeter/m and cross-sectional area/m2 of the test tube, respectively, and u is the average fluid velocity/m s-1.

Q¼V I

The method of Kline and Mcclintock [44] has been used for obtaining the uncertainty in calculating heat transfer parameters reported in Table 2. The following equation has been considered to calculate the uncertainty of parameter R which has also been used by Pakdaman et al. [45] and Esfe et al. [34]. "  2 #12 n X oR UR ¼ UV ð8Þ oVi i i¼1

Energy supplied  _ p Tb;out  Tb;in Q ¼ mC Energy absorbed 

ð1Þ ð2Þ

where V and I are electric voltage/v and current/A, respectively, m_ is mass flux/kg s-1, Cp is specific heat capacity/kg m-1 s-1, Tb,in and Tb,out are bulk temperatures/ k of fluid at inlet and outlet of test section. _ ðTw ð xÞ  Tb ð xÞÞ; hð xÞ ¼ q=

q_ ¼ Q=pDL

ð3Þ

hð xÞ ¼ Q=pDLðTw ð xÞ  Tb ð xÞÞ

ð4Þ

Nuð xÞ ¼ hð xÞD=k

ð5Þ

Re ¼ qvD=l

ð6Þ

Uncertainty analysis

where UR and UVi are uncertainties which correlates parameters R and Vi (independent variables) with uncertainties. Additionally, n is the number of independent variables. Following four equations have been considered to calculate the uncertainty of the energy supply, the convective heat transfer coefficient, Nusselt number and Reynolds number, respectively.

where q_ is the heat flux applied on the test section/w m-2 K-1, Tw and Tb are mean tube’s wall temperatures/k and mean bulk temperature of the fluid/k, respectively, x represents axial distance from the entrance of the test section/m, D is the tube diameter/m, L is the tube length/m, l is the viscosity of the fluid/kg m-1 s-1 and k is the fluid thermal conductivity/w m-1 K-1. By considering that physical properties are temperature independent, a linear temperature profile which obtains the mean bulk temperature of the fluid at the position of x in the test section, is as follows:

Table 2 Uncertainty errors

Nu

± 2.49

_ Tb ð xÞ ¼ Tb;in þ qSx=ðqC p uAÞ

Re

± 1.30

ð7Þ

Parameter

Uncertainty error/%

Q

± 1.77

h

± 2.46

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E. Dabiri et al.

Q ¼ I  UV þ V  UI ð9Þ " 2  2  2 UQ Q  UD Q  UL Uh ¼ þ þ pDL  DT pD2 L  DT pDL2  DT     #1 Q  UTW ðxÞ 2 Q  UTb ðxÞ 2 2 þ þ ð10Þ pDL  DT 2 pDL  DT 2 UNu

"  #12     D  Uh 2 h  UD 2 hd  UK 2 ¼ þ þ k k k2 "

URe ¼

Nu ¼

ðfi =8ÞðRe  1000Þ  Pr pffiffiffiffiffiffiffiffi  1:0 þ 12:7 fi =8 Pr2=3 1

2300 \ Re \ 5  104 ;

0:5 \ Pr \ 2000

where fi is the friction factor and can be calculated from Eq. 15, presented by Filonenko [47]. fi ¼ ½1:82LogðReÞ  1:642

ð11Þ

       #12 qv  UD 2 qD  Uv 2 Dv  Uq 2 qvD  Ul 2 þ þ þ l l l l2

ð12Þ By calculating above equations, values of uncertainties for each parameter are obtained and reported in Table 2.

ð15Þ

3000 \ Re \ 5  106 For the entrance region, Gnielinski modified Eq. 14 by Prb 0:11 introducing the correction factors ½1þ 13 ðDXÞ2=3  and ðPr Þ w to consider the influence of temperature on fluid properties. As a result, Gnielinski correlation is presented as follows for the developing region flow [46]: "   #  ðfi =8ÞðRe  1000Þ  Pr 1 D 2=3 Prb 0:11 pffiffiffiffiffiffiffiffi Nu ¼  1þ 3 X Prw 1:0 þ 12:7 fi =8 Pr2=3 1

Nanofluid preparation

ð16Þ

Two types of nanoparticles have been selected to disperse in water as the base fluid. Equation 13 is used to measure the required mass ðms Þ of nanoparticles for a specified concentration of nanofluid. ms ¼ qs  ;  V

ð13Þ 3

where V is the volume of nanofluid/m using in each experiment. Nanoparticles have been mixed with the distilled water by a magnetic stirred device for an hour; then, the suspension is imposed to ultrasonic waves generated by half-industrial ultrasonic vibration for 4–6 h with the power consumption of 500 W and frequency of 20 kHz. No sign of sedimentation or flocculation has been observed after 7 days. Because of the requirement to the high volume of nanofluid, flow mode of the ultrasonic processor was used. A peristaltic pump is used to set a flow rate of 0.125 L min-1 within the ultrasonic processor.

Heat transfer models In the present study, experimental values of Nusselt number have been compared with predictions of following equations for developing region flow of the tube: Gnielinski and Hausen correlations Gnielinski [46] introduced Eq. 14 which can be used for the fully developed transition region of single-phase turbulent flow through the circular tube.

123

ð14Þ

This equation has been widely used to model Nusselt number of nanofluids by considering nanofluid, as a singlephase fluid [32, 33, 48–51]. Hausen [52] suggested Eq. 17 for estimation of the local value of Nusselt number for single-phase fluids flowing in a tube under transition and turbulent entrance and fully developed flow. "  2=3 # 0:14 0:42   1 D Pr Nux ¼ 0:037Re0:75  180 Pr 1 þ 3 X Prw ð17Þ 0

D  1; \ 0:6 \ Pr \ 103 ; 2300  Re  105 x

Modified Gnielinski correlation and modified Hausen correlation To increase the accuracy of predictions on Nusselt number of nanofluids, Hausen and Gnielinski equations have been corrected using experimental data as follow: based on Buongiorno work [53], Gnielinski correlation has been modified by considering laminar sublayer. This modification can be used for prediction of turbulent nanofluid in the tube. The modified Gnielinski equation is defined as follows: "   #  ðfi =8ÞðRenf  1000Þ Prnf 1 D 2=3 Prnf 0:11   Nu ¼ 1þ pffiffiffiffiffiffiffiffi 2=3 3 X Prwnf 1 þ dþ fi =8 Prnf 1 V ð18Þ

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids… Table 3 Constants of modified Gnielinski correlation Nanoparticle

a

b

c

[

d

SiC

- 1061.8

405.62

- 55.991

12.65

0 B [ B 0.2%

MgO

- 3491.7

798.08

- 63.171

12.61

0 B [ B 0.12%

2300 \ Re \ 5  104 ; 0:5 \ Pr \ 2000; 3 2 dþ V ¼ A; þB; þC;þD

Cpnf

where dþ V is dimensionless thickness of laminar sublayer and is obtained by using experimental values of Nusselt number. The equation for calculation of dþ V is derived from average values of dþ for each nanofluid in the volV ume concentrations of nanofluids used. A, B, C, and D are also constants and are presented in Table 3 for each nanofluid. Hausen correlation has been modified by multiplying the equation by a correction factor obtained by comparison of Hausen correlation with experimental data. The modified Hausen equation is as follows: "  2=3 #  0:75  0:42 D Nu ¼ 0:037 Renf  180 Pr 1 þ nf X  0:14 Prnf  f ð ;Þ Prwnf

ð19Þ

    ;  qs  Cps þ ð1  ;Þ  tbf  Cpbf ¼ qnf

ð22Þ

Results and discussion Thermophysical properties Viscosity Viscosities of SiC/water and MgO/water nanofluids have been measured as a function of volume concentration of nanoparticles, and results have been compared with Batchelor [56] and Wang [57] equations. Batchelor modified Einstein’s [58] equation by considering the effect of Brownian motion of particles and proposed: lnf ¼ 1 þ 2:5; þ 6:5;2 ð23Þ lbf

D  1; \ 0:6 \ Pr \ 103 ; 2300  Re  105 ; f ð;Þ x a;b þc ¼ ð 1 þ ;Þ

Wang et al. expressed a model to predict the viscosity of nanofluids as follows [57]:   lnf ¼ lbf 1 þ 7:3; þ 123;2 ð24Þ

where a, b and c are constant. Values of constants are shown in Table 4 for SiC and MgO nanoparticles. In above correlations, Renf and Prnf are defined as follows:

It should be noted that these equations are valid for low volume concentrations of nanofluids. Figures 3 and 4 show that the increase in concentration of nanofluids results in higher values of viscosity for SiC/

Renf ¼ qnf  u  D=lnf

ð20Þ

Prnf ¼ Cp;nf  lnf =Knf

ð21Þ

In above equations, thermophysical properties of nanofluids have been obtained by experiments, except for the specific heat capacity (Cpnf) which is calculated by Eq. 22, suggested in the literature [54, 55].

1 Experimental data

0.995

Wang equaon Batchelor equaon

Viscosity/cP

0

0.99

0.985

0.98

Table 4 Constants of modified Hausen correlation Nanoparticle

a

b

c

[

SiC

0.03584

- 1.14

71.13

0 B [ B 0.2%

MgO

0.02638

- 1.188

52.2

0 B [ B 0.12%

0.975 0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16 0.18

0.2

Volume fraction/%

Fig. 3 Viscosity comparison for SiC/water nanofluid

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E. Dabiri et al. 1.025

0.989

Experimental data

0.987

Maxwell model

Batchelor equaon

1.015

K nf /Kbf

0.985

Viscosity/cP

Experimental data

1.02

Wang equaon

0.983

1.01

0.981

1.005

0.979

1

0.977

0.995 0

0.04

0.08

0.12

0.16

0.2

Volume fraction/%

0.975 0

0.02

0.04

0.06

0.08

0.1

0.12

Volume fraction/%

Fig. 7 Effect of SiC nanoparticle on thermal conductivity of water at 300 K

Fig. 4 Viscosity comparison for MgO/water nanofluid 1.003 Experimental data

1.0025

1.016

Mixing rule

1.002

1.001

1.014

Experimental data

1.012

Maxwell model

1.01 1.0005

K nf /Kbf

Density/g cm–3

1.0015

1

1.008 1.006

0.9995

1.004 0.999

1.002 0.9985

1 0.998 0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16 0.18

0.998

0.2

0

Volume fraction/%

0.03

0.06

0.09

0.12

Volume fraction/%

Fig. 5 Density comparison for SiC/water nanofluid

Fig. 8 Effect of MgO nanoparticle on thermal conductivity of water at 300 K

1.001 Experimental data

1.0005

1.025 SiC/water nanofluid

1

1.02

0.9995

1.015

K nf /Kbf

Density/g cm–3

Mixing rule

0.999

MgO/water nanofluid

1.01 1.005

0.9985

1 0.998

0.995 0

0.9975 0

0.02

0.04

0.06

0.08

0.1

0.12

0.04

0.08

0.12

0.16

0.2

Volume fraction/%

Volume fraction/%

Fig. 6 Density comparison for MgO/water nanofluid

Fig. 9 Comparison between the effect of SiC and MgO nanoparticles on thermal conductivity of water at 300 K

water and MgO/water nanofluids. In both figures, measured values of viscosities are higher than predictions of Batchelor and Wang equations. As can be seen in these figures,

Wang equation results have better agreement with the experimental data than predictions of Batchelor equation, especially for the MgO/water nanofluid over the volume concentration range used in this work.

123

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids…

6 and is compared with mixture model [59]. In the mixture model, densities of nanofluids are determined by the following expression:

350 300

qnf ¼ ;qs þ ð1  ;Þqbf

Nu

250

In almost over the measurement range, results of nanofluid densities are in good agreement with the theoretical model.

200 Experimental results

150

ð25Þ

Hausen

100

Thermal conductivity

Gnielinski

50

Density

Maxwell [60] proposed a model for determination of thermal conductivity of liquid–solid suspensions for low volume concentration of spherical particles. This model is described in Eq. 26.

ks þ 2kbf þ 2ðks  kbf Þ; knf ¼ ð26Þ kbf ks þ 2kbf  ðks  kbf Þ;

The increase in density of nanofluids with nanoparticle concentration at room temperature is shown in Figs. 5 and

where ks and kbs are thermal conductivities of nanoparticles and the base fluid, respectively. Maxwell model can be used for predicting the thermal conductivity of nanofluid

1

1.5

2

2.5

3

3.5

4

Re

4.5 ×10000

Fig. 10 Comparison of Nusselt numbers for water

(a)

11000 10000

Heat transfer coefficient/W m –2 K –1

9000

Dislled water

SiC (0.04%)

SiC (0.08%)

SiC (0.12%)

SiC (0.16%)

SiC (0.2%)

8000 7000 6000 5000 4000 3000 2000 1000 1

1.5

2

2.5

Re

3

3.5

4

4.5

×10000

(b)

11000 10000

Dislled water

MgO (0.02%)

MgO (0.05%)

MgO (0.07%)

MgO (0.09%)

MgO (0.12%)

9000

Heat transfer coefficient/W m –2 K –1

Fig. 11 Experimental heat transfer coefficients for water and a SiC/water and b MgO/ water nanofluids

8000 7000 6000 5000 4000 3000 2000 1

1.5

2

2.5

3

Re

3.5

4

4.5

×10000

123

E. Dabiri et al. Fig. 12 Experimental Nusselt numbers for water and a SiC/ water and b MgO/water nanofluids

(a) 400

Dislled water

SiC (0.04%)

SiC (0.08%)

SiC (0.12%)

SiC (0.16%)

SiC (0.2%)

350 300

Nu

250 200 150 100 50 1

1.5

2

2.5

3

3.5

4

Re

4.5

×10000

(b) 410

Dislled water

MgO (0.02%)

MgO (0.05%)

MgO (0.07%)

MgO (0.09%)

MgO (0.12%)

360 310

Nu

260 210 160 110 60 1

1.5

2

2.5

3

Re

[61]. No significant change between other classical and modern models and Maxwell model is observed because of very low concentrations of nanoparticles being used in this work. In the other word, theoretical models cannot predict thermal conductivities of very low concentrations of nanofluids. The thermal conductivity of SiC/water has been measured, and enhancement in thermal conductivity of base fluid has been observed. As presented in Fig. 7, predictions of Maxwell model are less than experimental data. Effect of MgO nanoparticle on thermal conductivity of water at room temperature and comparison with Maxwell model is illustrated in Fig. 8. Previous results and trends for SiC/water nanofluid are also observed for MgO/water nanofluid. Figure 9 shows a comparison between thermal conductivities of SiC/water and MgO/water nanofluids. Despite SiC nanoparticle has higher thermal conductivity than

123

3.5

4

4.5

×10000

MgO nanoparticle, no significant difference between thermal conductivity of nanofluids containing them has been observed. Increase in volume concentration of the nanofluid leads to no significant enhancement in thermal conductivity of SiC/water nanofluid compared to that of MgO/ water nanofluid. This result may be due to very low volume concentrations used in this study. Heat transfer study Water Nusselt number of distilled water as a function of Reynolds number is shown in Fig. 10 and has also been compared with calculated Nusselt numbers of Gnielinski and Hausen equations. A linear trend between Nusselt and Reynolds numbers of distilled water has been observed. According to the figure, there is good agreement between Gnielinski

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids… Fig. 13 The ratio of experimental heat transfer coefficient of a SiC/water and b MgO/water nanofluids to that of water

(a) 1.24

Re = 11000 Re = 30000

1.22

Re = 15000 Re = 35000

Re = 20000 Re = 40000

Re = 25000 Re = 45000

1.2 1.18

h (nanofluid)/h (water)

1.16 1.14 1.12 1.1 1.08 1.06 1.04 1.02 1 0.98 0

0.04

0.08

0.12

0.16

0.2

0.24

Volume fraction/%

(b)

1.14

Re = 11000 Re = 32000

1.13 1.12

Re = 17000 Re = 37000

Re = 22000 Re = 42000

Re = 27000 Re = 46000

h (nanofluid)/h (water)

1.11 1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Volume fraction/%

equation and the experimental data while Hausen equation underpredicts experimental results. The average absolute deviation of Gnielinski and Hausen equations from the experimental data is 4.46 and 23.2%, respectively. Nanofluid Effects of SiC and MgO nanoparticles on the convective heat transfer coefficient of base fluid have been investigated. Nanofluids with different concentrations including 0.04, 0.08, 0.12, 0.16 and 0.20 vol% of SiC/water nanofluid and 0.02, 0.05, 0.07, 0.09 and 0.12 vol% of MgO/water nanofluid have been used within Reynolds numbers varying between 11,000 and 46,000. Figure 11 shows heat transfer coefficients of SiC/water and MgO/water nanofluids versus Reynolds numbers, respectively. More deviation of heat transfer coefficient of

the nanofluid from that of distilled water is observed as the volumetric flow rate (or Reynolds number) increases. Nusselt numbers of nanofluids versus Reynolds numbers at different volume percent of nanofluids are shown in Fig. 12. It is obvious that the increase in nanoparticle concentration has led to enhancement of Nusselt numbers of nanofluids compared to distilled water. To better understand effects of nanoparticles concentration on the heat transfer performance, ratio of convective heat transfer coefficients of SiC/water and MgO/water nanofluids to that of distilled water has been plotted as a function of volume fractions of nanoparticles and Reynolds numbers in Fig. 13. This figure clearly shows that nanoparticles suspended in water increases Nusselt numbers even for low volume concentrations of nanofluids. The highest amount of augmentation in convective heat transfer coefficient of nanofluids is observed at Re = 45,000 for

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E. Dabiri et al. Fig. 14 The ratio of calculated heat transfer coefficient by modified Hausen correlation to the experimental heat transfer coefficient for a SiC/water and b MgO/water nanofluids

(a)

1.1

SiC (0.04%) SiC (0.16%)

1.08

SiC (0.08%) SiC (0.20%)

SiC (0.12%)

1.06

h (calculated)/h (exp)

1.04 1.02 1 0.98 0.96 0.94 0.92 0.9 0.8

1.3

1.8

2.3

2.8

3.3

3.8

4.3

Re

(b)

×10000

1.1

MgO (0.02%) MgO (0.05%) MgO (0.07%) MgO (0.09%) MgO (0.12%)

1.08 1.06

h (calculated)/h (exp)

4.8

1.04 1.02 1 0.98 0.96 0.94 0.92 0.9 0.9

1.4

1.9

2.4

2.9

3.4

3.9

4.4

Re

4.9

×10000

Table 5 Deviations of modified correlations from experimental data for SiC/water nanofluid

Table 6 Deviations of modified correlations from experimental data for MgO/water nanofluid

Volume concentration/%

Volume concentration/%

Deviation values/% Modified Hausen

Deviation values/% Modified Gnielinski

Deviation values/% Modified Hausen

Deviation values/% Modified Gnielinski

0.04

? 0.930

? 0.58

0.02

? 0.26

- 0.03

0.08

? 0.230

? 0.38

0.05

? 0.13

? 0.52

0.12

? 0.065

? 0.22

0.07

- 0.32

- 0.14

0.16

? 0.002

- 0.36

0.09

- 0.99

- 0.20

0.20

- 0.235

- 0.35

0.12

- 0.29

- 0.84

SiC/water nanofluid and Re = 46,000 for MgO/water nanofluid. At constant values of Reynolds numbers, the ratio of heat transfer coefficient increases as the concentration of nanoparticles raises. At Re = 20,000, the maximum enhancement in heat transfer coefficient is about

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12.6% with 0.2 vol% of SiC/water nanofluid, and at Re = 45,000, this maximum enhancement reaches to 17.8% in the same vol% of aqueous nanofluid containing SiC. As the same way, 6.2% increase in the heat transfer coefficient has been observed at Re = 17,000 with 0.12

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids…

(a) 1.06 SiC (0.04%) SiC (0.08%) 1.04

SiC (0.12%) SiC (0.16%)

h (calculated)/h (exp)

Fig. 15 The ratio of calculated heat transfer coefficient by modified Gnielinski equation to the experimental heat transfer coefficient for a SiC/water and b MgO/water nanofluids

SiC (0.20%)

1.02

1

0.98

0.96

0.94 0.8

1.3

1.8

2.3

2.8

3.3

3.8

4.3

4.8

×10000

Re

h (calculated)/h (exp)

(b) 1.08 MgO (0.02%) MgO (0.05%) MgO (0.07%) MgO (0.09%) MgO (0.12%)

1.07 1.06 1.05 1.04 1.03 1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.9

1.4

1.9

2.4

2.9

Re

vol% of MgO/water nanofluid, and at Re = 42,000, the maximum enhancement reaches to 9.8% in the same vol% of MgO/water nanofluid. The average increase in Nusselt numbers in comparison with distilled water for SiC/water and MgO/water nanofluids in the entire range of Reynolds number and volume concentrations studied is 8.88 and 5.71%, respectively. Figure 14 demonstrates the ratio of the calculated heat transfer coefficients by modified Hausen correlation to the experimental heat transfer coefficients at different Reynolds numbers for SiC/water and MgO/water nanofluids. As shown in this figure, ratios of heat transfer coefficients have shown two different trends versus Reynolds number. Generally, over Re \ 30,000, obtained values of heat

3.4

3.9

4.4

4.9

×10000

transfer coefficients of SiC/water nanofluid from modified Hausen correlation are greater than that of experiments and for Re [ 30,000, heat transfer coefficients of modified Hausen correlation are lower than that of experimental results. However, such trend is not observed for 0.16 vol% of nanofluid containing SiC. In the same way, the calculated heat transfer coefficients from modified Hausen correlation for MgO/water nanofluid are lower than that of experiments in Re [ 35,000. This means that modified Hausen correlation over predicts experimental convective heat transfer coefficients of nanofluids at low Reynolds numbers and under predicts at higher Reynolds numbers. Average deviations of modified Hausen correlation for each concentrations of SiC/water nanofluid over the

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E. Dabiri et al. Fig. 16 Comparison of Nusselt numbers for a SiC/water at 0.20 vol % and b MgO/water at 0.12 vol %

(a)

410

360

310

Nu

260

210

Experimental data Modified Gnielinski Gnielinski Modified Hausen Hausen

160

110

60 1

1.5

2

2.5

3

3.5

4

4.5

5

×10000

Re

(b) 410 360 310

Nu

260 210

Experimental data Modified Gnielinski Gnielinski Modified Hausen Hausen

160 110 60 1

1.5

2

2.5

3

Re

studied Reynolds number are calculated and reported in Table 5. With increasing concentrations, the over predicted values of heat transfer coefficient diminish and at its maximum applied concentration, the modified equation underpredicts the experimental heat transfer coefficient. The average deviation of modified Hausen correlation from experimental data for the studied volume concentrations of SiC/water nanofluid, is ? 0.992%. Deviation of modified Hausen correlation from experimental data for each concentration of MgO/water nanofluid is indicated in Table 6. Modified Hausen equation overestimates the experimental convective heat transfer coefficient in 0.02 and 0.05% volume concentrations of MgO/ water nanofluid and underestimates experiments in the 0.07, 0.09, and 0.12% volume concentrations. The average deviation of modified Hausen correlation from

123

3.5

4

4.5

5

×10000

experimental data for the volume concentrations of MgO/ water nanofluid ranging from 0.02 to 0.12% is - 0.24%. The ratio of the calculated heat transfer coefficient by modified Gnielinski equation to the experimental convective heat transfer coefficient for SiC/water and MgO/ water nanofluids are shown in Fig. 15. Similar trends have been obtained as compared to Fig. 14 and deviations of modified Gnielinski equation from experimental results for each nanofluid are presented in Tables 5 and 6. Average deviations of modified Gnielinski correlation from experimental data for aqueous nanofluids containing SiC and MgO nanoparticle with the whole volume concentrations used in this study are ? 0.47 and - 0.14%, respectively. The experimental Nusselt numbers of SiC/water and MgO/water nanofluids and corresponding Hausen and

Experimental investigation on turbulent convection heat transfer of SiC/W and MgO/W nanofluids…

Gnielinski equations and their modified forms at the highest concentration used in this study, are compared and shown in Fig. 16. As can be seen in the figure, well coincidence between experimental data and modified Hausen and Gnielinski equations are observed, while Hausen and Gnielinski equations under predict experimental results. Similar results have also been observed for other volume concentrations of nanofluids used in this paper (data are not shown). Therefore, the proposed modified Hausen and Gnielinski correlations are appropriate models for estimating Nusselt numbers in the case of SiC/water and MgO/ water nanofluids at low concentrations.

Conclusions In this experimental study, thermophysical properties and heat transfer characteristics of SiC/water and MgO/water nanofluids with low concentrations (maximum 0.2, and 0.12%, respectively) have been measured in a tube under turbulent flow condition. Results of thermophysical properties of nanofluids have shown that raising particle concentration will lead to an increase in the density, viscosity, and thermal conductivity of nanofluids. Uncertainty analysis of heat transfer parameters used in this work have been conducted and ± 1.77, 2.46, 2.49, and 1.31% are the obtained uncertainty values for the heat flux, heat transfer coefficient, Nusselt number, and Reynolds number, respectively. From the comparison of experimental results of convection heat performance of nanofluids and relevant theoretical correlations, such as Gnielinski and Hausen, it has been concluded that both correlations could not predict experimental results. Experimental data were used to develop two new models for prediction of convection heat parameters of nanofluids according to Gnielinski and Hausen equations and were able to precisely predict experimental results with maximum deviations less than 1%. It has been shown that both nanofluids have larger heat transfer coefficients than pure water under the same condition. With increasing volume concentration of nanoparticle and Reynolds number, more improvements in heat transfer rate have been observed. Although thermal conductivity value of SiC nanoparticle is approximately three times than that of MgO nanoparticle, Nusselt number of SiC/water nanofluid was about 10% higher than that of MgO/water nanofluid, at the same volume fraction of nanoparticles. Measurements have shown that the highest heat transfer coefficient improvement of aqueous nanofluids containing SiC and MgO nanoparticle founded to be around 17.8 and 12.6%, respectively, in the entire range of volume concentrations of nanofluids and Reynolds numbers studied.

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