water nanofluid heat transfer in

An experimental comparison of SiO2/ water nanofluid heat transfer in square and circular cross-sectional channels F. Pourfayaz, N. Sanjarian, A. Kasaeian, F. Razi Astaraei, M. Sameti & Sh. Nasirivatan Journal of Thermal Analysis and Calorimetry An International Forum for Thermal Studies ISSN 1388-6150 J Therm Anal Calorim DOI 10.1007/s10973-017-6500-4

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Author's personal copy J Therm Anal Calorim DOI 10.1007/s10973-017-6500-4

An experimental comparison of SiO2/water nanofluid heat transfer in square and circular cross-sectional channels F. Pourfayaz1 • N. Sanjarian1 • A. Kasaeian1 • F. Razi Astaraei1 M. Sameti3 • Sh. Nasirivatan2

•

Received: 17 January 2017 / Accepted: 22 May 2017 Akade´miai Kiado´, Budapest, Hungary 2017

Abstract In this paper, with the aim of enhancing the thermal conductivity of the fluid, a nanofluid is prepared based on SiO2. A series of experimental tests were carried out for both laminar and forced convection regimes in a horizontal tube with two different geometric shapes (circular and square cross section) subjected to constant wall heat flux (4735 W m-2). A comparative study has been done to investigate the effect of the geometry on the convective heat transfer. Moreover, the effect of the volume concentration on the behavior of the nanofluid and the base fluid was evaluated by comparing various volume concentrations (0.05, 0.07 and 0.2%). The experiments were done under two different conditions: constant Reynolds number and constant mass flow rate. It was found that the circular-shaped channel could be better for heat transfer purposes at the same flow rate, while the squareshaped channel has a higher heat transfer coefficient at the same Reynolds number. The slope of the lines for the square cross section is more than that for circular cross sections which result in a steeper increase in average heat transfer coefficient versus Reynolds number in the square-shaped channel. The increase of the Reynolds number may decrease the dead zones in the square channel that causes the double enhancement of the average heat transfer coefficient.

& F. Pourfayaz [email protected] 1

Department of Renewable Energies and Environment, Faculty of New Sciences and Technologies, University of Tehran, P.O. Box 14395-1561, Tehran, Iran

2

Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

3

Department of Building, Civil, and Environmental Engineering, Concordia University, Montreal, Quebec, Canada

Keywords Nanofluid Convection Square Circular SiO2/water List of symbols k Conductivity u Volume concentration l Viscosity q Density Cp Specific heat Qloss Heat loss V Supply voltage R Wire resistance Tout Outlet temperature Tin Inlet temperature m_ Mass flow rate P Cross-sectional perimeter L Pipe length Re Reynolds number Nu Nusselt number Pr Prandtl number D Pipe diameter x Axial distance h Convective heat transfer coefficient

Introduction According to the importance of energy in the world, so far, many attempts have been made to increase energy efficiency [1]. One way is the use of fluids with higher heat transfer coefficient, by the addition of metal, nonmetal and metal oxide particles with higher thermal conductivity into conventional fluids. Development of fluids thermal properties leads to more energy efficient, smaller size, lighter

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weight and lower operational costs for thermal systems like heat exchangers. The particles added to the base fluid should be in nanometer size, because the larger particles can cause problems such as erosion, sedimentation, clogging and higher fluid resistance. Masuda et al. [2] and Choi et al. [3] were the first raised the idea of using nanofluids. Bergman [4] investigated the effects of increasing thermal conductivity and reducing the specific heat of the nanofluid relative to the base fluid and quantified heat transfer enhancement. They show that use of nanofluid instead of pure liquids can either enhance or degrade thermal performance. Ferrouillat et al. [5] investigated experimentally convective heat transfer of SiO2–water nanofluid in the horizontal tube test section in cooling and/or heating conditions. They showed that the heat transfer coefficient compared to the pure water increased from 10 to 60%. Moreover, the viscosity of nanofluid was increased by adding nanoparticles, so more pumping power was needed. Rea et al. [6] studied experimentally laminar convective heat transfer and viscous pressure loss for alumina–water and zirconia–water nanofluids in the vertical heated tube. The heat transfer coefficients deduced for the entrance region and in the fully developed region. The zirconia nanofluid heat transfer coefficient enhancement was much lower in comparison with alumina–water. EbrahimniaBajestan et al. [7] studied numerically the heat transfer performance of Al2O3, CuO, carbon nanotube (CNT) and titanate nanotube (TNT) nanofluids in a laminar flow regime. The effects of the particle volume concentrations, particle diameter, particles Brownian motions, Reynolds number and type of the nanoparticles were determined. The results showed that the nanoparticles diameter decreases the heat transfer coefficient, while the others have opposite effect on the heat transfer coefficient. Peyghambarzadeh et al. [8] worked on convection heat transfer in a car radiator with different amounts of Al2O3 nanoparticle. The results demonstrate that nanofluids can enhance heat transfer of about 40% compared to the base fluids in the best condition. ¨ zerinç et al. [9] checked some classical correlations of O forced convection heat transfer for pure fluids and nanofluids by the use of nanofluid thermophysical properties. The single-phase model was considered as a thermal dispersion model. The results show that the single-phase assumption with temperature-dependent thermal conductivity and thermal dispersion is an accurate way for analysis of the convective heat transfer enhancement of the nanofluids. Lotfi et al. [10] studied different heat transfer models and demonstrated that the single-phase model and the two-phase Eulerian model underestimate the Nusselt number. Nassan et al. [11] compared the heat transfer

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characteristics of Al2O3–water and CuO–water nanofluids with uniform heat flux. The results indicate that both nanofluids have considerable heat transfer enhancement, but the CuO/water shows better heat transfer enhancement compared with the Al2O3/water. Escher et al. [12] investigated the characteristics of convective heat transfer for concentrated SiO2/water nanofluid by performing experimental and theoretical study of their applicability in cooling electronics. The authors obtained that increasing the effective thermal mass through increasing the fluid heat capacity or density, instead of the thermal conductivity, can lead to sink performance. Thermal conductivities and specific heat capacities of nanoparticles of Al2O3 dispersed in water and ethylene glycol as a function of the particle volume fraction and at temperatures between 298 and 338 K were measured by Barbe´s et al. [13]. In a study by Minea [14], essential aspects of the turbulent-flow convective heat transfer of nanofluids are compared in detail based on few figures of merits relevant to their applications. Moghadassi et al. [15] presented a novel model for the prediction of the effective thermal conductivity of nanofluids based on dimensionless groups. Hemmat Esfe et al. [16] presented that an experimental study was performed to measure the thermal conductivity of aqueous suspensions of Al2O3 nanoparticles with the diameter of 5 nm using the transient hot-wire approach. Channels with non-circular geometry are usually excluded from many applications. For one reason, this kind of ducts has very low rate of heat transfer. On the other hand, the pressure drop in non-circular cross sections is much less than that compared to circular cross sections. It should be stressed that the friction factors in rectangular and circular tubes equal to 56.92/Re and 64/Re, respectively. Therefore, heat transfer enhancement of the channels with non-circular ducts can result in its wide applications in different industries. Furthermore, they have other advantages such as high compaction in comparison with other kind of channels, high mechanical resistivity, easy forming using thin metal, and low-pressure drop, triangular and square ducts which make them beneficial to be utilized in compact heat exchangers, combustion engines, boilers, nuclear reactor and energy recovery equipment, furnaces, rockets, medical and electronics industries. Due to the importance of low-pressure drop in these applications, heat transfer enhancement can open up great opportunists [17]. Considering the literature review about nanofluids, the aim of this study is to investigate and compare the heat transfer enhancement of SiO2/water nanofluid through the square and circular cross-sectional ducts in the laminar flow regimes under constant heat flux boundary condition for the wall.

Author's personal copy An experimental comparison of SiO2/water nanofluid heat transfer in square and circular…

Preparation of nanofluid SiO2 nanoparticles were provided by Fadak Group (Iran). Nanofluids with different volume concentrations were produced by adding specific amounts of the nanoparticles to the distilled water. In this method, no surfactant was used in order to avoid influencing thermophysical properties of nanofluids. However, the stability of nanofluids can be achieved by using a variety of methods. In this study, it is accomplished by manipulating the pH of the nanofluid. At first, dry nanoparticles with a diameter between about 10 and 20 nm were added to distilled water and the pH value of nanofluid was adjusted to 10.5. In order to produce a homogeneous suspension, the nanoparticles were dispersed using sonication for about 30 min. A Zeiss EM 10C transmission electron microscope (TEM) was used to obtain the TEM image of the silica nanoparticles. Figure 1 shows the TEM micrograph of the SiO2 nanoparticles. In this figure, agglomerations of the nanoparticles are observable. The diameter of these nanoparticles is less than 20 nm. These agglomerated nanoparticles must be dispersed in the base fluid (here water).

Experimental The schematics diagram for the experimental setup is illustrated in Fig. 2. The setup is made up of the following components: • • • • •

Two circulating pumps Three reservoirs in different sizes Reynolds valve Heat transfer channel with 1 m length Fluid flowmeter

• • • • •

Heat exchanger in order to cool the fluid Dimer to provide constant heat flux Eleven sensors along the channel Data logger Two pipes at the beginning and end of the channel to measure pressure drop

At the beginning, the first designated reservoir is being filled with fluid. Then the circulating pump sends the fluid from the first reservoir to the second reservoir. When the second reservoir is filled, Reynolds valve is opened and the fluid flows inside the horizontal channel. After passing a short distance, the fluid enters the heat transfer channel and is exposed to the constant wall heat flux. The temperature on the wall is measured by nine sensors among eleven sensors, while the other two sensors measure the inlet and outlet temperature. At the end, the fluid enters the cooling heat exchanger to keep the inlet fluid temperature constant. Figure 1c illustrates the heat transfer channel. The flow loop consists of a test section, a fluid reservoir, pump, flow measuring apparatus, calming section, cooling unit, riser section and thermocouples. The test section itself is either a copper tube with inner diameter of about 8 mm, the thickness of 1 mm and length of 1000 mm or a square cross-sectional copper duct with hydraulic diameter, thickness and length of about 8, 1 and 1000 mm, respectively. The working fluid is pumped with maximum flow rate of 5800 L h-1 through a close loop using a MULTI 5800 SICCE pump from the first reservoir. The calming section is utilized to eliminate the entrance effect and to attain fully developed laminar flow. The test section completely covered with glass wool to minimize the heat loss. Two thermocouples were used to measure the inlet and outlet temperatures of fluid and nine SMT-160 thermocouples are placed along the test section to measure wall temperatures. The flow rate is determined by measuring the time in which the graduated cylinder is filled with the fluid. In order to measure the pressure drop of fluid flow along the test section, two manometers were used. In order to decrease fluid temperature, a heat exchanger is installed to cool fluid flow and keep the initial temperature of the fluid constant. The system is stabilized at the desired temperature level after a specific elapsed time of 5–10 min.

Physical properties of nanofluids

Fig. 1 TEM micrograph of the SiO2 nanoparticles

Sonication was used to disperse and homogenize the nanoparticles into the base fluid. Therefore, classical equations can be used to predict the thermophysical properties of nanofluids at different volume concentrations. In

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Author's personal copy F. Pourfayaz et al. (a)

Data acquisition Reservoir Manometer Thermocouples

Manometer

Tin

T1 T2 T3 T4 T5 T6 T7 T8 T9

AC power

Insulating

Computer

Tout

Flow meter

Copper tube Heater

Cooling unit Reservoir

Pump Drain valve Pump

Reservoir

(b)

(c)

Fig. 2 Schematics diagram for the nanofluid setup (a), experimental setup (b) and heat transfer channel (c)

order to achieve high accuracy, properties such as density, thermal conductivity and viscosity of base fluid were considered as temperature dependent and the average temperature was calculated by averaging the temperatures in inlet and outlet [18]. In this paper, the following equations are used for SiO2/water nanofluids [18]:

Table 1. Table 2 illustrates the amount of nanoparticles used to prepare the nanofluid.

ðqCp Þnf ¼ ð1 uÞðqCp Þbf þ uðqCp Þp

ð1Þ

qnf ¼ ð1 uÞqbf þ uqp

ð2Þ

In these experiments, the fluid enters the test section, while a constant heat flux is applied on the wall of the tube/duct. The heat transfer rate calculates by:

lnf ¼ ð1 þ 2:5uÞlbf

ð3Þ

In the correlations (1) to (3), nf, bf and p subscripts refer to nanofluid, base fluid and nanoparticle, respectively. kp þ 2kbf þ 2ðkp kbf Þu knf ¼ kbf ð4Þ kp þ 2kbf ðkp kbf Þu In Eqs. (1)–(4), u indicates the volumetric concentration of nanoparticles. The thermophysical properties of SiO2 nanoparticles at room temperatures are specified in

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Data reduction

Q1 ¼

V2 Qloss R

ð5Þ

In Eq. (5), V is the power supply voltage, R is the wire resistance, and Qloss is the heat loss which is equal to 3–6%. On the other hand, the heat flux can determine from Eq. (6) that Tout and Tin are the outlet and inlet temperatures of the fluid that can be measured directly from experiments. _ p ðTout Tin Þ Q2 ¼ mC

ð6Þ

Author's personal copy An experimental comparison of SiO2/water nanofluid heat transfer in square and circular… Table 1 Some thermophysical characteristics of SiO2 Density/kg m-3

Specific heat/J kg-1 K-1

Thermal conductivity/W m-1 K-1

SiO2

2400

691

8.4

Table 2 Amount of components for nanofluid preparation Nanoparticle/g

Water/L

Nanofluid volume concentration/%

0.25

5

0.05

0.035

5

0.07

2

5

0.2

where m_ and Cp are the mass flow rate and specific heat, respectively. The average heat transfer and total heat flux are obtained by Eqs. (7) and (8), respectively: Q ¼ 0:5ðQ1 þ Q2 Þ

ð7Þ

Q q ¼ PL

ð8Þ

00

where P is the cross-sectional perimeter and L is the channel length. The fluid temperature at any point of the channel can be calculated by the following equation, P and A are the perimeter and area of the cross section, respectively and x is axial distance. ðTf Þx ¼ Tin þ

q00 Px _ p mC

ð9Þ

The fluid heat transfer coefficient and Nusselt number are defined as: hð x Þ ¼

q00 ð T w Tf Þ x

Nuð xÞ ¼

hð xÞd k

ð10Þ ð11Þ

Heat transfer coefficient (h)/W m–2 K–1

Nanoparticle

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Experiment Shah equation

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Fig. 3 Validation of the convective heat transfer coefficient for pure water

Which is valid for RePr Dx 33:3 and for RePr Dx \33:3, Eq. (13) can be used: D Nu ¼ 4:364 þ 0:0722 RePr ð13Þ x The comparison is made for the laminar flow with Reynolds number of 1010.3 and constant heat flux of 9000 W m-2 which is illustrated in Fig. 3. It is clear that there is good agreement between experimental results and Shah equation prediction which confirms the reliability of the results. Heat transfer experiments were carried out on the pure water and three different volume fraction for nanofluid (0.05, 0.07 and 0.2%). Moreover, the experiments were performed on the heat transfer channels with circular and square cross sections. In each experiment, a constant heat flux in the range of 4000–6000 W m-2 was applied on the wall.

Results and discussion

Local heat transfer coefficient

To check the accuracy of the experiment results, the experiments were conducted initially on pure water. Then the convective heat transfer coefficient obtained from experimental results was compared with Shah Correlation as [19]: 1 D 3 Nu ¼ 1:953 RePr ð12Þ x

The curves in the section compare the convective heat transfer coefficients of nanofluids with different volume concentrations in the square and circular cross-sectional channels. The hydraulic diameter is the same for both the channels. Figure 4 compares the heat transfer coefficient for water in the channels with square and circular cross sections at the same Reynolds number for pure water.

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Fig. 4 Comparison of local heat transfer coefficients at the same Re number (pure water)

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1000 800 Circular Square

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Fig. 5 Comparison of local heat transfer coefficients at the same flow rate (pure water)

this case, the mass rate of flow equals to 0.0026 kg s-1. As seen in this figure, the heat transfer coefficients in the circular cross-sectional channel are higher as compared with these in the square cross-sectional channel. Figure 8 shows the heat transfer coefficient for nanofluids with 0.07% volume concentration at the same Re number. The Reynolds number equals to 621 for both the channels. As observed, the heat transfer coefficients change in ranges of 838–111 and 755–83 W m-2 K-1 in the square and circular cross-sectional channel, respectively. In all points, the convective heat transfer coefficients in the square channel are higher than these in the circular channel. Figure 9 illustrates the results for nanofluid with 0.07% volume concentration at the same mass flow rate. The mass flow rate equals to 0.0034 kg s-1 for both the channels. Ranges of the heat transfer coefficients changes are 998–164 and 837–112 W m-2 K-1 for the circular and square cross-sectional channels, respectively. Figure 10 depicts the local heat transfer coefficients for nanofluids with 0.2% volume concentration at the same Reynolds number of 700. As seen, the heat transfer Heat transfer coefficient (h)/W m–2 K–1


Reynolds number and the heat flux are taken to be 750 and 4735 W m-2, respectively. According to this curve, the heat transfer coefficient in the channel with a square cross section is better than the channel with a circular one. At the same Reynolds number and hydraulic diameter, the heat transfer area for the square cross-sectional channel is higher than that for the circular cross-sectional channel. Therefore, the heat transfer in the channel with the square cross section is more efficient than that in the channel with the circular cross section, resulting in higher convective heat transfer coefficients for the square cross-sectional channel. Figure 5 compares the local heat transfer coefficient for pure water and for two cross sections assuming the constant flow rate to be 0.0026 kg s-1. In this case, the fluid mass flow rate is the same for both the channels, but the Reynolds numbers are different in a way that it is higher for the channel with a circular cross section that the square one. The reason for this is that the two channels have the same hydraulic diameters with two different cross-sectional areas. The channel cross section for the square is more than the circle at the same hydraulic diameter. Therefore, at the same flow rate for both the channels, the flow velocity in the circular-shaped channel is more than the square-shaped channel. As a result, at the same flow rate through the channels, the Reynolds number of circleshaped channel is more than the square-shaped one which results in a higher heat transfer coefficient. Figures 6 and 7 make a comparison between the heat transfer coefficients for the two channels with two geometries in which the nanofluid volume concentration is 0.05%. In this case, the Reynolds number equals to 740. In Fig. 6, two channels have the same constant Reynolds number. As observed in this figure, the heat transfer coefficients in the channel with the square cross section are higher than these in the channel with the circular cross section. In Fig. 7, the mass flow rate is kept constant. In


F. Pourfayaz et al.

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Fig. 6 Comparison of local heat transfer coefficients at the same Re number (u ¼ 0:05%)

Author's personal copy 1000 800 Circular Square

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An experimental comparison of SiO2/water nanofluid heat transfer in square and circular…

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Fig. 9 Comparison of local heat transfer coefficients at the same mass flow rate (u ¼ 0:07%) Heat transfer coefficient (h)/W m–2 K–1


Fig. 7 Comparison of local heat transfer coefficients at the same mass flow rate (u ¼ 0:05%)

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coefficients in the square channel, which change between 1065 and 143 W m-2 K-1, are higher than these in the circular channel, which change in range 974–137 W m-2 K-1. Figure 11 illustrates the results for the nanofluids with 0.2% volume concentration at a same mass flow rate of 0.0034 kg s-1. The changes of the heat transfer coefficients are in ranges of 1025–143 and 856–80 W m-2 K-1 for the channel with the circular cross section and the channel with the square cross-sectional channel, respectively. Generally, in all the curves plotted for the same Reynolds number, the fluid heat transfer coefficient for the square-shaped channel is higher than the circular one and at the same flow rate through the channel, the coefficient of heat transfer for the circular cross section is more than the square one. Commonly, the formation of dead zones due to sharp edges of the square channels can reduce the heat transfer rate. However, for the fluid flow in the channels, at the same Reynolds number and the hydraulic diameter, the perimeter of the square-shaped channel is more than that of

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Fig. 10 Comparison of local heat transfer coefficients at the same Re number (u ¼ 0:2%) Heat transfer coefficient (h)/W m–2 K–1

Fig. 8 Comparison of local heat transfer coefficients at the same Re number (u ¼ 0:07%)

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Fig. 11 Comparison of local heat transfer coefficients at the same mass flow rate (u ¼ 0:2%)

the circular-shaped channel; therefore, the heat transfer rate between the wall and the fluid increases and the fluid heat transfer coefficient for square cross section is higher than the circular one. But at the same mass rate and the hydraulic diameter, due to the smaller cross-sectional area

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Fig. 12 Comparison of average heat transfer coefficients at the various Re numbers (pure water)

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In this section, the average heat transfer coefficients are illustrated in Figs. 12–15 based on the Reynolds number for pure water and various concentrations of nanoparticles. In each of the experiments, the average heat transfer coefficients are obtained in several test conditions for square and circular cross sections. As shown in both channels, the average heat transfer coefficient increased with increasing in Reynolds number. Two straight lines were used as the interpolating functions to obtain the slopes. As the charts show, the slope of the lines for the square cross section is more than that for circular cross sections which result in a steeper increase in average heat transfer coefficient versus Reynolds number in the squareshaped channel. It seems that the increase of the Reynolds number leads to reduce the dead zones in the square channel, resulting in the double enhancement of the average heat transfer coefficient [20, 21]. Tables 3 and 4 summarize the comparative heat transfer coefficients for square-shaped channel and the circular one at constant mass flow rates and Reynolds numbers, respectively. The constant wall heat flux is 4735 W m-2 applied in these experiments. All the above figures indicate that heat transfer coefficient increases with increasing Reynolds number and concentration of nanoparticles. It is deduced from the diagrams that the convective heat transfer coefficient of nanofluids is better than

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Fig. 13 Comparison of average heat transfer coefficients at the various Re numbers (u ¼ 0:05%)


Average heat transfer coefficient

pure fluid. Due to the presence of nanoparticles in the base fluid and collisions between nanoparticles and wall of the channel, the higher energy exchange rate occurs between

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flow velocity in the circle channel is higher as compared to that in the square channel. Therefore, the heat transfer coefficient is greater. Consequently, at the same hydraulic diameter, it is recommended to use the square as the cross section for the same Reynolds number and use circular cross section at the same mass flow rate to enhance the heat transfer mechanism.

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Author's personal copy An experimental comparison of SiO2/water nanofluid heat transfer in square and circular… Table 3 Comparative heat transfer coefficients at constant mass flow rates Volume concentration/% _ m=kg s1 hcir hsq =hsq /% 0.0026

0 (pure water)

0.0026

0.05

0.0034

0.07

0.0032

0.2

12.97 5 6.34 10.2

Table 4 Comparative heat transfer coefficients at constant Reynolds numbers Re Volume concentration/% hsq hcir =hcir /% 750

0 (pure water)

35.45

740

0.05

28.34

630

0.07

25.3

700

0.2

29.13

nanofluids and walls. On the other hand, nanoparticles interact with themselves more effectively to achieve higher heat transfer rate in nanofluids compared with the pure fluid [22–25]. There are several reasons for better heat transfer of nanofluids compared to pure fluid [26]. The higher thermal conductivity of nanofluids due to the presence of nanoparticles with higher thermal conductivity with respect to water improves the heat transfer characteristics of the fluid. Thermal dispersion is the mechanism of heat transfer in the nanofluid, sliding velocity and local turbulence inside nanofluid suspension, increases wall shear stress and reduces the boundary layer thickness which diminishes thermal resistance near the wall of the channel. So heat transfer rate improves between nanofluid and channel [23, 27]. Brownian motion and migration of particles make temperature transverse gradient along the cross section and flatten temperature profile that causes increasing in heat transfer coefficient. In addition, the particles collision with each other and with the walls of the channel is the other reason of higher heat transfer of nanofluids. Since the possibility of collision increases in higher concentration and velocity, it justifies the increasing heat transfer coefficient with increasing Reynolds number and nanoparticle volume concentration [28, 29]. According to the results of the experiments in the same mass flow rates, circular channels show a better heat transfer. Because of sharp edges of square channels, dead zones are formed which prevent proper heat transfer between the fluid and the channel.

Conclusions Experimental investigation of convective heat transfer for SiO2/water nanofluid performed through circular and square cross sections with the same hydraulic diameter.

Constant heat flux boundary condition and low volume concentrations of nanofluids (0.05, 0.07 and 0.2%) are the governing conditions of the experiment. In each of the experiments, the average heat transfer coefficients are obtained in several test conditions for square and circular cross sections. The greatest increase in heat transfer corresponds to a volume concentration of 0.2. In all the curves plotted for the same Reynolds number, the fluid heat transfer coefficient for the square-shaped channel is higher than the circular one and at the same flow rate through the channel, the coefficient of heat transfer for the circular cross section is more than the square one. At the same flow rate through the channels, the Reynolds number of circleshaped channel is more than the square-shaped one which results in a higher heat transfer coefficient. The increase of the Reynolds number may decrease the dead zones in the square channel that causes the double enhancement of the average heat transfer coefficient. The average heat transfer coefficient increased with increasing in Reynolds number. Two straight lines were used as the interpolating functions to obtain the slopes. Generally, the formation of dead zones due to sharp edges of the square channels can reduce the heat transfer rate. However, for the fluid flow in the channels, at the same Reynolds number and the hydraulic diameter, the perimeter of the square-shaped channel is more than that of the circular-shaped channel; therefore, the heat transfer rate between the wall and the fluid increases and the fluid heat transfer coefficient for square cross section is higher than the circular one.

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