Cong Qi*,Maoni Liu,Guiqing Wang,Yuhang Pan,Lin Liang

School of Electrical and Power Engineering,China University of Mining and Technology,Xuzhou 221116,China

Keywords:Heat transfer Nanoparticles Turbulent flow Triangular tube Comprehensive evaluation index

A B S T R A C T Stable TiO2–water nanofluids are prepared by a two-step method,stabilities of nanofluids are investigated by precipitation method and transmittance method respectively,and thermal conductivities and viscosities are also measured.An experimental system for studying the heat transfer enhancement of nanofluids is established,and heat transfer and flow characteristics of TiO2–water nanofluids in heat exchanger systems with a triangular tube and circular tube are experimentally studied.The effects of nanoparticle mass fractions(ω=0.1 wt%–0.5 wt%)and Reynolds numbers(Re=800–10000)on the heat transfer and flow performances of nanofluids are analyzed.Fitting formulas for Nusselt number and resistance coefficient of nanofluids in a triangular tube are put forward based on the experimental data.The comprehensive performances of nanofluids in a triangular tube are investigated.It is found that nanofluids in a triangular tube can significantly improve the heat transfer performance at the cost of a small increase in resistance coefficient compared with that in a circular tube,especially the resistance coefficients are almost the same between different nanoparticle mass fractions at turbulent flow.It is also found that the comprehensive evaluation indexηdecreases with Reynolds number at laminar flow but a critical maximum value appears at turbulent flow.

1.Introduction

Due to the excellent heat transfer performance[1],nanofluids are applied in many fields to enhance the heat transfer.Examples of these fields are as follows:solar photothermal conversion[2–5],clean water preparation[6],electronic component heat transfer[7],and boiling heat transfer[8,9].

Convection is an important heat transfer model in a heat-exchanger system and it is widely studied by many researchers.Convection heat transfer includes natural convection heat transfer and forced convection heat transfer.For natural convection heat transfer,Hu et al.[10,11]investigated the natural convection of eutectic binary nitrate salt based Al2O3nanocomposites and TiO2–water nanofluids in a square enclosure respectively.It was found that heat transfer performance of salt–Al2O3nanocomposite nanofluids firstly increases and then decreases with nanoparticle concentration,but TiO2–water nanofluids show deterioration compared with water.Wang et al.[12]studied the natural convection of graphene nanofluid in a square enclosure.It was found that graphene nanofluids can enhance the heat transfer by 12%compared with base fluid.Qi et al.investigated the effects of nanoparticle size on the natural convection of Ag–Ga nanofluids[13],Al2O3–H2O and Al2O3–Ga nanofluids[14],and Cu–Ga nanofluids[15]based on the two-phase lattice Boltzmann method,and also studied the effects of rotation angle[16]and aspect ratio[17]on natural convection heat transfer of TiO2–H2O and Al2O3–H2O nanofluids in enclosures by experiment and Fluent software.It was found that small nanoparticle size,small rotation angle and small aspect ratio are advantageous to heat transfer enhancement.Sheikholeslami et al.[18,19]studied the natural convection of magnetic nanofluids in porous media and an enclosure with elliptical cylinders respectively.It was found that Nusselt number increases with nanoparticle concentration and Rayleigh number but decreases with Hartmann number.Umavathi et al.[20]numerically investigated the natural convection of nanofluids in a vertical rectangular duct.It was found that Darcy number,Grashof number and Brinkman number are all advantageous to heat transfer enhancement.Kaka?[21]reviewed the convection heat transfer enhancement of nanofluids in recent years,and introduced the preparation,thermal properties,and heat transfer performance of nanofluids.

Fig.1.SEM pictures of TiO2 nanoparticles at different magnification times,(a)×10000,(b)×20000.

Forced convection heat transfer is applied in some fields that need high heat flux instead of natural convection heat transfer[22–24],and heat transfer characteristics of nanofluids in a straight tube,a pressurized water reactor and a coiled agitated vessel equipped with propeller are investigated respectively.In order to enhance the heat transfer of a heat exchanger,some enhanced tubes are used instead of the smooth tube,and nanofluids are adopted instead of water and ethylene glycol.Researchers also studied the flow and heat transfer performances of enhanced tubes filled with nanofluids.Qi et al.experimentally investigated the thermo-hydraulic performances of a horizontal elliptical tube[25],a corrugated tube[26],and a spirally fluted tube[27] filled with TiO2–H2O nanofluids,also analyzed the effects of nanoparticle mass fraction and Reynolds number on the flow and heat transfer characteristics.It was found the horizontal elliptical tube,corrugated tube and spirally fluted tube all show a better heat transfer performance than the smooth tube,and Nusselt number increases with nanoparticle mass fraction and Reynolds number.Arani et al.[28]experimentally investigated the convection heat transfer of an annular tube filled with Cu–oil nanofluids,and discussed the effects of nanoparticle concentration and Reynolds number on the heat transfer of nanofluids.It was found that Nusselt number of Cu–oil nanofluids with mass fraction 0.72%can be enhanced by 10%.Naphon et al.[29–31]experimentally and numerically studied the effects of magnetic field and nanoparticle concentration on the heat transfer of a spirally coiled tube filled with TiO2–H2O nanofluids respectively.It was found that Nusselt number can be enhanced with the increasing magnetic field strength,and it was also found that magnetic field coupling with other three factors(pulsating flow,nanofluids,curved tube)can improve the heat transfer by 18.3%.Darzi et al.[32,33]experimentally and numerically studied the heat transfer of helically corrugated tubes filled with Al2O3–water nanofluids.It was found that nanofluids in the helically corrugated tube can enhance the heat transfer by a factor of 3.2–3.31.Darzi et al.[34]also investigated the heat transfer of helically corrugated tubes filled with SiO2–water nanofluids.It was found that high height and small pitch of corrugations are advantageous to heat transfer enhancement at the cost of little increase in pressure drop.

Above researchers have made a great contribution to the application of enhanced tubes and nanofluids in heat exchanger systems,however,the research on the heat transfer and flow characteristics of nanofluids in heat exchanger systems with a triangular tube is little and needs to be investigated further.Hence,the heat transfer and flow characteristics of TiO2–water nanofluids in a triangular tube and circular tube are experimentally studied.The main innovations of the paper are as follows:in addition to the common precipitation method adopted by other published references,precipitation method is put forward and used to analyze the stabilities of nanofluids;the comprehensive performances of nanofluids in a triangular tube are investigated,and an interesting conclusion is obtained that nanofluids in a triangular tube can significantly improve the heat transfer at the cost of a small increase in resistance coefficient.Another interesting conclusion is obtained that the comprehensive evaluation index η decreases with Reynolds number at laminar flow but a critical maximum value appears at turbulent flow.

2.Nanofluid Preparation and Stability

TiO2and deionized water are selected as the nanoparticle and base fluid in this paper.Scanning electron microscope(SEM)images of TiO2nanoparticles are shown in Fig.1.TiO2nanoparticles are provided by Nanjing Tansail Advanced Materials Co.,Ltd.,the particle size is about 10 nm,and the crystal form is anatase.

Due to the nano-scale,TiO2nanoparticles easily gather together,hence,in order to prepare stable nanofluids,some measures should be adopted in the two-step method preparation process which is presented in Fig.2.The mass fraction of dispersing agent TDL-ND1 is 6 wt%of the base fluid.The stirring time on each-step is about 30 min,the pH value is adjusted to 8 by NaOH solution,and the ultrasonic vibrating time is around 40 min.

Fig.2.Preparation process of nanofluids.

Fig.3.Precipitation method for studying the stability of nanofluids,(a)before standing,(b)after standing 3 days,and(c)after standing 7 days.

The stable TiO2–water nanofluids with three different nanoparticle mass fractions(0.1 wt%,0.3 wt%and 0.5 wt%)prepared in this paper are shown in Fig.3.Precipitation method and transmittance method are used to observe the stability of TiO2–water nanofluids.For the precipitation method in Fig.3,it is found that TiO2–water nanofluids still keep a good stability without obvious precipitate after standing 7 days,which explains that the stability of the TiO2–water nanofluids prepared in this paper is good.For the transmittance method in Fig.4,the stability of TiO2–water nanofluids at different pH values(pH=7,8,9,10)along with standing time is investigated.It is found that TiO2–water nanofluids have the lowest transmittance at pH=8,which means that nanoparticles are evenly distributed in water and reflect the most light.Otherwise,if nanofluids have a bad stability,they will have a high transmittance.Hence,nanofluids in this experiment are all prepared at pH=8 to ensure the good stability.

3.Physical Property Parameters

Fig.4.Transmittance method for studying the stability of nanofluids,(a)ω=0.1 wt%,(b)ω=0.3 wt%,and(c)ω=0.5 wt%.

Fig.5.Thermophysical parameters and of nanofluids,(a)thermal conductivities,(b)viscosities.

Physical property parameters,especially the thermal conductivity and viscosity,play an important role in the flow and heat transfer characteristics of nanofluids.Thermal conductivities and viscosities of TiO2–water nanofluids with three nanoparticle mass fractions(0.1 wt%,0.3 wt%and 0.5 wt%)are shown in Fig.5,and they are measured by a thermal conductivity measuring instrument(DRE-III)provided by Xiangtan Xiangyi Instrument Co.,LTD and a Kinexus Pro super rotational rheometer provided by Malvern Co.,LTD respectively.It can be found that the thermal conductivities of water measured in this paper have a good agreement with the results of reference[35],which explains that the accuracy of the thermal conductivity measuring instrument is reliable.Also,it can be found that the thermal conductivities increase with the temperature and nanoparticle mass fraction.For viscosities of TiO2–water nanofluids,it can be found that there are some changes at the initial stage which is because a shear force is suddenly added into the nanofluids at the initial stage,and then viscosities keep stable values when the flow field reaches a balance.Also,the viscosities increase with the nanoparticle mass fraction which is caused by the increasing drag force(Stokes force)between nanoparticles and base fluid.

4.Experimental

4.1.Experimental system

Schematic diagram of the experimental system is shown in Fig.6.The heat transfer performance and flow resistance of the triangular tube filled with TiO2–water nanofluids are investigated.For the heat transfer performance part,ten T-type thermocouples connected to a data acquisition instrument are used to obtain the surface temperature of the triangular tube,and two T-type thermocouples are used to measure the inlet and outlet temperatures of TiO2–water nanofluids in the triangular tube.For the flow resistance test part,a pressure sensor is used to record the pressure drop.The triangular tube is heated by a resistance wire connected to a DC-power and is cooled by a low temperature thermostat bath.Insulating layer is used to prevent the heat loss.The details of the triangular tube are presented in Fig.7.The whole length of the triangular tube is L=1200 mm,the cross section is an equilateral triangle and the length of each side is l=25 mm,the wall thickness is δ=1 mm,and the material is stainless steel.The middle 1000 mm length is used as the test section and each 100 mm length is retained at two ends respectively in order to avoid the entrance effect.

Fig.7.Details of the triangular tube.

Fig.6.Schematic diagram of the experimental system.

4.2.Data processing

The definition of the hydraulic diameter of the triangular tube is as follows:

Heating power of the DC-power is as follows:

The effective heating power is as follows:

The effective heating power is equal to the quantity of heat absorbed by nanofluids in the triangular tube,and it can be also written as follows:

Specific heat and density equations of nanofluids are given as follows respectively[36]:

Average temperature of nanofluids in the tube is calculated as follows:

Average temperature of outside wall of triangular tube is shown as follows:

Average temperature of inside wall of triangular tube is presented as follows:

Convective heat transfer coefficient is given as follows:

Nusselt number is defined as follows:

Reynolds number is defined as follows:

Frictional resistance coefficient of nanofluids is calculated as follows[37]:

Two types of comprehensive evaluation indexes are defined as follows respectively[37]:

4.3.Uncertainty analysis

Uncertainty analysis for the experiment in this paper has been done,the corresponding equations for heat transfer and flow performances are shown as follows respectively[38]:

where the accuracies of DC power supply and thermocouple are±5.0%and±0.1%,the accuracies of pressure transducer,length and flow meter are±0.5%,±0.1%and±1.06%.

The details of errors are shown in Table 1 based on Eqs.(16)and(17),and it can be found that the error of Nusselt number is about±5.0%and the resistance coefficient is approximately±1.18%,which can ensure the precision of the experimental system.

Table 1Errors of each part in the experiment

5.Results and Discussions

In order to verify the reliability of the experimental system,heat transfer and flow performances of water in a circular tube are investigated.Fig.8 shows the results comparison between this paper and other published references[36,39–41].It can be found from Fig.8(a-1)and(a-2)that the max Nusselt number errors are 3.5%and 2.8%at laminar and turbulent flows respectively.Also it can be found from Fig.8(b-1)and(b-2)that the max resistance coefficient errors are all 2.1%at laminar and turbulent flows.The results in this paper have a good agreement with the published references[36,39–41],which ensures the reliability of the experimental system.

Heat transfer and flow characteristics of TiO2–water nanofluids in the triangular tube and circular tube are investigated.Fig.9 shows the Nusselt number comparisons between the triangular tube and circular tube.It can be found that Nusselt number increases with the nanoparticle mass fraction,and nanofluids in the triangular tube and circular tube can enhance the heattransfer by 13.6%and 16.1%at best compared with water at the same conditions respectively.This is mainly due to the high thermal conductivity of nanoparticle.Also the Brownian motion of nanoparticles makes a contribution to the heat transfer enhancement.It can be also found that Nusselt number in the triangular tube is higher than that in the circular tube,and nanofluids in the triangular tube can increase the heat transfer by 54.7%–200.6%at laminar flow and 8.7%–142.0%at turbulent flow compared with that in the circular tube at the same conditions.This is because the distance between the wall surface and the center of the triangular tube is shorter than that of the circular tube,which causes a bigger velocity near the wall surface of the triangular tube and reduces the laminar boundary layer.It is also found that there is a much more heat transfer enhancement ratio at laminar flow than that at turbulent flow.This is because the structure of the tube plays a major role on the heat transfer enhancement at laminar flow,but the increasing turbulivity begins to play a certain role and reduces the influence of tube structure at turbulent flow.In order to compare the heat transfer performance between the triangular tube and other different enhanced tubes,Fig.10 compares the Nusselt number of the triangular tube with that of the elliptical tube,corrugated tube and spirally fluted tube.For laminar flow,it can be found that the heat transfer performance of the spirally fluted tube is the best,followed by the triangular tube,and the worst is the corrugated tube.This is because the spirally fluted tube causes the greatest disturbance at laminar flow.For turbulent flow(Re＜8000),the spirally fluted tube shows the best heat transfer performance,followed by the triangular tube and elliptical tube,and the corrugated tube shows the worst heat transfer performance.For turbulent flow(Re＞8000),the corrugated tube shows the bes the at transfer performance,followed by the elliptical tube and triangular tube,and the heat transfer performance of the elliptical tube is close to that of the triangular tube.From the above discussion,it can be found that the spirally fluted tube and triangular tube show better heat transfer performance than the other two enhanced tubes at a wide range of Reynolds numbers(Re＜8000).

Fig.8.Experimental verification,Nusselt number comparison:(a-1)laminar flow,(a-2)turbulent flow;resistance coefficient comparison:(b-1)laminar flow,(b-2)turbulent flow.

Fig.9.Nusselt number comparisons between triangular tube and circular tube,(a)laminar flow,(b)turbulent flow.

Fig.10.Nusselt number comparisons between triangular tube,elliptical tube,corrugated tube and spirally fluted tube,(a)laminar flow,(b)turbulent flow.

In order to study the relationship between Nusselt number and Reynolds number,Fig.11 gives the fitting formulas of Nusselt number for nanofluids in the triangular tube at laminar flow and turbulent flow,and the fitting formulas are given in formulas(18)and(19).The constants in formulas(18)and(19)are presented in Tables 2 and 3.The relationship between Nusselt number and Reynolds number is linear at laminar flow and quadratic polynomial at turbulent flow.

Fig.11.Fitting formulas of Nusselt number for nanofluids in triangular tube,(a)laminar flow,(b)turbulent flow.

Table 2Constants in formula(18)at laminar flow

Table 3Constants in formula(19)at turbulent flow

Relationships between Nusselt number and Reynolds number are as follows:

Fig.12.Resistance coefficient comparisons between triangular tube and circular tube,(a)laminar flow,(b)turbulent flow.

In addition to heat transfer performances,the flow characteristics of nanofluids in the triangular tube and circular tube are also studied.Fig.12 presents the resistance coefficient comparisons between the triangular tube and circular tube.It can be found that the value of ln(100f)increases a little with the nanoparticle mass fraction,and nanofluids in the triangular tube and circular tube can enhance the value of ln(100f)by 3.9%and 6.7%at best compared with water at the same conditions respectively.The contribution of nanoparticle mass fraction to the increase of resistance coefficient is much smaller than that of Reynolds number.It can be also found that nanofluids in the triangular tube increase the value of ln(100f)by 36.0%–113.7%at laminar flow and 15.6%–34.8%at turbulent flow compared with nanofluids in the circular tube at the same conditions.The reason is similar to the heat transfer in Fig.9.The structure of the tube plays a major role on the resistance coefficient at laminar flow,but the increasing turbulivity begins to play a certain role and reduces the influence of tube structure at turbulent flow.

Fig.13.Pressure drop comparisons between triangular tube and circular tube,(a)laminar flow,(b)turbulent flow.

Fig.14.Fitting formulas of resistance coefficient for nanofluids in triangular tube,(a)laminar flow,(b)turbulent flow.

Table 4Constants in formulas(20)and(21)

Fig.13 shows the pressure drop comparisons between the triangular tube and circular tube.It can be found that the pressure drop increases little with the nanoparticle mass fraction,and the pressure drop of the triangular tube is higher than the circular tube.This phenomenon is consistent with that of resistance coefficient.

Fitting formulas of resistance coefficient for nanofluids in the triangular tube are given in Fig.14.The fitting formulas are given in formulas(20)and(21).The constants in formulas(20)and(21)are presented in Table 4.It can be found that the relationship between ln(100f)and Reynolds number is linear at laminar flow and quadratic polynomial at turbulent flow.Another interesting result shows that a samefitting formula is suited for the nanofluids with different nanoparticle mass fractions because of the small differences in resistance coefficient between them.

Relationships between ln(100f)and Reynolds number are as follows:

Nusselt number and resistance coefficient all increase with the Reynolds number,in order to comprehensively analyze the effects of Reynolds number on the thermo-hydraulic performances of nanofluids,Fig.15 presents the comprehensive performance η of nanofluids in the triangular tube based on formula(14).It can be found that comprehensive evaluation index η decreases with Reynolds number at laminar flow,which explains that the role of Reynolds number on heat transfer enhancement gradually declines while the resistance gradually rises.However,there are critical Reynolds numbers for the highest comprehensive evaluation index η of nanofluids,and they are 7000,6000,and 4000 for nanofluids with 0.1 wt%,0.3 wt%and 0.5 wt%respectively,which explains that the role of heat transfer enhancement is large when the Reynolds number is smaller than the critical value,while the role of resistance coefficient becomes big when the Reynolds number is larger than the critical value.It is also found that critical Reynolds numbers for the highest comprehensive evaluation index η under turbulent flow decrease with the increasing nanoparticle mass fraction.Fig.16 presents the comprehensive performance ξ of nanofluids in the triangular tube,circular tube,elliptical tube,corrugated tube and spirally fluted tube based on formula(15).It can be found that comprehensive performance ξ of nanofluids in the triangular tube is better than that in the circular tube,elliptical tube and corrugated tube when the Reynolds number is less than 10000,9000 and 7000 respectively.It can be also founded that comprehensive performance ξ of nanofluids in the spirally fluted tube is bigger than that in the triangular tube.From the above discussion,we can conclude that the comprehensive performance ξ of the spirally fluted tube and triangular tube is better than the other two enhanced tubes at a wide range of Reynolds numbers.

Fig.15.Comprehensive performance η of nanofluids in triangular tube.

6.Conclusions

In this paper,the stable TiO2–water nanofluids are prepared,stabilities are analyzed,physical property parameters are measured,and heat transfer and flow characteristics in heat exchanger systems with a triangular tube and circular tube are experimentally studied,some main results are obtained as follows:

(1)Nano fluids in the triangular tube can significantly improve the heat transfer at the cost of a small increase in resistance coefficient.Nusselt number can be increased by 200.6%at laminar flow and 142.0%at turbulent flow at best.The value of ln(100f)can be increased by 113.7%at laminar flow and 34.8%at turbulent flow at best.

(2)The relationship between Nusselt number and Reynolds number is linear at laminar flow and quadratic polynomial at turbulent lf ow.Meanwhile,the relationship between resistance coefficient and Reynolds number also meets the change rule.A same fitting formula is suited for the nanofluids with different nanoparticle mass fractions.

(3)Comprehensive evaluation index η decreases with Reynolds number at laminar flow and there are critical Reynolds numbers for the highest comprehensive evaluation index η of nanofluids at turbulent flow.

(4)Critical Reynolds numbers for the highest comprehensive evaluation index η under turbulent flow decrease with increasing nanoparticle mass fraction.

Nomenclature

Accross-sectional area of triangular tube,m2

cpspecific heat,J·kg-1·K-1

cpbfspecific heat of base fluid,J·kg-1·K-1

cppspecific heat of nanoparticle,J·kg-1·K-1

dehydraulic diameter of triangular tube,m

f frictional resistance coefficient of nanofluids

fbffrictional resistance coefficient of base fluid

h convective heat transfer coefficient,W·m-2·K-1

I electric current,A

L length of triangular tube,m

Nu Nusselt number of nanofluids

Fig.16.Comprehensive performance ξ comparisons of nanofluids between the triangular tube and other enhanced tubes,(a)circular tube,(b)elliptical tube,(c)corrugated tube,and(d)spirally fluted tube.

NubfNusselt number of base fluid

P wetted perimeter of triangular tube,m

ΔP/Δl pressure drop per unit length,Pa·m-1

Qfeffective heating power,W

Qlossheat loss,W

Q0heating power,W

qmmass flow rate,kg·s-1

Re Reynolds number

riinternal radius,m

roouter radius,m

Toutoutlet temperature,K

Tfaverage temperature of nanofluids,K

Tininlet temperature,K

Twiaverage temperature of inside wall of triangular tube,K

Twoaverage temperature of outside wall of triangular tube,K

U voltage,V

u flow velocity of nanofluids,m·s-1

η,ξ two types of comprehensive evaluation indexes

λ thermal conductivity of wall of triangular tube,W·m-1·K-1

λfthermal conductivity of nanofluids,W·m-1·K-1

μfdynamic viscosity of nanofluids,Pa·s

ρ density of nanofluid,kg·m-3

ρbfdensity of base fluid,kg·m-3

ρpdensity of nanoparticle,kg·m-3

φ nanoparticle volume fraction

ω nanoparticle mass fraction

Subscripts

bf base fluid

f nanofluids

i internal

o outer

p nanoparticle

wi inside wall

wo outside wall