Chuanshuai Dong,Lin Lu,Tao Wen,Shaojie Zhang,

1 Key Laboratory of Enhanced Heat Transfer and Energy Conservation of Education Ministry,School of Chemistry and Chemical Engineering,South China University of Technology,Guangzhou 510000,China

2 Department of Building Services Engineering,The Hong Kong Polytechnic University,11 Yuk Choi Road,Hung Hom,Kowloon,Hong Kong,China

3 Department of Chemical Engineering,Imperial College London,London,United Kingdom

Keywords:Heat transfer enhancement Nanoparticles Friction factor Self-rotating twist tapes Thermal performance factor

ABSTRACT In view of the practical importance of the heat transfer devices in various thermal engineering fields including chemical and nuclear engineering,this study aims at developing an effective method of heat transfer enhancement by using self-rotating twisted tapes (SRTTs) and Al2O3 nanoparticles.The effect of the self-rotating twisted tapes and Al2O3 nanoparticles on the thermal performance was comprehensively investigated in a circular pipe.The experimental results indicated the heat transfer rate was effectively improved by SRTTs in comparison of plain tube.In addition,the heat transfer multiplier with SRTTs decreased from 1.38 to 1.08 with the Reynolds number increasing from 19,322 to 64,407,while the friction factor multiplier decreased from 1.61 to 1.32.Besides,the results indicated that the employment of Al2O3 nanoparticles and SRTTs demonstrated superior thermal performance to the single SRTTs.As Reynolds number increases from 19,322 to 64,407,the heat transfer multiplier decreased from 2.08 to 1.18 in the mass concentration of 3.0% and from 1.38 to 1.08 in mass concentration of 0.0%.Finally,the new heat transfer and friction factor correlations considering the combined effect of Al2O3 nanoparticle and SRTTs were developed within 10% deviation of experimental values.

1.Introduction

In the recent decades,energy issues have attracted many attentions in the world.Heat transfer devices play a significant role in energy conversion efficiently for energy saving.Since heat exchangers are convenient to be maintained,they are widely used in many engineering applications,such as chemical columns,nuclear reactors and air-conditioning systems,etc.[1–4].Heat transfer coefficient is the key standard to evaluate and optimize heat transfer performance.To improve the heat transfer coefficient,several enhancement methods including the optimization of configuration and addition of nano-fluids,have been proposed [5,6].Amongst the existing enhancement methods,twisted tapes are very promising due to many advantages,such as low cost,simplicity of the geometry and significant thermal efficiency.

The thermal boundary layer dominates the overall heat transfer rate in a circular pipe.The built-in twist tapes could induce the swirl flow and increase the flow turbulence as well.Therefore,the thermal boundary layer was effectively disturbed,which could significantly benefit improvement of heat transfer coefficient [7].In 2013,Bhuiya et al.[8] conducted an experimental study on a heat exchanger tube fitted with double counter twisted tape inserts and found that the heat transfer rate and friction factor were obtained to be around 60% to 240% and 91% to 286% higher than those of the plain tube values.Eiamsa-ard et al.[9] also analyzed the experimental results of the mean Nusselt number,friction factor and enhancement efficiency in a circular tube fitted with short-length twisted tape inserts.The experimental results indicated that the full-length twisted tapes demonstrated superior working performance than the short length tape insert.

Additionally,Naphon [10] compared the heat transfer coefficient and pressure drop in the horizontal double pipe with and without twist tape insert.The comparison results indicated that the heat transfer coefficient was significantly increased by the twist tape insert,while the pressure drop was also rapidly increased.In 2019,Zhang[11]conducted a comprehensive investigation on the performance evaluation of a circular pipe fitted with self-rotating twisted tapes and analyzed the effect of twist ratios on the thermal performance of a circular pipe.The maximum thermal performance factors of 1.03,0.9444,0.924,and 0.898 could be achieved at the start of rotating behavior for Y=2.2,3,4,and 6,respectively.Zhang et al.[12] also optimized the geometry of the self-rotating twist tapes in terms of the perforation ratios.The experimental results showed that perforation ratio significantly affects the initial stage of rotation behavior and rotational speed.

Although the employment of twist tapes could effectively increase the heat transfer coefficient,the pressure drop was also increased,which consumes more pumping power.Therefore,some other heat transfer enhancement methods (e.g.nanoparticles)were proposed to improve heat transfer by increasing thermal conductivity of working fluids.Early in 1993,Masuda et al.[13] used nanoparticles for the enhancement of the thermal conductivity of a fluid.Tremendous efforts have been put to investigate the effect of nanoparticle on the heat transfer performance.A large amount of experimental research showed a significant enhancement of convective heat transfer in parallel channels [14],tubes [15–17]and annular flow channels [18].In addition,several researchers investigated the flow and heat transfer characteristics of various nanoparticles with different concentrations (e.g.Al2O3[19],CuO[20] and Fe2O3[21,22]).The research results showed that the employment of nanoparticles could be a feasible approach to enhance heat transfer performance with less increase in flow resistance.

Despite the investigation of twist tapes and nanoparticles have been conducted for several years,most of experiments were conducted separately and the combined effect of twist tapes and nanoparticles on the thermal performance is rarely examined.Hence,this paper is aiming at investigating the combined effect of twist tapes and nanoparticles on the heat transfer and pressure drop characteristics in a circular pipe.To overcome the large pressure drop loss by the normal twist tapes,a newly-designed selfrotating twisted tapes (SRTTs) and Al2O3nanoparticle are used in the experiment.Firstly,an experimental setup of a double pipe with SRTTs and nanoparticles are prepared.Then,a comprehensive experimental study is conducted with the Reynolds number ranging from 19,322 to 64,407.The pressure drop and heat transfer coefficient were measured in the experiment to analyse combined effect of SRTTs and nanoparticle on the heat transfer and flow characteristics.Finally,a heat transfer coefficient correlation and a friction factor correlation considering the combined effect of SRTTs and nanoparticles are developed.Some research findings derived from this study could offer valuable guide to the practical applications.

2.Nanoparticles Preparation

The Al2O3nanoparticles were purchased from Ningbo Jinlei Nano Material and Technology,Co.,Ltd,China.As presented in Fig.1,Al2O3aqueous solution were prepared by using two-step method in this experiment.First of all,the dispersant agents were added to base liquid (deionized water) to prevent agglomeration between particles.Then,the liquid should be stirred for 50 minutes by magnetic stirring apparatus.After adding nanoparticles to the fluids,the mixture should be stirred by 1 hour mechanically.Secondly,NaOH also was needed to adjust PH value to avoid agglomeration.Finally,mixed fluids were oscillated for 45 minutes for uniform distribution by using ultrasonic wave.The time of oscillation should not be too long to avoid the temperature increase of the fluids.

As presented in Fig.2(a),the scanning electron microscope(SEM) photograph of Al2O3aqueous soluton was provided by Ningbo Jinlei Nano Material and Technology,Co.,Ltd,China.It is observed that average particle size of Al2O3is approximate 30 nm,which could enhance Brownian motion and prevent sedimentation.The detailed physical properties of Al2O3particles are shown in Table 1.After two-step method,stable Al2O3aqueous soluton with mass concentration of 1%,1.5%,2%and 3%were used in the experiment.The method used in this study could offer stable nanofluids without sedimentation to satisfy experimental requirements.

3.Experimental Methodology

As presented in Fig.3,an experimental platform is mainly consisted of three sub-system,namely,test section,hot water supplied system and heat sink system.A double pipe with 2000 mm length was used in this experiment as test section.The outer tube was made of stainless steel,and the inner tube was manufactured by copper.Two RTDs and pressure tapes were taped at inlet and outlet of test section to record the temperature and pressure drop of the test section.Twenty thermocouples were distributed equidistantly on the external surface of the test tube to record the tube wall temperature at eight different cross sections.Each cross section was attached by three thermocouples with interval angle of 120° for accurate measurement,as shown in Fig.3(a).The average temperature of the tube surface at each cross section was the average value of the three thermocouples.To reduce the thermal contact resistance,the thermocouples were buried in the small holes with 5 mm in depth at the outer surface.To avoid the thermal entrance effect on the overall heat transfer performance,the first cross section was placed 90D far from entrance of test tube.The thermocouples were calibrated by the high-precision thermistor before the experiment.The calibration correlations of each thermocouples were developed based on the experimental data.An electrical heater inside water tank could provide stable heat for hot supply system.After heat transfer process,hot water in inner tube was delivered back to water tank for secondary heating.Heat sink functions in releasing heat from cold water to outdoor environment in outer tube.In addition,the newly-designed self-rotating twisted tapes (SRTTs) with twist ratio of 4 were manufactured from polymer straight tapes (Fig.3(b)).Different from conventional twisted tapes,SRTTs could perform rotation behaviour due to their unique design,when fluids velocity reaches a certain value.

During the experiment,hot water with inlet temperature of 50°C was flowed through the inner tube,and cold water with inlet temperature of 30 °C flowed through the outer tube,respectively.For entire heat transfer process,supplied hot by electrical heater was transfer to outdoor environment through hot water,cold water and heat sink.The flow was fully turbulent with the Reynolds number ranging from 19,322 to 64,407.The Prandtl number was estimated based on the average temperature of working fluids at the inlet and outlet of the test tube.By adjusting output power of water pump,volume flow rate of water could be controlled.Since heat exchangers usually operate stably in reality,each experimental run needed 20 minutes to record measured values (e.g.pressure drop,water temperature and volume flow rate)at equilibrium state.

4.Data Reduction and Uncertainty Analysis

4.1.Data reduction

Table 2 summarizes the measured physical properties of Al2O3nanofluids with different mass concentration.The density and viscosity of the nanofluids were measured using a densitometer and a rotary viscosimeter,respectively,under atmospheric conditions.The specific heat capacity of the nanofluids was measured using differential scanning calorimeter (DSC) and the thermoconductivity of the nanofluids was measured using transient hot-wire method with the measuring uncertainty of 3%.The thermal conductivity of the working fluids was effectively improved by the addition of Al2O3nanoparticles with the enhancing ratio of 14.5%at the mass concentration of 3%.

Table 2 Physical properties of Al2O3 nanofluids with different mass concentration

Fig.1.Procedure of fabricating Al2O3 aqueous solution by two-step method.

Fig.2.(a) SEM Al2O3;(b) Al2O3 nanofluids with different mass concentrations.

Table 1 Physical properties of nanosized particles (Al2O3)

To evaluate the heat transfer and pressure drop characteristic in a circular pipe,there are five performance indices(e.g.overall Nusselt number,heat transfer multiplier,friction factor,friction factor multiplier and thermal performance factor) were adopted in this study.The definitions of the performance indices are stated as follows.

The overall Nusselt number,Nu,refers to the overall heat transfer performance in a circular pipe.

where Diis the inner diameter of the circular pipe.

The convective heat transfer rate from the hot water to the cold water is defined as:

Fig.3.(a) Schematic of the test rig;(b) Pictorial view of self-rotating twisted tapes with twist ratio of 4.

Therefore,the heat transfer coefficient was estimated as follows.

The heat transfer multiplier,φh,is the ratio of the heat transfer coefficient for the heat exchanger with SRTTs or nanoparticles to that for the plain heat exchanger [23,24].

The frication factor is given as follows.

where ΔP is the pressure drop along the test section.

The frication factor multiplier means the ratio of the friction factor for the heat exchanger with SRTTs or nanoparticles to that for the plain heat exchanger.

To better evaluate the combined effect of SRTTs and nanoparticles on heat transfer and friction factor characteristics,the thermal performance factor was proposed [25,26].The definition of the thermal performance factor is given as follows.

4.2.Uncertainty analysis

Due to the existing measurement errors,the uncertainty analysis is necessary.The uncertainty analysis is conducted using the following equation [27,28].

where δyis the combined uncertainties of desired variables Y.?xiis the uncertainties of the ithmeasured variables.In this paper,the measurement errors of the thermocouples,pressure tapes and water flow meter are±1.6%,±5.6%and±3.1%,respectively.The measurement uncertainties of the densitometer and the rotary viscosimeter are 0.001 g﹒cm-3and ±5%,respectively.The measurement uncertainties of the differential scanning calorimeter(DSC) and the transient hot-wire method are ±5% and ±3%,respectively.Therefore,the uncertainty of the Nusselt number and friction factor are ±9.6% and ±9.9%,respectively.

5.Results and Discussion

5.1.Validation of the experimental results

Before the analysis of the experimental results,the energy conservation analysis of the test system needs to be performed to validate the reliability of the test system.Fig.4 presents the variation of the ratio of Qhto Qc(blank)with Reynolds number.In the experiment,the liquid velocity ranges from 0.99 m﹒s-1to 2.4 m﹒s-1,with the Reynolds number ranging from 19,322 to 64,407.All the ratios fell within ±5% error,validating the reliability of the test system.

What’s more,the measured heat transfer coefficient and friction factor of the plain tube are compared with calculated values by several well-known equations to further validate the experimental setup.Dittus-Boelter equation and Gnielinski equation are used to calculate the heat transfer coefficient,while Blasius equation and Petukhov equation are used to estimate the friction factor.

Heat transfer coefficient:

Dittus-Boelter equation

Fig.5 presents the comparison between the measured and calculated heat transfer coefficient by Dittus-Boelter equation and Gnielinski equation and Fig.6 shows the comparison between the measured and calculated friction factor by Blasius equation and Petukhov equation of the plain tube,respectively.All the measured data fell within ±10% error of the calculate values.The relative deviations of Dittus-Boelter equation and Gnielinski equation are 3.74% and 3.14%,and that of Blasius equation and Petukhov equation are 0.616% and -0.411%,respectively,validating the experimental results.

5.2.Effect of self-rotating twist tapes(SRTTs)on thermal performance

A novel type of twisted tapes,namely self-rotating twist tapes(SRTTs),was adopted to evaluate its effects on the thermal performance in a circular pipe.

5.2.1.Heat transfer performance

Fig.7 reveals comparison results of heat transfer performance between the tube with SRTTs and plain tube.It is found that employment of SRTTs in the tube could effectively improve heat transfer rate by 15.5% at given Reynolds number increasing from 19,322 to 64,407.This can be explained by the stronger swirl flow and turbulence generated by SRTTs and existence of rotation behaviour for excellent fluids mixture.This is also consistent of previous work on analysis of applications of SRTTs [11].In addition,Fig.7(b) showed that the heat transfer multiplier decreased with the Reynolds number,decreasing from 1.38 to 1.08.This can be attributed to more dominating effects of Reynolds number on increasing residence time and disturbing thermal boundary layer for heat transfer enhancement.

5.2.2.Friction factor

It happened that the wedding of the King s eldest24 son was to be celebrated25, so the poor woman went up and placed herself by the door of the hall to look on.30 When all the candles were lit, and people, each more beautiful than the other, entered, and all was full of pomp and splendour, she thought of her lot with a sad heart, and cursed the pride and haughtiness31 which had humbled28 her and brought her to so great poverty.

Fig.8 presents the effect of SRTTs on the flow characteristic in turbulence region in a circular pipe.It is obviously found that the friction factor of the tube with SRTTs was larger than that of the plain tube.As shown in Fig.8(a),the friction factor of the tube with SRTTs decreased from 0.0400 to 0.0288 with the Reynolds number increasing from 19,322 to 64,407,while the friction factor of the plain tube only decreased from 0.0245 to 0.0218.The higher friction factor mainly results from the increased turbulence by SRTTs that causes flow blockage.Extra energy to rotate the SRTTs can be responsible for increase in pressure drop.In addition,the friction factor multiplier 1.61 to 1.32 with the Reynolds number increasing from 19,322 to 64,407.As the Reynolds number increases,the pressure drops increase and the extra energy to rotate the SRTTs occupied lower ratio of the whole pressure drop.Therefore,the friction factor decreases with the Reynolds number.

5.2.3.Thermal performance factor

Fig.4.Variation of the ratio of Qh to Qc with Reynolds number.

Fig.5.Comparison between the measured and calculated heat transfer coefficient.

Fig.6.Comparison between the measured and calculated friction factor.

As discussed above,the introduction of SRTTs in the tube could improve the heat transfer rate but the friction factor.Heat transfer enhancement is optimized to promote heat transfer coefficient within less increase in pressure drop.As presented in Fig.9,the thermal performance factor is larger at lower Reynolds number.This can be explained that rotating behaviour is more dominate to be responsible for excellent fluid mixture with less increase in pressure drop under lower Reynolds number.However,when the Reynolds number is larger than 57967,the thermal performance factor decreases to be lower than 1.This finding implies SRTTs could not be an alternative approach to improve heat transfer in terms of energy saving,when operation condition is lager Reynolds number.This can be attributed to less influences of SRTTs on producing turbulence and large pressure drop caused by fluids motion with high velocity under larger Reynolds number.Additionally,general trends of thermal performance factor decrease with increase of Reynolds number.This is consistent with previous research on evaluating thermal efficiency of SRTTs [11,12].

5.3.Conjugated effect of Al2O3 nanoparticle and SRTTs on thermal performance

As mentioned above,SRTTs are not applicable for the operation condition of high Reynolds number.To overcome this issue,Al2O3nanoparticle is introduced to be combined with SRTTs for further improvement of heat transfer.Hence,combined effect of Al2O3nanoparticle and SRTTs on the thermal performance is analysed in a circular pipe.

5.3.1.Heat transfer coefficient

Fig.10 presents the combined effect of Al2O3nanoparticle and SRTTs on heat transfer performance in a circular pipe.The mass concentration of 0.0% means only SRTTs is used while that of 3.0% means both the Al2O3nanoparticle (3.0% (mass)) and the SRTTs is used in the experiment.It is clearly observed in Fig.10(a) that the introduction of Al2O3nanoparticle could effectively improve the heat transfer coefficient of the circular pipe fitted with SRTTs.Besides,the heat transfer coefficient increased with the mass concentration.The increase of heat transfer coefficient is mainly attributed to the increase of heat conductivity and the Marangoni effect induced by the Al2O3nanoparticle.Besides,the random movement of particles suspended in the nanofluids,which is also called Brownian Motion,might be another reason for the heat transfer enhancement.The Brownian Motion could further intensify the heat transfer between the core part to the surface part.As shown in Fig.10(b),the heat transfer multiplier decreases from 2.08 to 1.18 in the mass concentration of 3.0% and from 1.38 to 1.08 in mass concentration of 0.0% with Reynolds number increasing from 19,322 to 64,407.The highest heat transfer multiplier occurs in the highest mass concentration of Al2O3nanoparticle.As mentioned in Section 5.2,the employment of SRTTs could benefit heat transfer process by producing higher level of turbulence.Hence,heat transfer augmentation could be achieved by conjugated effects of nanoparticles and SRTTs on increasing swirl flow and thermal conductivity.

Fig.7.Effect of SRTTs on heat transfer performance in a circular pipe.

Fig.8.Effect of SRTTs on the friction factor of in a circular pipe.

5.3.2.Friction factor

Fig.9.Effect of SRTTs on the thermal performance factor.

Fig.10.Effect of Al2O3 nanoparticle and SRTTs on heat transfer performance in a circular pipe.

Fig.11.Effect of Al2O3 nanoparticle and SRTTs on the friction factor in a circular pipe.

Fig.12.Effect of Al2O3 nanoparticle and SRTTs on the thermal performance factor in a circular pipe.

Fig.11 presents the combined effect of Al2O3nanoparticle and SRTTs on the friction factor in a circular pipe.As shown in Fig.11(a),the friction factor only increases from 0.0400 in the mass concentration of 0.0% to 0.0452 in mass concentration of 3.0% while the heat transfer coefficient rapidly increased from 128.1 to 193.5,as shown in Fig.11(a),when the Reynolds number is 19322.The highest friction multiplier increased from 1.61 in mass concentration of 0.0% to 1.84 in mass concentration of 3.0%.The increase of the friction factor with the mass concentration was attributed to the increase of the viscosity that results in large increase in flow blockage.This is also supported by previous research regarding effects of Al2O3concentration on friction factor[19].Besides,when the Reynolds number is larger than 45085,there are less discrepancies of friction factor between different mass concentrations of Al2O3.This represents that effects of mass concentration is less significant for pressure drop at larger Reynolds number.It is observed from Fig.11 that friction factor of the Al2O3with different mass concentrations in the circular pipe fitted with SRTTs is much higher than plain tube.This can be attributed to higher swirl flow and viscosity caused by combined effects of SRTTs and Al2O3nanoparticles,which is responsible for significant increase in pressure drop.

Fig.13.Comparison between the experimental and calculated heat transfer coefficient and friction factor.

Fig.12 shows the combined effect of Al2O3nanoparticle and SRTTs on the thermal performance factor in a circular pipe.Although the thermal performance factor decreased with the Reynolds number,the thermal performance factors of SRTTs with mass concentration of 2.0%and 3.0%are always higher than 1.0.As mentioned in section 5.2,use of SRTTs tends to decrease thermal performance factor to be lower than 1 at high Reynolds number conditions.This can be explained that employment of Al2O3with higher mass concentrations plays more dominant role in enhancing heat transfer with less increase in flow resistance for combination of Al2O3and SRTTs.By combining Al2O3and SRTTs in a circular pipe,it is feasible to improve thermal efficiency for energy saving even under higher Reynolds number.

5.4.Correlation development

To better demonstrate the effect of mass concentration of Al2O3nanoparticle on the heat transfer and friction factor characteristics in a circular pipe,a new heat transfer correlation and a new friction factor correlation were developed using the form of Dittus-Boelter correlation and Blasius equation.The detailed specifications of the newly-developed correlations are expressed as follows.

where φ is the mass concentration of the Al2O3nanoparticles.

Fig.13 presents the predictive performance of the new correlations.As shown in Fig.13(a),95.0% of the calculated heat transfer coefficient fell within ±10% error of the experimental results with the mean relative deviation of 0.143%.Besides,Fig.13(b) demonstrated that all the calculated friction factor fell within ±10% error of the experimental results with the mean relative deviation of 0.264%.Therefore,the newly-developed heat transfer and a friction factor correlations were well validated.

6.Conclusions

Since the thermal performance enhancement for heat transfer devices is very crucial,this paper develops a novel methods of thermal performance enhancement using SRTTs and Al2O3nanoparticles.The performance enhancement characteristics are comprehensively investigated.The main achievements are as follows.

(a) A novel self-rotating twisted tape was developed and the effect of the self-rotating twisted tapes on the heat transfer and friction factor characteristics were analysed as well.The heat transfer coefficient was effectively improved by SRTTs.The heat transfer multiplier in a circular pipe with SRTTs decreased from 1.38 to 1.08 with the Reynolds number increasing from 19,322 to 64,407,while the friction factor multiplier decreased from 1.61 to 1.32.

(b) A new Al2O3nanoparticle was synthesized and characterized.The combined effect of Al2O3nanoparticle and SRTTs on thermal performance in a circular pipe was comprehensive investigated.The results indicated that the introduction of Al2O3nanoparticle demonstrated superior thermal performance to the single SRTTs.The heat transfer multiplier decreased from 2.08 to 1.18 in the mass concentration of 3.0% and from 1.38 to 1.08 in mass concentration of 0.0%with Reynolds number increasing from 19,322 to 64,407.

(c) The new heat transfer and friction factor correlations considering the combined effect of Al2O3nanoparticle and SRTTs on thermal performance in a circular pipe were developed.The calculated heat transfer coefficient and friction factor agreed well with the experimental results.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This project is supported by the National Natural Science Foundation of China(51906071),Science and Technology Planning Project of Guangdong Province (2018A050501005),the Postdoctoral Science Foundation of China(2019M652889),the National Natural Science Foundation of Guangdong (No.2019A1515011536),the Fundamental Research Funds for the Central Universities(D2191890) and Key Laboratory of Advanced Reactor Engineering and Safety,Ministry of Education (ares-2019-09).

Nomenclature

A Surface area,m2

CpSpecific heat capacity,kJ﹒(kg﹒K)-1

D,DiTube diameter,m

f Frication factor

h Heat transfer coefficient,W﹒(m2﹒K)-1

L Length of test tube,m

Nu Nusselt number

ΔP Pressure drop,Pa

Pr Prandtl number

Q Heat transfer rate,W

Re Reynolds number

T Temperature,K

T-Mean temperature,K

ν Fluids velocity,m﹒s-1

λ Thermal conductivity,W﹒(m﹒K)-1

μ Dynamic viscosity,Pa﹒s

ρ Density,kg﹒m-3

? Thermal performance factor

φfFriction factor multiplier

φhHeat transfer multiplier

Subscripts

b Bulk

conv Convective

nf Nano-fluid

in Inlet

out Outlet

Plain Plain tube

pp Pumping power

s Surface

SRTTs Self-rotating twisted tapes

w Water