Yongliang Wan ,Runhan Wu ,Cong Qi*,Gang Duan ,Ruizhao Yang

1 Automotive Engineering Research Institute,Shaanxi Heavy Duty Automobile Co.,Ltd,Xi'an 710200,China

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

Keywords:Nano fluids Heat transfer enhancement Nanoparticle Corrugated tube

A B S T R A C T Thermo-hydraulic characteristics of TiO2-water nanofluids in thin-wall stainless steel test tubes(corrugated tube and circular tube) filled with copper foam(40 PPI)are experimentally investigated and compared with those in test tubes without copper foam.The effects of nanoparticle mass concentration on flow and heat transfer performances are investigated.In addition,the mutual restriction relationships between Reynolds number(Re),Nusselt number(Nu)and resistance coefficient(f)are discussed respectively.Also,the comprehensive coefficient of performance(CCP)between heat transfer and pressure drop is evaluated.The results show that core-enhancement region for heat transfer using experimental tubes filled with copper foam is notably different from that of tubes without copper foam.There is a corresponding Reynolds number(about Re=2400)for the maximum CCP of each condition.And the heat transfer can be enhanced dramatically and sustained at 8000≤Re≤12000.

1.Introduction

Heat exchanger technology has a wide application in heating ventilation air conditioning(HVAC)and power train cooling industry covering automotive,power energy,aerospace and so forth.Convective heat transfer,especially forced convection heat transfer,is one significant heat transfer model for heat exchanger.Nevertheless,due to the increasing thermal load,it becomes more and more difficult to meet the requirements of high intensity heat transfer using traditional tube(circular tube)and working medium(water,oil,ethylene glycol,etc.).Hence,the heat transfer can be enhanced by improving the heat transfer coefficient,the area and temperature difference,and the first two approaches are adopted to enhance the heat transfer in this paper.

Based on the Maxwell theory[1]and the research of Choi et al.[2],nanofluids,with higher thermal conductivities than common fluids,are selected as the working medium by many researchers to improve the heat transfer coefficient.He et al.[3,4]and Yang et al.[5,6]have investigated the thermophysical properties of many kinds of nanofluids,and found that liquid metal based nanofluids and metal nanoparticle can enhance the thermal performance of fluids.Also,He et al.[7–9]made an enormous contribution to natural convection heat transfer of nanofluids,and pointed that nanofluids with certain mass fractions can improve the heat transfer effectively.Forboiling heat transfer,Qi et al.[10,11]revealed the mechanism of heat transfer enhancement of nanofluids by experimental approach and LBMrespectively.Besides,He et al.[12–14]analyzed the boiling heat transfer of nanofluids in a confined space,and found that the heat transfer coefficient and critical heat flux are enhanced due to the surface wet tability reduction and nanoparticle coating on heater surface.In order to improve the heat transfer,forced convection heat transfer has been applied in some fields instead of natural convection heat transfer[15–17].Sun et al.[18–22]experimentally studied the flow and heat transfer of nanofluids in different kinds of enhanced heat transfer tubes.Yang et al.[23,24]discussed the heat transfer performances of viscoelastic fluid-based nanofluids in laminar and turbulent flow.Above researches covered the natural convection,forced convection and boiling heat transfer,all of investigations indicate that nanofluids with certain mass concentrations(0–6 wt%)can improve the heat transfer by 3 wt%at least compared with the base fluids.In addition,Hartnett et al.[25]pointed out that the tubes with special constructions,such as corrugated tube,spiral grooved tube,transverse groove tube,can improve the heat transfer to a large extent.Nanan et al.[26]studied the flow and thermal mechanisms in a heat exchanger tube inserted with twisted cross-baffle turbulators.It can be obtained that the special constructions can enhance the heat transfer by 5%–90%.Abadi et al.[27]experimentally explored the heat transfer and pressure drop in a metal-foam- filled tube heat exchanger,and indicated that the porous metal foam has a better heat transfer rate andcoefficient,which is due to the special characteristics including higher thermal conductivity,larger specific surface area and higher permeability.

Table 1Thermophysical properties of TiO2 nanoparticle and de-ionized water

From above researches,it can be found that the researchers have contributed enormously to the enhanced heat transfer,and proved that heat transfer can be enhanced by each one of nanofluids,enhanced heat transfer tube and porous metal foam.However,the comprehensive performance and heat transfer mechanism of them together are investigated rarely.Besides,the effect of core-enhancement region on heat transfer,and the effect of Reynolds number on sustainability of heat transfer enhancement have been scarcely studied so far.Hence,the coupling heat transfer characteristics and resistance performance of nanofluids,enhanced heat transfer tube(corrugated tube)and porous metal foam(copper foam)are investigated to reveal the heat transfer mechanism in depth.

2.Nano fluids and Thermophysical Properties

Table 1 shows the thermophysical properties of nanoparticle and de-ionized water,and the following models are adopted to calculate the density and specific heat capacity of nanofluids respectively based on the researches of Xuan et al.[28]and Duangthongsuk et al.[29].

where β is the volume fraction,subscript “nf”stands for nanofluids,“p”stands for nanoparticle,and“w”stands for base fluid(de-ionized water).

The details of preparation,stability,and thermophysical properties of TiO2-water nanofluids have been investigated in our previous work[31].The UV analyses with time for nanofluids stability are shown in Fig.1.It can be found that nanofluids with pH=8 and a certain dispersant mass fraction m=6 wt%show a lowest transmittance,which means a good stability.It's known that TiO2nanoparticles will reflect the most light and have a high reflectance when the nanoparticles are uniformly distributed in the base fluid(de-ionized water).Hence,the stabilities of nanofluids are inversely proportion to the transmittance,and the stable nanofluids have a low transmittance.As a consequence,m=6 wt.%and pH=8 are selected to prepare the experimental nanofluids.And the nanofluids after standing 7 days still keep a good stability.

Fig.1.Transmittance of nanofluid with mass fraction of ?=0.5 wt%at different quiescent time,(a)m=5 wt%;(b)m=6 wt%;(c)m=7 wt%;(d)m=8 wt%.

3.Experimental System and Method

3.1.Experimental system

The schematic diagram of experimental system is shown in Fig.2(a).The experimental system mainly consists of five sections,including heat transfer system,section for flow resistance,adjusting and checking flow system,temperature control system and data acquisition system.

In the heat transfer system,the nickel flat wire with 2 mm in width and 0.15 mm in thickness is wrapped regularly around the experimental tubes(a stainless steel circular tube and corrugated tube with the same of inner diameter of 10 mm,thickness of 2 mm and length of 1 m) filled with copper foam(40 PPI),and a DC power supplies a constant heat flux boundary condition(796 W·m-2)for the experimental tubes.A layer of mica is coated on the wall of the tubes to achieve the insulation between experimental tubes and nickel flat wire.Ten thermocouples(OMEGA TC-TT-T-24-3.0M-Foil)are arranged evenly across the wall of the test tubes to measure the average temperature of the wall,and one pairs of thermocouples(OMEGA TMQSS-M030-160 mm–3000 mm)are installed in the inlet and outlet of tubes to measure the inlet and outlet temperature of fluids.In order to avoid the heat loss as much as possible,clad materials that silicate-aluminum thermal insulation asbestos with 30 mm in thickness and aluminum-rubber insulation tubing with 10 mm in thickness are wrapped horizontally around the test tube completely.Moreover,the inlet and outlet of test tube are connected with a plastic sleeve with 200 mm in length to reduce the heat loss along the test tube axially.The installation schematic of thermocouple and insulation layer is presented in Fig.2(b).

For flow resistance test section,the pressure drop of the experimental tube is directly measured by SSTCC pressure sensor.For adjusting and checking flow system,LZB-10 rotameter is used to measure the flow rate,and there is a three-way value to check the measurement result manually.

Additionally,the microscopic features of copper foam(40 PPI)at different magnifications are measured by scanning electron microscope(SEM)and presented in Fig.2(c).It displays that there is a high permeability for copper foam,and the hole diameter is about 0.8 mm,which is acceptable for the experimental system.

3.2.Data analysis

Heat supplied by the DC power(Q):

Fig.2.Flow and heat transfer system,(a)schematic diagram;(b)installation schematic of thermocouple and insulation layer;(c)copper foam at different magnifications measured by SEM(c1)copper foam;(c2)×40;(c3)×60;(c4)×80.

where U is the heating voltage from the DC power,I is the electric current supplied by the DC power.

Heat absorbed by test fluids(Q r):

where cpis the specific heat capacity of test fluid,qmis the mass flow rate,Toutand Tinare the outlet temperature and inlet temperature of test fluid respectively.

Convective heat transfer coefficient(hnf)can be estimated as follows:

where deand L are the equivalent diameter and characteristic length of test tube respectively,Twis the inner wall average temperature of test tube,Tfis the average temperature of test fluid.Tfand Twcan be calculated as follows respectively:

where Tw(i)is the inner wall temperature of test tube,and it can be calculated as follows:

where Two(i)is the outside wall temperature of test tube,roand riare the outside radius and inner radius of test tube respectively,and k is the thermal conductivity of test tube.

Nusselt number can be defined as:

where knfis the thermal conductivity of nanofluids.

Resistance coefficient(f)can be calculated as follows:

where ρ is the density of test fluid,u is the velocity of test fluid,and△p/△L is the pressure drop per unit length along the test section.

Reynolds number(Re)is defined as follows:

where μnfis the dynamic viscosity of the test fluid.

3.3.Experimental uncertainty

To ensure the experimental accuracy,it's quite necessary to analyze the uncertainty of the system.And the uncertainties of Nusselt number and flow resistance coefficient are defined as follows:

The accuracies of Q,Qr,knf,Tw,Tf,L,de,p and qmis±1.0%,±1.6%,±3.0%,±1.0%,±1.0%,±0.5%,±0.5%,±1.5%and ± 1.06%respectively.Hence,the maximum uncertainties of Nusselt numbers and resistance coefficient f are about±3.88%and±1.97%.Based on the research of Kline–McClintock method[32],the maximum uncertainty can be acceptable.

3.4.Thermal equilibrium

Heat loss plays a major role in the thermal equilibrium.Although there is an insulating layer to prevent the heat loss,in order to evaluate the effect of heat loss on the thermal equilibrium,an evaluation criterion between the supplied heat(Q)from the DC power and the absorbed heat(Qr)is established based on thermal equilibrium index(Eq.(14))which is put forward by Fei.[33].Fig.3 gives the index of TiO2-water nanofluids at different conditions.It can be found that the index is less than 4%absolutely,and the thermal equilibrium is quite workable to a certain degree.It can be also found that the index in turbulent flow is lower than that in laminar flow,which means it can reach a thermal equilibrium state more easily in turbulent flow.

Fig.3.Thermal equilibrium indexes at different flow patterns.

3.5.System validation

The reliability of the experimental system is directly related to the results of the experiment,thus the system validation has a significant impact on experimental results.Fig.4 presents the comparison between the results(heat transfer characteristics and resistance performance of deionized water in a circular tube)of this experiment system and other published literatures[28,34–36].It can be obtained that experimental results in this paper have a good agreement with that in other published literatures[28,34–36].The maximum relative error between experimental values and predicted values is less than 3.5%,thus the experimental system is trustworthy to a great degree.

Equations in the published literatures[35,36]are as follows respectively:

Sieder-Tate equation[35]:

Fig.4.Comparisons of Nusselt number and resistance,Nusselt number:(a)laminar flow,(b)turbulent flow;Resistance comparison:(c)laminar flow,(d)turbulent flow.

where the subscript“f”stands for the test fluid,and the subscript“w”stands for the surface of test tube.

4.Results and Discussion

Based on the error analysis and system validation,the experiments using TiO2-water nanofluids,copper foam(40 PPI)and corrugated tube are performed.Four separate experiments are conducted:(1)de-ionized water flowing through a circular tube and corrugated tube without copper foam,(2)de-ionized water flowing through a circular tube and corrugated tube filled with copper foam,(3)nanofluids(? =0.1 wt%,? =0.3 wt%and ? =0.5 wt%)flowing through a circular tube and corrugated tube without copper foam,(4)nanofluids flowing through a circular tube and corrugated tube filled with copper foam.

Fig.5.Nusselt numbers in experimental tubes,(a)circular tube;(b)corrugated tube.

4.1.Heat transfer performance

Fig.6.Relative heat transfer enhancement at different conditions,(a)(crt+c f)/ct;(b)(crt+c f)/crt;(c)(ct+c f)/ct;(d)(ct+c f)/crt;(e)(crt+c f)/(ct+c f);(f)crt/ct.

The effects of copper foam on the heat transfer at different flow patterns are shown in Fig.5.It can be found that the heat transfer performances of tube with copper foam are improved efficiently compared with that without copper foam in both laminar region and turbulentregion.Three main reasons may play a major role in enhancing heat transfer by copper foam:(1)the high thermal conductivity of copper foam(383.8 W·m-1·K-1),(2)the large specific surface area and high permeability of copper foam,(3)high intensity disturbance near the inside wall of tube and thin laminar boundary layer.In addition,it can be found from Fig.5 that the Nusselt number is proportional to Reynolds number.There are various reasons for that,but the reduction of the laminar boundary layer thickness which is caused by the irregular movement of test fluids in large Reynolds numbers should be more concerned about.Also,it can be found that the heat transfer can be enhanced by nanoparticle concentration.This phenomenon is mainly due to the increase in thermal conductivity of nanofluids by adding nanoparticle into base fluid(de-ionized water).

Moreover,the relative heat transfer enhancement(E)caused by copper foam is presented in Fig.6,which can be calculated by Eq.(17).It can be found that heat transfer has a larger enhancement when a foam metal is filled in the test tube.And the experimental results indicate that the combinations of nanofluids,corrugated tube and copper foam can improve the thermal performance most,and the enhancement ratio can reach 20%–600%compared with that without copper foam.In addition to the effect of copper foam and nanoparticle on the heat transfer enhancement,another reason is that the cyclical peaks and troughs of the corrugated tube can disrupt the flow and thermal boundary to a certain degree,and it has a larger heat transfer area than circular tube when their equivalent diameters are equal.Also,core-enhancement region for heat transfer using experimental tubes filled with copper foam is different compared with that of tubes without copper foam.It shows that core-enhancement region for copper foam is centered upon laminar flow and transition region(1600≤Re≤2400),and that without copper foam is focused on fully developed turbulent flow(Re＞8000).The main reason is that heat conduction plays a crucial role on heat transfer to a large extent using tubes filled with copper foam.Due to higher thermal conductivity of copper foam and its special structure,heat transfer is improved to a large extent in laminar flow.However, flow patterns contribute more in heat transfer enhancement using tubes without copper foam.

where Nu1and Nu2stand for the Nusselt numbers at different conditions.Besides,the subscripts “crt”,“ct”,and “cf”stand for corrugated tube,circular tube and copper foam.

4.2.Flow resistance characteristics

Although the copper foam enhances the heat transfer by 20%–600%compared with that without copper foam,higher flow resistance also increases.Hence,the flow resistance characteristics are also studied.Fig.7 shows the resistance coefficients in experimental tubes.It indicates that the resistance of tube with copper foam increases by 2–4 times of that without copper foam.There are four reasons for this:(1)stuffing copper foam into tubes increases the pressure drop,(2)adding nanoparticle into de-ionized water enlarges the heat transfer resistance,(3)increasing Reynolds numbers makes a contribution to the increase in flow resistance,(4)additional pressure loss is added because of cyclical peaks and troughs of corrugated tube.

4.3.Comprehensive coefficient of performance(CCP)

The heat transfer performance can be enhanced effectively by copper foam,however,the flow resistance also increases at the same time which is disadvantageous to the convective heat transfer.Hence,it's necessary to weigh the effects of flow resistance increase and the benefits of cooper foam on the heat transfer enhancement.Therefore,comprehensive coefficient of performance defined as Eq.(18)is employed to evaluate the pressure drop and the heat transfer benefits brought by copper foam,and the results are displayed in Fig.8.It can be found that the variation trend of CCP is basically consistent with that of relative heat transfer enhancement(E).Meanwhile,the most effective way to enhance heat transfer is the combination of corrugated tube and copper foam,and the CCP can reach about 4.5 at best.Furthermore,it can be also indicated that high CCP region focus on the laminar flow and transition region,and there is a corresponding Reynolds number(about Re=2400)for the maximum CCP.Additionally,there is a stable stage for maintaining the high efficient heat transfer at 8000≤Re≤12000,which can be obtained that the combination of copper foam and experimental tubes can enhance the heat transfer dramatically.And the reason that caused above-mentioned phenomena has been discussed in the section of“heat transfer performance”in detail.

where f1and f2represent flow resistance coefficient at different conditions.

Fig.7.Resistance coefficients in experimental tubes,(a)circular tube;(b)corrugated tube.

5.Conclusions

An experimental set was established successfully to investigate the flow and heat transfer behaviors of nanofluids in a corrugated tube and a circular tube filled with cooper foam.Some main conclusions are as follows:

Fig.8.Comparison of CCP at different conditions,(a)(crt+c f)/ct;(b)(crt+c f)/crt;(c)(ct+c f)/ct;(d)(ct+c f)/crt;(e)(crt+c f)/(ct+c f).

(1)The combinations of nanofluid,corrugated tube and copper foam can enhance the heat transfer by 20%–600%compared with that without copper foam,and the Nusselt number is proportional to Reynolds number.

Fig.8(continued).

(2)Core-enhancement region for heat transfer of experimental tubes filled with copper foam is notably different from that of tubes without copper foam.The core-enhancement region for copper foam is centered upon laminar flow and transition region(1600≤Re≤2400),and that without copper foam is focused on fully developed turbulent flow(Re＞8000).

(3)The resistance of tube with copper foam increases by 2–4 times of that without copper foam.

(4)There is a corresponding Reynolds number(about Re=2400)for the maximum CCP of each condition.The heat transfer can be enhanced and sustained dramatically at 8000≤Re≤12000.