On laminar convective cooling performance of hybrid water-based suspensions of Al2O3 nanoparticles and MEPCM particles in a circular tube

International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

On laminar convective cooling performance of hybrid water-based suspensions of Al2O3 nanoparticles and MEPCM particles in a circular tube C.J. Ho a,⇑, J.B. Huang a, P.S. Tsai b, Y.M. Yang c a

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC Department of Chemical and Material Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan, ROC c Department of Chemical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC b

a r t i c l e

i n f o

Article history: Received 5 November 2010 Received in revised form 1 January 2011 Accepted 1 January 2011 Available online 24 February 2011 Keywords: Forced convection Nanoparticles Microencapsulated PCM Hybrid suspensions

a b s t r a c t Laminar forced convection of a hybrid water-based suspension of Al2O3 nanoparticles and microencapsulated phase change material (MEPCM) particles through a circular tube was investigated experimentally. In addition, an integral energy balance with scaling estimation is presented to elucidate influences of thermal properties of the hybrid suspension on its internal convection effectiveness. Experimental results show considerable enhancement in cooling effectiveness of the hybrid suspension over the pure PCM suspension, nanofluid, or water. However, the convection efficacy of utilizing the hybrid suspension appears severely outweighed by pressure drop penalty from its drastically increased viscosity with respect to the pure PCM suspension or the pure nanofluid. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Over the past few decades, the development of functional thermal fluids [1] by compounding different substances or different phases of matter (solid, liquid, or gas) has raised increasing interest in view of their potential applications in technologies. A particular form of the functional thermal fluids appears as colloidal suspensions of particles in the conventional heat transfer liquids of low thermal conductivity (such as mineral oils, water, and ethylene glycol), whereby the effective thermal properties (such as specific heat, heat capacity, and thermal conductivity) could be drastically modified or improved relative to the base fluids. These characteristics are highly desirable for thermal engineering applications where there exists a need for innovative heat transfer fluids to meet the new challenges in improving heat transfer effectiveness and intensifying thermal management for various industrial processes and technologies. In particular, the nanofluids and the solid-liquid phase change material suspensions (PCM suspensions), in which the solid particles (100 nm or smaller) and the microencapsulated phase change material (MEPCM) particles (10 lm or smaller) are, respectively, incorporated as the dispersed phase in the suspensions, are currently focus of great attention [2–4] because of their perspective potentials as high-performance heat transfer fluids. The potential advantage of utilizing the nanofluid lies mainly in its drastic increase in the thermal conductivity well

beyond the limits of classical Maxwell-Garnett effective medium theory [5–8]. On the other hand, the PCM suspension can serve as a dual functional thermal fluid for energy transport and/or storage [9–11], primarily due to its advantage of providing higher effective specific heat resulted from latent heat absorption associated with melting behaviors within the MEPCM particles. To improve forced convective heat transfer effectiveness, there have been several experimental investigations on laminar flow of the nanofluids containing various nanoparticles in tubes; see for example [12–17]. The use of nanofluids of various nanoparticles was reported to provide significant heat transfer enhancement over their respective base fluids, depending mainly on the particle fraction, as summarized in [3,4]. On the other hand, the feasibility of utilizing PCM suspensions for forced convective heat transfer enhancement in circular tubes has been demonstrated experimentally and numerically [18–26]. Above all, the convective heat transfer efficacy of utilizing the colloidal suspensions as the heat transfer fluids in the tube flows relies essentially on the relative changes in the thermal properties compared to the base fluids, as can be elaborated on a scaling analysis of the energy equation for the thermally developing forced convection in a circular tube [27]. The local heat transfer coefficient hbtd, based on temperature difference between the local wall and bulk fluid, in the thermally developing tube flow can be scaled with the relevant variables and thermal properties as:

 þ 1 þ 1=2 q00i km 1=2 1=2 1=2  Q 1=2 di ðx Þ  m qm c p;m km ðT w;i  T b Þ dt;m 1=2 1=2  þ 1 þ 1=2 ¼ Q 1=2 di ðx Þ m C m km

hbtd ¼ ⇑ Corresponding author. Tel.: +886 6 2757575x62146, fax: +886 6 2352973. E-mail address: [email protected] (C.J. Ho). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.02.022

ð1Þ

2398

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

Nomenclature cp C þ þ di ; do f FTw F h h hls k þ lh Dp Pe Q q q00 r+ rþ ; rþ o i Re  Sbm Stem T TM DTref,m

specific heat (kJ kg-1 K-1) heat capacity (kJ m-3 K-1) inner and outer diameter tube .h(m) i  of   þ þ Darcy friction factor, Dp di =l qf uþb 2 =2 figure of merit on wall temperature suppression, ½ðT w;i  T in Þmax;f =ðT w;i  T in Þmax;m =ðfm =ff Þ1=3 figure of merit on average heat transfer enhancement, m =h  Þ=ðfm =f Þ1=3 ðh f f heat transfer coefficient (W/m2 K) latent heat of fusion (J/kg) thermal conductivity (W/m K) length of heated section (m) pressure drop (Pa) Peclet number volumetric flow rate (cm3/min) heat input (W) heat flux (W/m2) radial coordinate (m) inner and outer radius of tube (m) Reynolds number modified inlet subcooling parameter (TM  Tin)/DTref,m modified Stefan number based on suspension properties, cp;m DT ref ;m =hls temperature (K) melting temperature of phase change material reference temperature difference based on suspension properties (K), q00i r þ =km i

where dt,m denotes the thermal boundary layer thickness. Clearly, it can be inferred from Eq. (1) that the local heat transfer efficacy for utilization of a colloidal suspension to replace its base fluid at þ fixed flow rate Qm through a tube of given diameter di depends closely on combined effects of changes in the thermal conductivity km and heat capacity Cm relative to the base fluid. Compared with the base fluid, as reflected from Eq. (1), the beneficial effect due to the significantly augmented thermal conductivity of nanofluid appears counteracted by its increasingly lower specific heat [28,29] or heat capacity with the particle fraction. In contrast, the benefit of latent-heat-induced increase in specific heat of the melting-on-going PCM suspension can be degraded with its lower thermal conductivity due to the inherently low thermal conductivity of phase change material (such as paraffin with k  0.15 W/m K) [2] encapsulated in the MEPCM particles. As pointed out in Ref. [30], a desirable colloidal suspension for heat transfer enhancement in tube flow is to be the one exhibiting simultaneous increases in both thermal conductivity and heat capacity with respect to the base fluid. To this end, we have successfully formulated a hybrid water-based suspension of Al2O3 nanoparticles and MEPCM particles [31] and experimentally demonstrated that the melting-on-going hybrid suspension can possess the desirable characteristics as a functional forced convection fluid exhibiting simultaneously enhanced thermal conductivity and heat capacity in comparison with water. The work presented herein is the second phase of our continuing effort aiming primarily to explore the heat transfer efficacy of using the hybrid water-based suspensions containing Al2O3 nanoparticles and MEPCM particles as a functional forced convection fluid. Here we investigate experimentally the laminar forced convection cooling characteristics of the hybrid water-based suspensions containing various mass fractions of nanoparticles and/or MEPCM particles in an iso-flux heated tube.

u+ x+

axial velocity (m/s) axial coordinates (m)

Greek symbols a thermal diffusivity (m2/s) thermal boundary thickness (m) dt eh local heat transfer effectiveness, hitd,m/hitd,f   eh average heat transfer effectiveness, h itd;m =hitd;f ehw effectiveness of wall temperature suppression l dynamic viscosity (kg/m K) q density (kg/m3) x mass fraction of particles in suspension Subscripts b bulk quantities eff effective quantities f base fluid fd fully developed i inner surface of tube m suspension mepcm micro-encapsulated phase change material particle np nanoparticles o outer surface of tube pcm phase change material w tube wall

2. Experiments 2.1. Experimental apparatus The flow loop heat transfer system used in the present study is illustrates schematically in Fig. 1 to supply working fluid to the test tube at the desired pressure, temperature, and flow rate. The working fluid enters the loop from a reservoir through a filter and is continuously circulated by a centrifugal pump. A constant temperature bath installed upstream of the test tube controls the inlet flow temperature. Exiting from the test section, the fluid passes through another constant temperature bath to restore its temperature before returning to the reservoir. Volumetric flow rate inside the loop was monitored by a flow meter. The test section fabricated is a circular copper tube with inner and outer diameters of 3.4 mm and 4.0 mm, respectively. The test section consists of a hydrodynamic entrance section, a heating section, and a downstream section. The hydrodynamic entrance section was 0.7 m in length to produce a fully-developed flow entering the heating test section which was 0.4 m in length. The outer surface of the heating test section was wrapped with an equally spaced winding of electrically insulated copper wire along the axial direction of the copper tube, which was connected to a DC power supply to provide constant heat rate to the outer surface of the test section. The power supplied was determined using the measured voltage and current supplied to the heating wire. A Bakelite tube with an inner diameter of 6 mm was positioned co-axially to provide rigidity of the whole test section assembly. To further minimize the heat loss, the test section was wrapped with foam insulation layer of 2 cm in thickness. The temperatures on the outer surface of the test section were measured ten T-type thermocouples along the axial direction. All thermocouples were calibrated against a standard thermometer. Two RTDs and pressure taps were positioned to measure the temperature rise and pressure drop across the test

2399

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

manometer

Fluid/wall thermocouple to DAS

Test section lh = 400

lexit =200

Data acquisition system Entrance region le = 700

x

RTD Pt100

RTD Lauda R46

Flow _

+

DC Power supply

Flow meter

Cooling Bath

Heating Bath

Tekdrive TDS -F8 Flow control valve

Centrifugal Pump Lowara CEA 1206 Buffer Bottle Bypass valve

Unit :mm

Fig. 1. Schematics of forced convection experiment flow loop.

section, respectively. A data acquisition system was assembled to log all the measured quantities during the experiments. 2.2. Preparation and properties of hybrid suspension Preparation of the hybrid water-based suspensions has been described in more detail in Ref. [31] and therefore only its essential features are summarized here. First, with ultra-pure Milli-Q water as the base fluid, nanoparticles of Al2O3 having a density of 3600 kg/m3 and an averaged particle size about 33 nm (Nanotech, Kanto Chemical Co. Inc., Japan) and MEPCM particles (laboratorymade) with n-eicosane as the core phase change material and the particle size in the range of 4–10 lm were, respectively, used to formulate the nanofluid of various particle fractions (xnp = 2–10 wt.%) and PCM suspension containing three mass fractions of phase change material (xpcm = 2, 5, and 10 wt.%). Then, the hybrid water-based suspensions were prepared by mixing the nanofluid with PCM suspension in an ultrasonic vibration bath for at least 2 h. In Table 1 the density and specific heat for the base fluid (water), the Al2O3 nanoparticle, and the MEPCM particle

formulated are listed. Here the effective density and specific heat of the MEPCM particle were evaluated following the approach adopted in Ref. [32] based on the respective mass fractions of n-eicosane and urea-formaldhyde inside the particle. The melting and freezing temperatures of the MEPCM particles were found to be 36.4 °C and 34.2 °C, respectively, which indicates the existence of supercooling for freezing of the core phase change material. The effective thermal properties of the hybrid water-based suspensions formulated pertinent to the present experiment, including the density q, the specific heat cp, the thermal conductivity k, and the dynamic viscosity l, were measured using various techniques as described in Ref. [31]. The ranges of temperature conducting the properties measurements were selected to cover the phase change temperatures of the MEPCM particles. The measured results of these effective thermal properties as given in Ref. [31] clearly demonstrate the synergic benefit in mixing the nanofluid and melting-on-going PCM suspension, leading to simultaneous increases in thermal conductivity and heat capacity, in comparison with water. Meanwhile, the effective dynamic viscosity of the hybrid suspension was found increased drastically relative to water.

Table 1 Thermophysical properties of nanoparticle, MEPCM particle, and base fluid at 30 °C. Properties

q (kg/m3)

Nanoparticle (alumina)

3600

Base fluid (water)

997.0

MEPCM composition n-Eicosane

Urea-formaldehyde

MEPCM particle

856 (solid) 778 (liquid)

1500

961.4

cp (kJ/kg K)

0.765

4.178

2.210

1.672

2.136

k (W/m K)

36.0

0.620

0.35 (solid) 0.15 (liquid)

0.420

0.310

2400

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

2.3. Data reduction

3. Integral energy analysis and scaling estimation for forced convection efficacy of hybrid suspension

In the present study, forced convection experiments have been performed for the horizontal tube using the pure water, the hybrid water-based suspension containing various mass fractions of MEPCM particles (xpcm = 2, 5, and 10 wt.%; or xmepcm = 3.7, 9.1, and 18.2 wt.%), and the Al2O3 particles (xnp = 2, 6, and 10 wt.%) as the working fluids under the following operating conditions: the volume flow rate Q = 12.5–240 cm3/min (the Reynolds number Ref = 101–1801), the heating power applied at the outer wall of the tube qo = 10, 20, 30, 40 W, and the inlet fluid temperature Tin = 32.8–33.2 °C. The electric input power qo applied during the experiments for the water-based suspensions was corrected to account for heat loss due to conduction losses through the housing and insulation, which was estimated comparing the supplied heat input to the steady-state heat transfer rate removed by the pure water flowing through the tube as

qo;corr  qo  qf Qcp;f ðT out  T in Þ

ð2Þ

The effective heat input reaching the inner wall of the heated section was further corrected from the corrected electric power input, qo,corr, for the axial wall conduction heat loss estimated from the measured outer wall temperature distribution along the non-directly heated regions adjacent to the leading and rear edges of the heated section of the tube. The total heat loss was found to increase when the flow rate is decreased and be within 2–12% of the electric power input for the experiments conducted. Experimental results for the temperature at a given flow rate generally reached steady state after approximately 30–60 min. The steady-state quantities measured in the experiments primarily include the volume flow rate (Q), the temperatures of thermocouples embedded in the outer wall of the tube (Tw,o), as well as the inlet and outlet fluid temperatures (Tin and Tout). The inner wall temperature of the tube (Tw,i) was estimated from the measured Tw,o adopting 1-D conduction across the wall thickness of the tube. For temperature control applications, the local heat transfer coefficient, hitd, can be defined based on the temperature difference between the inner wall and inlet bulk fluid as

hitd ¼

q00i ðT w;i  T in Þ

ð3Þ

The bulk fluid velocity uþ b of the flow through the tube was calculated from the measured volume flow rate Q. Thereby, the corresponding Reynolds number and Peclet number  are defined based þ on the properties of the base fluid as Ref ¼ qf uþ d =lf and b i   þ þ Pef ¼ ub di =af , respectively. Moreover, the measured results of pressure drop Dp over the test section were presented in terms of friction factor f as þ

f ¼

Dpdi =l

þ

qf ðuþb Þ2 =2

ð4Þ

Here the properties of the base fluid involved in evaluating the above dimensionless parameters were evaluated based a mean fluid temperature of Tmean (=(Tin + Tout)/2). Uncertainties in the measured quantities for the present study were estimated to be ±0.3 °C in the temperature, ±3.5–5.0% in the measured power input, ±0.4–1.2% in the flow rate, and ±0.075 Pa in the pressure drop. Following the uncertainty propagation analysis, the uncertainties for the deducted experimental results were estimated as follows: ±0.4–0.5 °C for the inner wall temperature, ±0.4–1.2% for the Peclet number, ±3.27–4.71% for the heat transfer coefficient, and ±3.85–5.84% for the friction factor, respectively.

Consider thermally developing laminar forced convection of a homogenous suspension containing nanoparticles and/or MEPCM þ particles with a flow rate Qm through a tube of diameter di and þ 00 length lh heated with a constant uniform heat flux qi . Adopting the homogeneous mixture model, the steady state energy equation for the thermally developing melting-on-going suspension flow with negligible streamwise conduction can be expressed as [21,22]

uþ

      @T 1 @ hls þ @T þ @nl  u ¼ a r x m pcm @xþ r þ @r þ @r þ cp;m @xþ

ð5Þ

On the right-hand side of Eq. (5), the second term accounts for the latent-heat absorption associated with melting progress in the MEPCM particles in the hybrid suspension of mass fraction xpcm, in which hls is the latent heat of fusion of the phase change material and nl denotes the volumetric fraction of liquid phase of phase change material in the MEPCM particles. Moreover, with xpcm = 0, Eq. (5) reduces to that for the suspension of nanoparticles (nanofluid) as well as the base fluid (xnp = 0). How the bulk temperature of the suspension flow varies along the heated section is of technical interest. In this aspect, an integral energy balance for the suspension flow can be performed by integrating Eq. (5) over arbitrary length from inlet of the heated section, leading to

T b ðxþ Þ  T in ¼

q00i



pdþi xþ

CmQ m

 

 þ   q00i di =2 cp;eff 1 km cp;m

ð6Þ

Here Tb is the bulk temperature and nb denotes the mean melted fraction of the MEPCM particles in the suspension flow. The effective specific heat of the suspension, cp,eff, in Eq. (6) is related with the latent heat absorption associated with melting progress within the MEPCM particles and can be expressed as

    xpcm hls Dnb xpcm Dnb ¼ cp;m 1 þ cp;eff ¼ cp;m 1 þ cp;m DT ref ;m Stem

ð7Þ

Such latent-heat-induced enhancement in the specific heat depends clearly on the Stefan number Stem (=cp,mDTref,m/hls), the mass fraction of phase change material xpcm, and the melting progress Dnb in the MEPCM particles. On the right-hand side of Eq. (6), the first term denotes a linear rise in the bulk temperature depending on the heat capacity and flow rate, as can be anticipated for the non-melting suspension flow (i.e. cp,eff/cp,m = 1) over a heated section of uniform heat flux; while the second term represents a retardation in the bulk temperature rise largely due to the latent-heat induced increase in the specific heat (i.e. cp,eff/cp,m > 1). Meanwhile, the increase in thermal conductivity due to the nanoparticles in the hybrid suspension can be seen to play a role counteracting, instead of supplementing, to that of the latent-heat induced increase in specific heat for hindering the bulk temperature rise. As a result, the bulk temperature of the melting-on-going suspension flow can rise rather nonlinearly, instead of linearly, along the iso-flux-heat tube. Alternatively, the bulk temperature rise of the melting-on-going suspension flow over the heated section may be viewed as a quantity reflecting the relative contribution by convective transport of sensible heat to that of latent heat in removing heat input at the tube. Further, Eq. (6) can be recast to relate the temperature difference between the inner wall and inlet suspension, [Tw,i(x+)  Tin], to that between the inner wall and bulk suspension, [Tw,i(x+)  Tb(x+)], as

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

 00

þ

q pdi x ½T w;i ðxþ Þ  T in  ¼ ½T w;i ðxþ Þ  T b ðxþ Þ þ i CmQ m  þ   q00i di =2 cp;eff  1 km cp;m

 þ

ð8Þ

Furthermore, in terms of the local heat transfer coefficients, hbtd (or þ the local Nusselt number, Nubtd ¼ hbtd di =km ), and hitd (or þ Nuitd ¼ hitd di =km ), Eq. (8) can be rewritten as

  1 1 pdþ xþ 1 dþi cp;eff ¼ þ i  1 hitd hbtd Cm Q m 2 km cp;m   þ 1 1 ðxþ =di Þ 1 cp;eff ¼ þ4  1 Nuitd Nubtd Pem 2 cp;m

ð9Þ ð10Þ

where Pem is the Peclet number of the suspension flow. Clearly, Eqs. (9) and (10) indicate that the magnitude of hitd (or Nuitd) for the non-melting suspension flow, including that for the pure nanofluid or water, should be increasingly lower than that of hbtd (or Nubtd) over the heated section of the tube, continuing to decline even linearly in the thermally fully developed region where hbtd (or Nubtd) is constant. In contrast, for the melting-on-going suspension flow, the streamwise decline of hitd (or Nuitd) may be significantly attenuated, depending on the combined effect of the simultaneous increases in the effective specific heat associated with the melting progress in MEPCM particles and the thermal conductivity (or thermal diffusivity) due to the nanoparticles contained. Further incorporating the scaling of Eq. (1), the temperature difference [Tw,i(x+)  Tb(x+)] in Eq. (8) (or the local heat transfer coefficient hbtd) may be scaled in the thermally developing (entrance) and fully-developed regions, respectively, as

½T w;i ðxþ Þ  T b ðxþ Þt;entrance ¼

q00i q00 dt;m  i hbtd km þ



q00i di ðxþ Þ1=2 1=2

1=2 1=2 Qm C m km ðcp;eff =cp;m Þ1=2

ð11aÞ

and þ

½T w;i ðxþ Þ  T b ðxþ Þt;fd ¼

q00i q00 ðd =2Þ  i i hbtd km

ð11bÞ

Here, the fact that temperature difference [Tw,i(x+)  Tb(x+)] must be invariant in the thermally fully developed region necessitates that the melting-on-going MEPCM particles of hybrid suspension should be fully melted in the thermally developing region. In other words, the hybrid suspension without the latent heat effect in the fully developed region behaves similar to the pure nanofluid, featuring increased thermal conductivity compared with the pure water. Further substitution of the above expressions for [Tw,i(x+)  Tb(x+)] into Eq. (8) yields the scaling for the rise of wall temperature (or the local heat transfer coefficient hitd) along the heated section as:

½T w;i ðxþ Þ  T in t;entrance ¼

q00i hitd

" þ 1=2 q00i ðdi =2Þ 2ðxþ Þ1=2 km  1=2 1=2 km Q m C m ðcp;eff =cp:m Þ1=2  þ    q00i pdi xþ cp;eff þ þ 1 cp;m Cm Q m

½T w;i ðx Þ  T in t;fd

 þ   þ  q00i di =2 q00i pdi xþ q00i ¼  þ km CmQ m hitd

latent-heat-increased specific heat of the hybrid suspension can act synergistically with the enhanced thermal conductivity due to the nanoparticles dispersed, promoting its effectiveness in suppressing primarily the rises of both [Tw,i(x+)  Tb(x+)] and [Tw,i(x+)  Tin], thus enhancing the local heat transfer coefficients, hbtd and hitd, over that of the pure water. One distinctive feature inherent in the suspension flow containing MEPCM particles is the inlet subcooling effect that there may be an entry length from the inlet of heated section for the onset of melting process if the inlet temperature of suspension is below the melting temperature of phase change material contained in MEPCM particles. Over such entry length for the onset of melting, the hybrid suspension flows without the latent heat effect (i.e. cp,eff/cp,m = 1) and its effectiveness in suppressing the streamwise increases of [Tw,i(x+)  Tb(x+)] and [Tw,i(x+)  Tin] would then rely solely on its increase in thermal conductivity due to nanoparticles dispersed, while offsetting by its decrease in heat capacity (or specific heat) compared with the pure water. Once the suspension flow in the tube becomes thermally fully developed, the temperature difference [Tw,i(x+)  Tb(x+)] reaches a constant, as indicated in Eq. (11b), while the wall temperature or [Tw,i(x+)  Tin] proceeds to rise linearly, in parallel with the bulk temperature, at a slope inversely proportional to the heat capacity and flow rate as revealed in Eq. (12b). In the fully developed region, the hybrid suspension flow, in which the MEPCM particles are expected fully-melted, behaves as that of pure nanofluid without the latent-heat effect, and thus its effectiveness in managing the isoflux-heated wall temperature rests solely on the increase in thermal conductivity compared with the pure water. Consequently, the constant temperature difference [Tw,i(x+)  Tb(x+)] for the hybrid suspension in the fully developed region can be expected smaller, in effect giving rise to enhancement in hbtd over that of pure water. In the aspect of effectiveness in suppressing the wall temperature rise, as indicated in Eq. (12b), the beneficial effect from the increased thermal conductivity of the hybrid suspension can be offset incrementally by the detrimental influence due to its lower heat capacity along the fully developed region particularly for the low flow rate. All in all, for local heat transfer enhancement, the beneficial effect from the latent-heated induced increase in specific heat associated with the melting-on-going MEPCM particles dispersed in the hybrid suspension can only arise in the thermally developing region, while that from increased thermal conductivity due to the nanoparticles dispersed can persist through the thermally developing and fully-developed regions. Nevertheless, the heat transfer efficacy of using the hybrid suspension to replace the pure water as forced convection fluid in the thermal developing and/or fully developed regions can be undermined by the detrimental influence due to its intrinsic decrease in heat capacity. 4. Heat transfer experiment results

ð12aÞ

and þ

2401

ð12bÞ

From Eqs. (11a) and (12a), it can be inferred that the temperature differences of ½T w;i ðxþ Þ  T b ðxþ Þ as well as [Tw,i(x+)  Tin] for the melting-on-going hybrid suspension flow can increase nonlinearly in the thermally developing region of an iso-flux heated tube. The

In this section, results obtained from the heat transfer experiments undertaken are presented to unveil the forced convective cooling effectiveness of utilizing the hybrid water-based suspensions containing various mass fractions of Al2O3 nanoparticles and MEPCM particles, compared with the pure PCM suspension (xnp = 0%), the pure nanofluid (xpcm = 0%), and the pure water (xpcm = 0% and xnp = 0%), respectively. First, to validate the experimental set-up as well as to form the basis for comparison of results for the hybrid suspensions, the heat transfer results obtained with the pure water as the working fluid in the tube were presented. Fig. 2 shows the streamwise variations of the local Nusselt numbers Nubtd/Nuitd, which are based on temperature differences between the inner wall and the local/inlet bulk fluid, respectively. The results of Nubtd were compared with

2402

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407 22

ωnp=0% , ωpcm=0%

20

Nu

 þ where x ¼ xþ =di =Pef . As can be discerned in Fig. 2, there exists very good agreement between the present experimental data and the predictions using Eq. (13), validating thus the experimental set-up constructed in the present study. Also included in Fig. 2 is the comparison of the experimental results of Nuitd with the predictions based on Eq. (10), showing good agreement as well and hence confirming its continuing decline trend over the heated section along the tube. Next, to quantify capability of the hybrid suspension flow in managing the iso-flux-heated tube wall temperature, local heat transfer effectiveness, eh, is defined as the ratio of its local heat transfer coefficient hitd over that of the pure water flow as

Exp.

Corr.

Nubtd

18

Nuitd

16

Nu

14 12 10 8 6 4 2 0

eh ¼ 0

0.05

+

0.1

+

x / (di Pe f )

0.15

In Figs. 3 and 4, the axial variations of local heat transfer effectiveness are illustrated for the hybrid suspensions through the heated section imposed by different heating flux at the lowest and highest flow rates of Qf (=12.5 and 240 cm3/min), respectively. From the results for the pure PCM suspensions (xnp = 0%) in Figs. 3 and 4, one can notice that in the presence of inlet subcooling effect, there may exist an entry length from inlet of the heated section, over which the wall temperature suppression capability of the pure PCM suspension appears inferior to that of the pure water and/or nanofluid (symbolized by the fully-filled circles in the figures), depending on the heating flux and flow rate. The entry

the predictions from following correlation [33] for laminar thermally developing flow in an iso-flux tube as: 8 1=3 1 for x 6 0:00005 > < 1:302x 1=3 Nubtd ¼ 1:302x  0:5 for 0:00005 6 x 6 0:0015 > : 3  0:506 41x e for x P 0:0015 4:364 þ 8:68ð10 x Þ

ð13Þ ωpcm Symbols 2% 1.5 5% 10%

ð14Þ

0.2

Fig. 2. Validation of the experimental set-up.

1.6

hitd;m hitd;f

ωpcm Symbols ωnp=2% 0% * Stem=0.0939±0.0023 2% * 5% Sbm=0.6867±0.0313 10%

ωnp=0% Ste*m=0.1001±0.0021 *

Sbm=0.6553±0.0286

1.4

ωpcm Symbols ωnp=10% 0% * Stem=0.0817±0.0024 2% * 5% Sbm=0.7392±0.0358 10%

εh

1.3

1.2

1.1

1

Nanofluid 0.9

0

0.05

0.1 +

+

0.15

0.2

0

0.05

0.1 +

x / (di Pe f )

+

Nanofluid

0.15

0

0.2

0.05

x / (di Pe f )

0.1 +

+

0.15

0.2

x / (di Pe f ) "

3

2

(a) qo′′ = 1989 W/m 2 1.6

ωpcm Symbols 2% 1.5 5% 10%

ωpcm Symbols ωnp=2% 0% Ste*m=0.3005±0.0073 2% 5% Sb*m=0.2148±0.0098 10%

ωnp=0% Ste =0.3199±0.0068 * m

Sb*m=0.2049±0.0090

1.4

ωpcm Symbols ωnp=10% 0% Stem*=0.2614±0.0079 2% 5% Sb*m=0.2312±0.0111 10%

εh

1.3

1.2

1.1

1

Nanofluid 0.9

0

0.05

0.1 +

+ i

0.15

0.2

0

0.05

0.1 +

x / (d Pe f )

+ i

Nanofluid

0.15

0

0.2

x / (d Pe f ) 3

0.05

0.1 +

+

0.15

0.2

x / (di Pe f ) "

2

(b) qo′′ = 5968.3 W/m 2 Fig. 3. Local heat transfer effectiveness for the hybrid water-based suspensions at the lowest flow rate of Qf = 12.5 cm3/min along the tube heated at the heat flux of (a) 1989 W/m2 and (b) 5968.3 W/m2.

2403

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

By comparing with those for the pure PCM suspension, the data for the hybrid suspensions shown in Figs. 3 and 4 clearly reveal that adding Al2O3 nanoparticles into the pure PCM suspension of fixed xpcm may improve or worsen the local heat transfer effectiveness, depending on the nanoparticle fraction, the flow rate, and/or heating flux. Under the lowest flow rate of Qf = 12.5 cm3/min in the tube imposed with the heat flux of q00o ¼ 1989 W=m2 , adding the nanoparticles of xnp = 2% in the pure PCM suspension of xpcm = 10% produces the most synergistic benefit of the hybrid suspension, further augmenting the largest local heat transfer enhancement to 45% as shown in Fig. 3. Meanwhile, the adding of nanoparticles may promote the inlet subcooling effect for the MEPCM particles, leading to longer entry length for onset of melting and thus significant local heat transfer enhancement under the condition of high flow rate and low heating flux, in particular. In contrast to that above-elaborated for the pure PCM suspension, the pure nanofluid appears most effective in suppressing the wall temperature at the inlet of heated section with a generally decline trend toward downstream as illustrated in Figs. 3 and 4. Specifically, at the lowest flow rate of Qf = 12.5 cm3/min (shown in Fig. 3), the local heat transfer enhancement can only arise for the nanofluid over an entry length from the inlet of heated section, depending on the particle fraction. Beyond the entry length, marked deterioration, instead of enhancement, in local heat transfer coefficient occurs for the pure nanofluid particularly in the thermally fully developed region, which can be contributed to its

length for onset of significant heat transfer enhancement for the pure PCM suspension flow of fixed xpcm appears noticeably shifted upstream with increasing heating flux and/or decreasing flow rate. Beyond the entry length, the effect of latent-heat absorption due to melting progress in the MEPCM particles becomes increasingly predominant toward downstream, giving rise to highly enhanced effectiveness in the local wall temperature suppression over that of the pure water or nanofluid, which appears increasingly distinctive with the increase of MEPCM particle fraction. Specifically, as can be discerned in Fig. 3, the largest enhancement of about 42% in the local heat transfer coefficient can be achieved for the pure PCM suspension of xpcm = 10% under the condition of the lowest flow rate of Qf = 12.5 cm3/min through the tube to impart the heat flux of q00o ¼ 1989 W=m2 . Further scrutiny of Fig. 3 reveals that with increasing heating flux, the above-delineated axially increasing trend of the local heat transfer effectiveness for the pure PCM suspension becomes significantly subdued with increasingly upstream shifting of the axial location for the occurrence of the highest local heat transfer enhancement from exit of the heat section. With increasing flow rate of the pure PCM suspension, the residence time and hence, in effect, the melting progress of the MEPCM particles over the heated section becomes increasingly retarded. As shown in Fig. 4, with the flow rate increased up to 240 cm3/min (Ref = 1801), the largest local heat transfer enhancement for the pure PCM suspension of xpcm = 10% decreases to around 15% under the condition of heating flux at 5969.3 W/m2.

1.3

ωpcm Symbols ωnp=2% 0% Ste*m=0.2186±0.0053 2% * 5% Sbm=0.2953±0.0134 10%

ωpcm Symbols ωnp=0% 2% Ste*m=0.2325±0.0050 5% * 10% Sbm=0.2818±0.0123

1.25 1.2

εh

1.15

ωpcm Symbols ωnp=10% 0% Ste*m=0.1901±0.0057 2% * 5% Sbm=0.3179±0.0155 10% Nanofluid

Nanofluid

1.1 1.05 1 0.95 0.9

0

0.005 +

+

x / (di Pe f )

0.01

0

0.005 +

+

x / (di Pe f )

0.01

0

0.005 +

+

x / (di Pe f )

0.01

(a) qo′′ = 3978.8 W/m 2 1.3

ωpcm Symbols ωnp=0% 2% Ste*m=0.3489±0.0075 1.25 5% 10% Sb*m=0.1878±0.0082

ωpcm Symbols ωnp=2% 0% Ste*m=0.3295±0.0063 2% 5% Sbm*=0.2004±0.0125 10%

1.2

ωpcm Symbols ωnp=10% 0% Stem*=0.2806±0.0132 2% * 5% Sbm=0.2157±0.0141 10%

εh

1.15 1.1 1.05 1 0.95 0.9

Nanofluid

Nanofluid 0

0.005 +

+

x / (di Pe f )

0.01

0

0.005 +

+

x / (di Pe f )

0.01

0

0.005 +

+

x / (di Pe f )

0.01

(b) qo′′ = 5968.3 W/m 2 Fig. 4. Local heat transfer effectiveness for the hybrid water-based suspensions at the highest flow rate of Qf = 240 cm3/min along the tube heated at the heat flux of (a) 3978.8 W/m2 and (b) 5968.3 W/m2.

2404

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

nanofluid or the pure PCM suspension particularly in the thermally developing region in which the synergistic benefit from the simultaneous increases in thermal conductivity and specific heat predominates. To produce the best synergistic benefit for the local heat transfer enhancement in the tube flow, there may be optimum composition of MEPCM particles and nanoparticles for the hybrid suspension under certain operation condition, including the flow rate and/or heating flux. Furthermore, the benefit of using the hybrid suspension flow for managing the surface-averaged wall temperature is examined based on an effectiveness of the average heat transfer coefficient over the heated section eh , which takes the form of

relatively lower heat capacity than the pure water, as deducted earlier in Eq. (12b). Such detrimental effect can become increasingly minute with the increase in the flow rate. As shown in Fig. 4, with flow rate increased up to 240 cm3/min (Ref = 1801), the local heat transfer effectiveness of the nanofluid becomes significantly improved, displaying a somewhat uniform enhancement of around 6% in the local heat transfer coefficient over the heated section for the nanofluid of xnp = 10%. Nevertheless, within the ranges of parameters considered, the pure nanofluid performs generally inferior to the pure PCM suspension in the effectiveness in suppressing the iso-flux-heated wall temperature. To further upgrade the effectiveness in the wall temperature management, utilizing the hybrid suspension to replace the pure nanofluid does produce the highly beneficial effect; in particular, giving rise to significantly enhanced heat transfer effectiveness over the region where the heat transfer deterioration arises for the pure nanofluid, as illustrated in Figs. 3 and 4. However, adding the MEPCM particles in the pure nanofluid may inevitably introduce the inherent inlet subcooling effect elaborated earlier that the local heat transfer performance of the resulting hybrid suspension may thus become markedly deteriorated, instead of enhanced, compared with the pure nanofluid particularly under the condition of lower heating flux. More noteworthy is that the benefit from using the hybrid suspension to replace the pure nanofluid to improve the cooling effectiveness appears much better than that to replace the pure PCM suspension. Lastly, an overview of Figs. 3 and 4 reveals that compared with the pure water, the hybrid suspensions can outperform the pure

1.3

ωnp ωpcm Symbols 2% 1.25 5% 10% 0%

Ste*m=0.2212±0.0164 * m

Sb =0.2981±0.0286

 h

eh ¼ idt;m hidt;f

ð15Þ

For the conditions considered, the results shown in Fig. 5 clearly demonstrate that the hybrid suspensions are generally capable of further promoting the effectiveness in suppressing the surfaceaveraged wall temperature over the iso-flux heated tube compared with the pure PCM suspension, the pure nanofluid, or the pure water. The largest enhancement of around 23% in the averaged heat transfer coefficient over that of the pure water can be detected for the hybrid suspension of xpcm = 10% and xnp = 2% with the heating flux of q00o ¼ 3978 W=m2 . Similar to what observed for the local heat transfer effectiveness, adding MEPCM particles to the pure nanofluid of fixed xnp is relatively more conducive to upgrade the surface-averaged cooling effectiveness over the entire range of flow rate considered. Specifically, at lowest flow rate of 12.5 cm3/min,

ωnp ωpcm Symbols Ste*=0.2079±0.0160 m

ωnp ωpcm Symbols Ste*=0.1809±0.0149 m

2%

10% 0% 2% 5% 10%

1.2

0% 2% 5% 10%

* m

Sb =0.3125±0.0306

*

Sbm=0.3364±0.0340

1.15

εh

|

1.1 1.05 1

Nanofluid 0.95 +

+

lh / ( di Pe f ) 1.3

ωnp ωpcm Symbols 2% 1.25 5% 10% 0%

0.1

0.2

*

Stem=0.4559±0.0193 * m

Sb =0.1437±0.0090

1.2

+

+

lh / ( di Pe f ) qo" = 3978.8W / m 2

Nanofluid 0.1

0.2

+

+

lh / ( di Pe f )

0.1

ωnp ωpcm Symbols Ste*=0.4285±0.0190 m

ωnp ωpcm Symbols Ste*=0.3733±0.0183 m

2%

10% 0% 2% 5% 10%

0% 2% 5% 10%

* m

Sb =0.1502±0.0093

0.2

*

Sbm=0.1615±0.0103

1.15

εh

|

1.1 1.05 1

Nanofluid 0.95 +

+

lh / ( di Pe f )

0.1

0.2

+

+

lh / ( di Pe f ) qo" = 7957.7W / m 2

Nanofluid 0.1

0.2

+

+

lh / ( di Pe f )

0.1

0.2

Fig. 5. Effectiveness of surface-averaged heat transfer enhancement of the hybrid water-based suspensions in the tube heated at different heating fluxes.

2405

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

3

ωnp

2

0%

ωnp 2%

ωpcm Symbols 0% 2% 5% 10%

ωnp 10%

ωpcm Symbols 0% 2% 5% 10%

f

1

ωpcm Symbols 0% 2% 5% 10%

64/Ref

64/Ref

1000

64/Ref

2000

1000

2000

1000

Ref

Ref

2000

Ref

Fig. 6. Friction factor versus the Reynolds number for the pure water and the hybrid water-based suspension flows.

the deterioration in the averaged heat transfer coefficient of the pure nanofluid of xnp = 10%, as indicated by a value of 0.98 for eh in Fig. 5, can be reversed yielding an enhancement of about 20% with the adding of MEPCM particles up to xpcm = 10%. By contrast, the benefit of adding nanoparticles into the pure PCM suspension appears rather moderate, strongly dependent of the flow rate and heating flux. Next, the measured results of the pressure drop across the test section of tube for the hybrid suspensions of various particle fractions are presented in terms of the Darcy friction factor against the

1.2

ωnp

ωpcm

0%

2% 5% 10%

1.1

ωnp

Symbols Ste*m=0.2212±0.0164

2%

* m

Sb =0.2981±0.0286

ωpcm 0% 2% 5% 10%

Reynolds number Ref, as shown in Fig. 6. In the case of pure water, the experimental data appear in good agreement with those predicted by the classic formula for the hydrodynamically fully developed laminar flow (f = 64/Ref). Resulted from the drastic increase in the dynamic viscosity found in Ref. [31], the friction factors for the hybrid suspension flow appear increasingly enhanced with the MEPCM particle fraction, in particular. Specifically, a sharp increase of more than two times in the friction factor over that for the pure water can be detected for the hybrid suspension of xpcm = 10% and xnp = 10%.

Symbols

ωnp ωpcm 10% 0% 2% 5% 10%

Ste*m=0.2079±0.0160 * m

Sb =0.3125±0.0306 Nanofluid

Symbols

Ste*m=0.1809±0.0149 *

Sbm=0.3364±0.0340 Nanofluid

FT w

1 0.9 0.8 0.7 0.6 +

+

lh / ( di Pe f )

1.2 1.1

ωnp

ωpcm

0%

2% 5% 10%

0.1

0.2

+

ωnp

Symbols Stem*=0.4559±0.0193

2%

* m

Sb =0.1437±0.0090

+

lh / ( di Pe f ) qo" = 3978.8W / m 2 ωpcm 0% 2% 5% 10%

Symbols

0.1

0.2

+

ωnp ωpcm 10% 0% 2% 5% 10%

*

Stem=0.4285±0.0190 * m

Sb =0.1502±0.0093 Nanofluid

+

lh / ( di Pe f ) Symbols

0.1

0.2

*

Stem=0.3733±0.0183 * m

Sb =0.1615±0.0103 Nanofluid

FT w

1 0.9 0.8 0.7 0.6 +

+

lh / ( di Pe f )

0.1

0.2

+

+

lh / ( di Pe f ) qo" = 7957.7W / m 2

0.1

0.2

+

+

lh / ( di Pe f )

0.1

0.2

Fig. 7. Figure of merit ðF T w Þ on the maximum wall temperature suppression for the hybrid water-based suspensions in the tube heated at different heat fluxes.

2406

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

pure PCM suspension with the particle fraction and flow rate exhibit a strong dependence on the heating flux imposed over the heated section. Most noteworthy is that there might be a distinctive flow rate beyond which the general trend of increasing F T w of the pure PCM suspension with the particle fraction xpcm reverses that its merit parameter tends to decrease significantly with the particle fraction, which becomes distinctive with decreasing flow rate, in particular. Similar trends of the pure PCM suspension and nanofluid, as elucidated in Fig. 8, can be observed for variations of the merit factor in the surface- averaged heat transfer enhancement, F h .

Finally, the efficacy of using the hybrid suspensions flow formulated for improving forced convective cooling performance is further assessed by means of two figures of merit F T w and F h defined respectively as

½ðT w;i  T in Þmax;f =ðT w;i  T in Þmax;m 

FTw ¼

ð16Þ

ðfm =ff Þ1=3

and

  h idt;m =hidt;f

F h ¼

ð17Þ

ðfm =ff Þ1=3

5. Conclusions

which, in effect, weigh quantitatively the enhancements in the maximum wall temperature (or the hotspot) management and the surface-averaged heat transfer coefficient against the corresponding pressure drop penalty, respectively. Results are illustrated in Figs. 7 and 8 for the hybrid suspensions formulated as they vary with the  þ  þ parameter lh = di Pef . Penalized by the drastically higher pressure drop than that for the pure water displayed in Fig. 6, the values of both F T w and F h for the hybrid suspensions clearly reveal their generally inferior efficacy to that of the pure PCM suspension and/or nanofluid to replace the pure water as the forced convection fluid in the tube flow. Specifically from Fig. 7, one can notice that the values of F T w for the pure PCM suspension and nanofluid appear quiet comparable, falling into the ranges of 0.93–1.03 and 0.89–0.99, respectively, which depends markedly on the particle fraction and flow rate. Regardless of the heating flux, the figure of merit for the pure nanofluid tends to decrease with the particle fraction while increase with the flow rate. In contrast, the variations of F T w for the ωnp ωpcm Symbols 2% 1.2 5% 10% 0%

Ste*m=0.2212±0.0164 * m

Sb =0.2981±0.0286

An experimental study of the laminar forced convection of water-based hybrid suspensions of Al2O3 nanoparticles and MEPCM particles in a circular tube heated with constant heat flux was presented together with an integral energy analysis and scaling estimation to relate the thermal properties of the hybrid suspensions formulated to the forced convective cooling effectiveness. The relative changes in the thermal conductivity, the specific heat, and the heat capacity of the hybrid suspension with respect to the base fluid can have different bearing on the axial variations of the bulk temperature, the wall temperature, and the local heat transfer characteristics over the thermally developing and fully-developed regions in the tube. For local heat transfer enhancement, the beneficial effect from the latent-heated induced increase in specific heat associated with the melting-on-going MEPCM particles contained in the hybrid suspension can only arise in the thermally developing region, while that from increased

ωnp ωpcm Symbols Ste*=0.2079±0.0160 m

ωnp ωpcm Symbols Ste*=0.1809±0.0149 m

2%

10% 0% 2% 5% 10%

0% 2% 5% 10%

* m

Sb =0.3125±0.0306 Nanofluid

*

Sbm=0.3364±0.0340 Nanofluid

1

Fh

|

0.8

0.6 +

+

lh / ( di Pe f )

0.1

0.2

+

+

lh / ( di Pe f ) q = 3978.8W / m 2

0.1

0.2

+

+

lh / ( di Pe f )

0.1

0.2

" o

ωnp ωpcm Symbols 2% 1.2 5% 10% 0%

Ste*m=0.4559±0.0193 * m

Sb =0.1437±0.0090

ωnp ωpcm Symbols Ste*=0.4285±0.0190 m

ωnp ωpcm Symbols Ste*=0.3733±0.0183 m

2%

10% 0% 2% 5% 10%

0% 2% 5% 10%

* m

Sb =0.1502±0.0093 Nanofluid

*

Sbm=0.1615±0.0103 Nanofluid

1

Fh

|

0.8

0.6 +

+

lh / ( di Pe f )

0.1

0.2

+

+

lh / ( di Pe f ) qo" = 7957.7W / m 2

0.1

0.2

+

+

lh / ( di Pe f )

0.1

0.2

Fig. 8. Figure of merit ðF h Þ on the surface-averaged heat transfer enhancement for the hybrid water-based suspensions in the tube heated at different heat fluxes.

C.J. Ho et al. / International Journal of Heat and Mass Transfer 54 (2011) 2397–2407

thermal conductivity due to the nanoparticles dispersed persists through the thermally developing and fully-developed regions. Nevertheless, the intrinsic decrease in heat capacity of the hybrid suspension compared with the pure water tends to affect detrimentally, undermining its heat transfer efficacy in the thermal developing and/or fully developed regions. Results of the heat transfer experiments generally demonstrate that because of the synergistic benefit from the simultaneous increases in the specific heat and thermal conductivity, the forced convective cooling effectiveness of the hybrid suspension can be significantly upgraded as compared with the pure PCM suspension, the pure nanofluid, or the pure water. In particular, the efficacy of using the hybrid suspension for improving the cooling performance versus the pure nanofluid is found much better than that versus the pure PCM suspension. However, when taking into account the pressure drop penalty from its drastically increased viscosity, the merits of the hybrid suspension being effective coolant in an iso-flux heated tube can be severely degraded compared with the pure PCM suspension or the pure nanofluid. This suggests a need of developing effective means to reduce viscosity of the hybrid suspension for improving its convective cooling outlook. Acknowledgement The present study was supported by National Science Council (NSC) of ROC in Taiwan under Project Nos. NSC94-2212-E006101 and NSC95-2212-E006-233. References [1] H. Inaba, New challenge in advanced thermal energy transportation using functionally thermal fluids, Int. J. Therm. Sci. 39 (2000) 991–1003. [2] R. Hart, F. Thorton, Microencapsulation of phase change materials, Final Report Contract No. 82-80, Department of Energy, Ohio, 1982. [3] W. Yu, D.M. France, J.L. Routbort, S.U.S. Choi, Review and comparison of nanofluid thermal conductivity and heat transfer enhancements, Heat Transfer Eng. 29 (2008) 432–460. [4] S.U.S. Choi, Nanofluids: from vision to reality through research, J. Heat Transfer 131 (2009) 033106. [5] X. Wang, X. Xu, S.U.S. Choi, Thermal conductivity of nanoparticle–fluid mixture, J. Thermophys. Heat Transfer 13 (1999) 474–480. [6] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal conductivity and viscosity of liquids by dispersing ultra-fine particles (dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles), Netsu Bussei (Japan) 4 (1993) 227–233. [7] S.K. Das, N. Putra, P. Thiesen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, J. Heat Transfer 125 (2003) 567–574. [8] J.C. Maxwell, A Treatise on Electricity and Magnetism, second ed., Oxford University Press, Cambridge, 1904. pp. 435–441. [9] C.W. Sohn, M.M. Chen, Microconvective thermal conductivity in disperse twophase mixtures as observed in a low velocity Couette flow experiment, ASME J. Heat Transfer 103 (1981) 47–51. [10] C.W. Sohn, M.M. Chen, Heat transfer enhancement in laminar slurry pipe flows with power law thermal conductivities, ASME J. Heat Transfer 106 (1984) 539–542.

2407

[11] K.E. Kasza, M.M. Chen, Improvement of the performance of solar energy or waste heat utilization systems by using phase-change slurry as an enhanced heat-transfer storage fluid, ASME J. Solar Energy Eng. 107 (1985) 229–236. [12] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer 11 (1998) 151–170. [13] Y. Xuan, Q. Li, Investigation on convective heat transfer and fluid flow features of nanofluids, J. Heat Transfer 125 (2003) 151–155. [14] D. Wen, Y. Ding, Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions, Int. J. Heat Mass Transfer 47 (2004) 5181–5188. [15] S.E.B. Maïga, C.T. Nguyen, Heat transfer behaviours of nanofluids in a uniformly heated tube, Superlattices Microstruct. 35 (2004) 543–557. [16] K.S. Hwang, S.P. Jang, S.U.S. Choi, Flow and convective heat transfer characteristics of water-based Al2 O3 nanofluids in fully developed laminar flow regime, Int. J. Heat Mass Transfer 52 (2009) 193–199. [17] U. Rea, T. McKrell, L.W. Hu, J. Boungiorno, Laminar convective heat transfer and viscous pressure loss of alumina–water and zirconia–water nanofluids, Int. J. Heat Mass Transfer 52 (2009) 2042–2048. [18] P. Charunkyakorn, S. Sengupta, S.K. Roy, Forced convective heat transfer in microencapsulated phase change material slurries: flow in circular ducts, Int. J. Heat Mass Transfer 34 (1991) 819–833. [19] M. Goel, S.K. Roy, S. Sengupta, Laminar forced convective heat transfer in microencapsulated phase change material suspensions, Int. J. Heat Mass Transfer 37 (1994) 593–604. [20] Y. Yamagishi, H. Takeuchi, A.T. Pyatenko, N. Kayukwa, Characteristics of microencapsulated PCM slurry as a heat transfer fluid, AIChE J. 45 (1999) 696– 707. [21] C.J. Ho, J.F. Lin, S.Y. Chiu, Heat transfer of solid–liquid phase-change material suspensions in circular pipes: effects of wall conduction, Numer. Heat Transfer A 45 (2004) 171–190. [22] J.F. Lin, C.J. Ho, Thermally developing forced convection for PCM suspensions in a circular duct, J. Chinese Soc. Mech. Eng. 26 (2005) 45–53. [23] B. Chen, X. Wang, Y. Zhang, H. Xu, R. Yang, Experimental research on laminar performance of phase change emulsion, Appl. Therm. Eng. 26 (2006) 1238–1245. [24] X. Wang, J. Niu, Y. Li, X. Wang, B. Chen, R. Zeng, Q. Song, Y. Zhang, Flow and heat transfer behaviors of phase change material slurries in a horizontal circular tube, Int. J. Heat Mass Transfer 50 (2007) 2480–2491. [25] B. Chen, X. Wang, R. Zeng, Y. Zhang, X. Wang, J. Niu, Y. Li, H. Di, An experimental study of convective heat transfer with microencapsulated phase change material suspension: laminar flow in a circular tube under constant heat flux, Exp. Therm. Fluid Sci. 32 (2008) 1638–6146. [26] R. Zeng, X. Wang, B. Chen, Y. Zhang, J. Niu, H. Di, Heat transfer characteristics microencapsulated phase change material slurry in laminar flow under constant heat flux, Appl. Energy 86 (2009) 2661–2670. [27] A. Bejan, Convection Heat Transfer, second ed., Wiley, 1995. [28] S.Q. Zhou, R. Ni, Measurement of the specific heat capacity of water-based Al2 O3 nanofluid, Appl. Phys. Lett. 92 (2008) 093123. [29] R.S. Vajiha, D.K. Das, Specific heat measurement of three nanofluids and development of new correlations, J. Heat Transfer 131 (2009) 071601. [30] T.L. Bergman, Effect of reduced specific heats of nanofluids on single phase laminar internal forced convection, Int. J. Heat Mass Transfer 52 (2009) 1240–1244. [31] C.J. Ho, J.B. Huang, P.S. Tsai, Y.M. Yang, Preparation and properties of hybrid water-based suspension of Al2 O3 nanoparticles and MEPCM particles as functional forced convection fluid, Int. Commun. Heat Mass Transfer 37 (2010) 490–494. [32] Y.H. Tseng, M.H. Fang, P.S. Tsai, Y.M. Yang, Preparation of microencapsulated phase-change materials (MCPCMs) by means of interfacial polycondensation, J. Microencapsulation 22 (2005) 37–46. [33] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts, Supplement 1 to Advances in Heat Transfer, Academic, New York, 1978.