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International Journal of Thermal Sciences 63 (2013) 115e124

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International Journal of Thermal Sciences

journal homepage: www.elsevier .com/locate/ i j ts

Natural convection heat transfer inside vertical circular enclosure filled withwater-based Al2O3 nanofluids

Mohamed Ali a,b,*, O. Zeitoun a,b, Salem Almotairi a

aKing Saud University, College of Engineering, Mechanical Engineering Department, P. O. Box 800, Riyadh 11421, Saudi ArabiabKing Abdullah Institute for Nanotechnology, Saudi Arabia

a r t i c l e i n f o

Article history:Received 15 September 2011Received in revised form18 July 2012Accepted 19 July 2012Available online 24 August 2012

Keywords:EnclosureNanofluidNatural convectionExperimental correlations

* Corresponding author. King Saud University, CollegEngineering Department, P. O. Box 800, Riyadh 11421,6672; fax: þ966 1 467 6652.

E-mail address: mali@ksu.edu.sa (M. Ali).

1290-0729/$ e see front matter � 2012 Elsevier Mashttp://dx.doi.org/10.1016/j.ijthermalsci.2012.07.008

a b s t r a c t

Experimental investigation on natural convection heat transfer has been carried out inside verticalcircular enclosures filled with Al2O3 nanofluid with different concentrations; 0.0%, 0.85% (0.21%), 1.98(0.51%) and 2.95% (0.75%) by mass (volume). Two enclosures are used with 0.20 m inside diameter andwith two different aspect ratios. The bottom surface of the enclosure is heated using a constant heat fluxflexible heater while the upper surface is cooled by an ambient air stream. Various uniform heat fluxeshave been used to generate the natural convection heat transfer data. The average Nusselt number isobtained and correlated with the modified Rayleigh number at each concentration ratio of the nanofluid.The average Nusselt number is obtained for each enclosure and correlated with the modified Rayleighnumber using the concentration ratio as a parameter. The results show that the heat transfer coefficientincreases as the concentration increases up to a specific value of the concentration and then it decreasesas the concentration continues to increase compared to the basic fluid of pure water. Furthermore,a general correlation is obtained using the volume fraction and the aspect ratio as parameters.

� 2012 Elsevier Masson SAS. All rights reserved.

1. Introduction

Natural convection heat transfer in enclosures has many engi-neering applications such as heating and cooling of buildings, solarcollectors, double pane windows and many other applications. Thecomprehensive review of such enclosures has been reported byOstrach [1]. Recently, nanofluid is used as a working fluid insideenclosures for its promising physical properties specially thethermal conductivity. A comparative numerical study of differentmodels based on the physical properties of the nanofluid wasanalyzed in detail by Khanafer et al. [2] for two-dimensional rect-angular enclosure with differentially heated side walls. Their studyhas shown that the suspended nanoparticles substantially increasethe heat transfer rate at any given Grashof number. In addition,their results have illustrated that nanofluid heat transfer rateincreases with an increase in the nanoparticles volume fraction. Jouand Tzeng [3] have studied numerically the heat transferenhancement in a rectangular enclosure filled with nanofluid. Theirstudy has shown that increasing the buoyancy parameter and the

e of Engineering, MechanicalSaudi Arabia. Tel.: þ966 1 467

son SAS. All rights reserved.

volume fraction of nanofluids causes an increase in the averageheat transfer coefficient. Hwang et al. [4] have shown theoreticallythat inside a rectangular cavity heated from below the ratio of heattransfer coefficient of the nanofluids to that of the base fluiddecreases as the size of nanoparticles increases. Putra et al. [5] haveconducted an experimental study of Al2O3 nanofluid naturalconvection in a horizontal cylindrical cavity heated from one sideand cooled from the other. Their results showed heat transferdeterioration with increasing both the nanoparticle concentrationand the aspect ratio. Natural convection of Titanium oxide nano-fluid in a circular enclosure heated from below has been reportedby Wen and Ding [6]. In their experimental study they have showna systematic decrease in the natural convection heat transfercoefficient with increasing the particle concentration. The influ-ences due to adopting various formulas for the effective thermalconductivity and dynamic viscosity of alumina-water nanofluid onthe heat transfer characteristics have been investigated numericallyfor natural convection in a vertical square enclosure by Ho et al. [7].Their results have revealed that, in contrast to the numerical resultsin [2], using the nanofluid inside the enclosure does not alwaysresult in an increase of the averaged Nusselt number. This behaviordepends mainly on the Rayleigh number as well as the formulasused for the effective dynamic viscosity. Heat transfer enhance-ment using copperewater nanofluid in a two dimensional enclo-sure has been numerically studied for a wide range of Rayleigh

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124116

number and a solid volume fraction by Santra et al. [8]. Their resultsagreed with [5] and [6] where the average Nusselt number steadilydecreased for increasing the nanoparticle concentration for someRayleigh numbers however, it increased with the Rayleigh numberfor a particular concentration. Santra et al. [9] have confirmed theresults of [8] by considering the nanofluid to be non-Newtonianusing neural network. Chang et al. [10] have showed, for circularenclosure filled with Al2O3 nanofluid and heated from below, alsoa decrease in Nusselt number compared to that of the pure water.This behavior was pronounced at lower Rayleigh number andhigher particle concentration. Oztop and Abu-Nada [11] have re-ported a numerical study of natural convection in partially heatedvertical rectangular enclosures filled with nanofluids. In theirresults they have found that the heat transfer enhancement is morepronounced at low aspect ratio than at high aspect ratio. Localisedheat source at the bottom of a nanofluid filled enclosure has beenstudied numerically by Aminossadati and Ghasemi [12]. Theirresults indicated that adding nanoparticles into pure waterimproves its cooling performance especially at low Rayleighnumbers. Similar results have been obtained by Ghasemi andAminossadati [13] using an oscillating heat flux on the left wall ofa vertical enclosure. Kumar et al. [14] have shown numerically anincrease in the average Nusselt number as the solid volume fractionincreases using four different models of thermo-physical nano-fluids in a vertical enclosure. Abu-Nada et al. [15] have shown thatusing nanofluids in a vertical enclosure reduces the average Nusseltnumber for high Rayleigh number as the volume fraction increaseshowever, a slight increase in the Nusselt number was observed atlow Rayleigh number as the volume fraction increases. Numericaland analytical analyses have done by Alloui et al. [16] for naturalconvection of nanofluids in a shallow cavity heated from below.Their results showed that when the Rayleigh number is relativelysmall and below a value that depends upon both concentrationsand the type of nanofluid, it was found that the heat transfer is lessthan that for pure water. On the other hand, above this value, thistrend was reversed and depended on the type of nanofluids. Hoet al. [17] have shown experimentally that the efficacy of applyingthe nanofluid for natural convection heat transfer enhancement inenclosure is inferred to be generally infeasible. They have also re-ported that the average heat transfer rate across the differentiallyheated vertical enclosure revealed systematic heat transfer degra-dation for the nanofluid containing nanoparticles of�2% (vol.) overthe entire range of the Rayleigh number. However, for the nanofluidcontaining much lower particle fraction of 0.1% (vol.), a heattransfer enhancement of around 18% compared with that of waterwas found at sufficiently high Rayleigh number. Li and Peterson[18] have reported a heat transfer deterioration of the Al2O3 waternanofluid in an enclosure heated from above. On the other hand, Yuet al. [19] have reported that at constant Grashof numbers the timeaveraged Nusselt number was lowered as more nanoparticles wereadded to the base liquid and would be overestimated if thebrowning motion effects were not considered. Natural convectionin tilted enclosure filled with different nanofluids has been re-ported numerically by Kahveci [20]. His results showed an increasein the average heat transfer rate by various amounts dependson the Rayleigh number and the inclination angle of the enclosure.The effect of non-uniform particle diameter and temperature onthe thermal conductivity of nanofluids in a vertical enclosure hasbeen studied by Lin and Violi [21].

As seen, from the previous review of natural convection inrectangular and square enclosures filled with nanofluids, theaveraged Nusselt number decreases as the volume fraction of thenanoparticles increases and this behavior mostly supported byexperimental studies. On the other hand, other studies have shownthe reverse effect and this is mostly supported by numerical

studies. In the present study experiments have done on naturalconvection heat transfer in vertical circular enclosures heated frombelow using Al2O3 nanofluid with four various concentrations; 0.0,0.21, 0.51 and 0.75 percentage by volume.

2. Experimental apparatus

The enclosure experimental apparatus is shown in Fig. 1 whereall components used in the present study are shown. The maincomponent of the experimental test rig is the enclosure which isshown in details in Fig. 1(a). As seen in this figure, two circularenclosures (7) are made of Bakelite (k ¼ 0.15 W/mK [22]) with aninside diameter of 0.20 m and with two different aspect ratios(k ¼ L/D ¼ 0.0635 and 0.127). The outer dimensions of the enclo-sures are 0.30 � 0.30 m2. The Bakelite enclosure is sandwichedbetween two nickel electroplated copper plates (5) of dimensions0.30� 0.30� 0.005 m3 (k¼ 398W/mK [22]). Two gasket sheets (6)are placed between the Bakelite and the copper plate to preventany leakage problem. The enclosure is heated using a flexible foilheater (4) with a diameter of 0.20 m, a maximum thickness of2.54 � 10�4 m (0.01in), and a maximum power of 1.55 � 104 W/m2

(10 W/in2). The heater is insulated by a Bakelite material (2) whosedimensions are 0.30 � 0.30 � 0.02 m3 followed by an insulatingmaterial made of polystyrene (1) (k ¼ 0.035 W/mK [22])0.30 � 0.30 � 0.10 m3. The enclosure parts (2e7) are assembled asone unit in the same order as it shown in Fig. 1(aeb) using six0.012 m bolts as shown in Fig. 1(c). Fig. 1(c) also shows two holes onthe sides of the enclosure used for two-way valves (8): one forfilling the enclosure and the other for ventilation. The surfacetemperatures are measured at eleven points along the diameter ofthe enclosure 0.02 m apart below the heater (shown as little holesin Fig. 1(a)) at the bottom copper surface (hot surface (5)) andsimilar temperature measurements are taken at the top coppersurface (cold surface (5)). In order to calculate the heat which mayleakage away from the enclosure cavity, eleven more thermocou-ples are distributed along the lower surface of the covering Bakeliteplate (3) as seen in Fig. 1(a). Four more thermocouples aredistributed on the outer surfaces of the enclosure, one on each sideto measure the heat leakage from the sides. Chromel Alumel (typeK) self adhesive thermocouples (0.3 s time response with flattenedbead) are used to measure the surface temperatures as explainedearlier. Those thermocouples are connected to a 40-channels dataacquisition system, which in turn are connected to a computerwhere the measured temperatures are stored for further analysis. Itshould be mentioned that the cold surface (copper) (5) is subject toa stream of ambient air of 5 m/s using a fan as shown in Fig. 1(d) tohelp in cooling the surface. It is worth mentioning that theconsumed power, by the heater, is measured by a Wattmeter anduniformly distributed (as specified by the manufacturer) across thecavity. The heat flux is calculated by dividing the consumed power(after deducting the heat lost from the back side of the heater andfrom the enclosure sides by conduction) by the surface area as willbe seen in the experimental analyses section. Heat transfer data aregenerated by controlling the input power to the heater such that foreach enclosure at least six power intervals are chosen, whilemaking sure that the maximum hot plate surface temperature doesnot exceed 90 �C to avoid the possible boiling of the nanofluid.

3. The tested fluid

The alumina nanofluid (Al2O3 dispersed in water) used in thepresent study is supplied by the Nanostructured and AmorphousMaterials, Inc. (USA) with a mass concentration of 20%. The speci-fications provided by themanufacturer are given in Table 1. In orderto characterize the size of the particles, a sample of the diluted

Fig. 1. Schematic of the enclosure; (a) enclosure parts, (1) polystyrene, (2) Bakelite, (3) thermocouples, (4) heater, (5) copper plates, (6) gasket sheet, (7) circular enclosure, (8) two-way valve, (b) assembled enclosure, (c) bolts and valve locations and (d) complete setup.

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124 117

dispersed suspension provided by the manufacturer (20 m%) isdried and ground into fine particles. Fig. 2 shows the secondaryelectron imaging using a Scanning Electron Microscope (JEOL-6610LV) (SEM). As seen in this figure the minimum size is around311 nm and some are agglomerated to bigger sizes. The highlyconcentrated nanofluid provided by the manufacturer was dilutedto 0.85%, 1.98% and 2.95% by mass using distilled pure water. Thesenewdiluted solutions are ultrasonically vibrated to insure completedispersions of the nanoparticles and to be sure that agglomerationsseen in Fig. 2 are broken to some extent into nanometer range [5].The equivalent volume fractions of the diluted mass percentage are0.21%, 0.51% and 0.75% respectively. The stability of the nanofluidsamples is checked by taking a photo of the sample just after theultrasonic vibration and two days later where no precipitation is

Table 1Specifications of the nanofluid as provided by the manufacturer forconcentration ratio 20% by mass.

Average particle size 10 nmDynamics viscosity 40 cP (at 20 �C)Appearance Transparent liquidpH value 4.5Purity �99.9%

observed in those two days period. The nanofluid physical prop-erties equations provided byWilliams et al. [23] are used, since theparticle sizes in their experiments are similar to the ones in thecurrent experiment,

Fig. 2. SEM photographs of nanoparticles show the agglomeration to bigger sizes.

0 4 8 12 16 20χ, %

0.001

0.01

0.0020.003

0.005

0.020.03

0.05

0.0005

μ f,Pas

Measured viscosityCalculated from Eq. (4)Williams et al. [23]

Value reported by themanufacturer at 20 oC

+20%

-20%

Fig. 4. Nanofluid viscosity at 24.5 �C.

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124118

rf ¼ frp þ ð1� fÞrb (1)

Cf ¼ frpCp þ ð1� fÞrbCbrf

(2)

kf ¼ kbð1þ 4:5503fÞ (3)

mf ¼ mbexp�

4:91f0:2092� f

�(4)

where f is the nanoparticles’ volumetric concentration ratio. Therelation between mass concentration c and volumetric concen-tration f can be estimated from the following equation and Eq. (1),

1rf

¼ crp

þ ð1� cÞrb

(5)

Nanofluid density is measured using DMA 35N density meterprovided by Anton Paar GmbH. Fig. 3 shows the effect of massconcentration on the measured nanofluid density at an ambienttemperature of 25.5 �C. The Nanofluid viscosity at an ambienttemperature 24.5 �C is measured using Viscolite 700 PortableViscometer manufactured by Hydramotion Viscosity. The Effect ofnanoparticles concentration on viscosity is shown in Fig. 4.Comparison with measurements of Williams et al. [23] is alsoshown in this figure. The measured viscosity falls within �20% ofEq. (4) where those differences could be related to the accuracy ofthe used viscometer. Nanofluid thermal conductivity is measuredusing KD2Pro manufactured by Decagon Devices, Inc. The Effect ofnanoparticles concentration on thermal conductivity is shown inFig. 5 along with the results of [23] for comparison. The measuredthermal conductivity falls within �5% of Eq. (3). The conversionbetween mass and volume fraction (f) was done through the bulkdensity of alumina as shown by Eq. (5). The physical properties ofAl2O3 nanoparticles are given in Table 2 [13].

4. Experimental analyses

The heat generated by the heater is dissipated through thecopper hot plate and then to the fluid medium by convection. Inaddition to that, there is heat lost through the Bakelite sides and thelower Bakelite plate by conduction. It should be mentioned that theradiation heat transfer is neglected since the fluid is liquid witha maximum temperature of 80 �C.

0 4 8 12 16 20χ, %

900

1000

1100

1200

ρ f,kg/m3

Measured densityCalculated from Eq. (5)

Fig. 3. Nanofluid density at ambient temperature of 25.5 �C.

Qtotal ¼ IV ¼ QBk:b þ QBk:s þ Qcv (6)

QBk:b ¼ ABk:bkBkTh � TBkdBk:b

(7)

QBk:s ¼ ABk:skBkTf � TsdBk:s

(8)

Qcv ¼ IV� QBk:b � QBk:s (9)

Where Qtotal is the electrical input power, QBk.b is the heat lost byconduction through the Bakelite plate below the heater towardsthe insulation layer (if any), QBk.s is the heat lost by conductionthrough the Bakelite sides of the enclosure, Qcv is the heat transferby convection through the fluid in the vertical direction and ABk.band ABk.s are the surface area of the Bakelite plate below the heaterand the Bakelite sides respectively. It should be noted that, allphysical properties of the nanofluid are evaluated at the meantemperature of the nanofluid Tf ¼ ðTh þ TcÞ=2. It is also assumedthat the Bakelite side’s inner temperature is equal to Tf in calcu-lating the heat lost from the sides. WhereTc, Th and TBk are theaverage surface temperatures of the cold, hot and Bakelite surfacesrespectively and Ts is the Bakelite outside average side tempera-ture. Measurements show that, the fraction of the heat lost byconduction through the Bakelite plate below the heater and thatfrom the Bakelite sides are 4.7% and 1.3% respectively at most.

0 4 8 12χ, %

0.5

0.6

0.7

0.8

k f,W/mK

Measured thermal conductivityCalculated from Eq. (3)Williams et al. [23] +5%

-5%

Fig. 5. Nanofluid thermal conductivity at 26.5 �C.

Table 3The maximum percentage uncertainties of variousquantities.

Quantity Range (%)

Qtotal 2.09qcv 2.33h 8.52Ra* 2.81Nu 8.53

Table 2The physical properties of Al2O3 nanoparticles used in Eqs. (4)e(8).

The bulk density 3970 kg/m3

The thermal conductivity 40 W/mKThe thermal expansion coefficient 0.0000085 1/K

0.0 0.2 0.4 0.6 0.8 1.0x /D

0.8

1.2

1.6

2.0

2.4

2.8

t/t

513.7

1106.6

2044.4

q" = 3110 W/m2

4517.2

5215.9

Cold surface= 0.75% vol

a

b 5.0

Hot surface= 0.75% vol

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124 119

4.1. Average heat transfer coefficient h

In this case the average surface temperatures are used tocalculate the average heat transfer coefficient at each convectionheat transfer Qcv

Qcv ¼ Th � TcPR

(10)

WhereP

R is the overall enclosure thermal resistance given by:

XR ¼ Rcopper þ Rfluid þ Rcopper (11)

Rcopper ¼ DxcopperAcopperkcopper

; Rfluid ¼ 1

Ah(12)

Where the copper surface area Acopper is equal to the convectionsurface area A of the enclosure, kcopper ¼ 398 W/m K [22] andDxcopper is the thickness of the copper plate. By substituting Eqs.(11) and (12) into (10), the heat transfer through the enclosure isobtained:

Qcv ¼ Th � Tc

2Dxcopper

Acopperkcopperþ 1

Ah

(13)

0 200 400 600 800Time, minutes

0

10

20

30

40

50

Tem

pera

ture

,o C

C o ld S urfaceH ot Surface

Steady stateUnsteady state

Fig. 6. Samples of temperature variation with time showing the steady state conditionfor the enclosure (k ¼ 0.0635).

And the average heat transfer coefficient can be obtained as:

h ¼ 1

A

"Th � TcQcv

� 2DxcopperAcopperkcopper

# (14)

The non-dimensional average Nusselt number, the modifiedRayleigh numbers and the ordinary Rayleigh numbers are obtainedas:

Nu ¼ hLk

(15)

0.0 0.2 0.4 0.6 0.8 1.0x/D

1.0

2.0

3.0

4.0

t/t

513.7

1106.6

2044.4

q" = 3110 W/m2

4517.2

5215.9

Fig. 7. Temperature distribution along the diameter of the shallow enclosure(k ¼ 0.0635) filled with nanofluid of concentration 0.75% by volume (2.95%m); (a) coldsurface and (b) hot surface.

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124120

Ra* ¼ gbQcvL4

knaA; and Ra ¼ gbDTL3

na(16)

4.2. Experimental uncertainty

In this section, the experimental uncertainty is to be estimatedin the calculated results on the basis of the uncertainties in theprimary measurements. It should be mentioned that some of theexperiments are repeated more than twice to check the calculatedresults and the general trends of the data. The error in measuringthe temperature and in calculating the surface area is �0.2 �C, and�1.57 � 10�5 m2, respectively. The accuracy in measuring thevoltage is taken from the manual of the Wattmeter as 0.5% of

1E+5 1E+6 1E+7

Ra*

2

4

6

8

1.0

10.0

Nu

= 0.0635

2.95% m (0.75% vol)1.98% m (0.51% vol)0.85% m (0.21% vol)0.00% m (0.00% vol)

a

1E+6 1E+7 1E+8 1E+9

Ra*

6

7

8

9

10

Nu

b

κ= 0.127

0.00% m (0.00% vol)0.85% m (0.21% vol)1.98% m (0.51% vol)2.95% m (0.75% vol)

Fig. 8. Effect of nanofluid concentration on Nusselt number as function of the modifiedRayleigh number in the enclosure (a) k ¼ 0.0635 and (b) k ¼ 0.127.

reading �2 counts with a resolution of 0.1 V and the correspondingone for the current is 0.7% of reading �5 counts þ 1 mA witha resolution of 1 mA. At each run, forty scans of the temperaturemeasurement are collected by the data acquisition system for eachchannel and the mathematical averages of those scans are ob-tained. Using the above mentioned errors turns to maximumitemized uncertainties of the calculated results shown in Table 3using the method recommended by Moffat [24]. The uncer-tainties of themeasured density, viscosity and thermal conductivitydata presented in Figs. 3e5 as given by the manufacturers’ usermanuals are: �0.001 g/cm3, �2% of the reading above 0.01 Pa s(10 cP) and �0.0005 Pa s (0.5 cP) for readings below 0.01 Pa s(10 cP), and �5% from 0.2 to 2 W/(m K) and �0.01 W/(m K) from0.02 to 0.2 W/(m K) respectively.

5. Results and discussion

Temperaturemeasurements are taken at steady state conditionswhichnormally reached at themaximumof 300min as seen in Fig. 6for a sample rate of thirty samples perminute. Fig. 7(a, b) showsomesamples of the temperature distribution along the diameter of thecold and hot surfaces of the enclosure respectively for the shallowenclosure (k ¼ 0.0635) filled with nanofluid of f ¼ 0.75% concen-tration by volume (2.95% bymass). It is clear in these figures that; asthe heat flux increases the surface temperature increases and itsmaximum located near the center of the circular enclosure and

2 4 6 8 10Nuexp

2

4

6

8

10

Nu p

red

Eq. (17 )Ideal

+10%

-10%

6 7 8 9 10Nuexp

6

7

8

9

10

Nu p

red

Eq. (18)Ideal

+5%

-5%

a

b

Fig. 9. The correlation and band width of the predicted and the experimental Nusseltnumbers of the enclosure (a) k ¼ 0.0635 and (b) k ¼ 0.127.

2 4 6 8 10N uexp

2

4

6

8

10

Nu p

red

Eq. (19)Ideal

+10%-10%

Fig. 10. The correlation and band width of the predicted and the experimental Nusseltnumbers for both enclosures using the aspect ratio k as a parameter.

0.00 0.20 0.40 0.60 0.80

φ %

4

5

6

7

8

Nu

Ra*= 5x106=3x106=1x106

= 0.0635a

0.00 0.20 0.40 0.60 0.80

φ %

7

8

9

10

Nu

Ra*= 1x108

Ra*=2x107

Ra*= 6x106

b

κ=0.127

Fig. 11. Effect of nanofluid concentration on Nusselt number for different values of themodified Rayleigh numbers, (a) k ¼ 0.0635 and (b) k ¼ 0.127.

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124 121

decreases as it moves towards the edges of the enclosure due to theendeffects. It shouldbenoted thatother concentrationshave similartemperature profiles. The heat transfer coefficient is presented ina dimensionless form of the averageNusselt number in Fig. 8(a, b) asa function of the modified Rayleigh number for both enclosures. Asseen in Fig. 8(a) for the shallow enclosure (k ¼ 0.0635) the averageNu increases for small volume fraction over that of the base fluid ata fixed Ra*. However as the modified Rayleigh number increasesmore, enhancement can be seen in Nu for small volume fraction.Furthermore, as the volume fraction increasesmore a decrease inNuis noticed (f ¼ 0.75% vol.) below that of the base fluid. In otherwords, enhancement in Nu occurs for f � 0.51% (vol.) and deterio-ration in Nu is obtained beyond that. This observation could beattributed to the competition between the increase of both thermalconductivity and viscosity of the nanofluid as the volume fractionincreases. However, for volume fraction f > 0.51% the effect ofviscosity is dominated which in turns deteriorates the heat transferas seen as a decrease of Nu. It should be noted that similar obser-vations are obtained by [5, 10, 15, 17, and 19]. Fig. 8(b) shows theeffect of enclosure aspect ratio on the natural convection usingnanofluidwhere thebehavior is the sameas thatof Fig. 8(a) howeverthe experimental data getting close to each other but with the sametrend as explained in Fig. 8(a). It should benoted that the data for thewide gap enclosure are close to each other and can’t clearly bedistinct. Comparison between Fig. 8(a) and (b) shows that the heattransfer enhancement is more pronounced at low aspect ratio thanat high aspect one as previously observed by [5] and [11]. Theaverage Nusselt numbers presented in Fig. 8(a, b) are correlated interms of Ra* and the particle volume fraction (0 � f � 0.75% vol.).The correlation for the shallowenclosure (k¼0.0635) is obtained as:

Nu ¼0:571�Ra*

�0:155�1þ 106:346f� 17286:975f2

�;

3� 105� Ra* � 9� 106 ð17Þ

with a confidence coefficient R2 ¼ 95.9%. The correspondingcorrelation for the other enclosure (k ¼ 0.127) is given by

Nu ¼1:603�Ra*

�0:097�1þ 12:814f� 2055:99f2

�;

4� 106� Ra* � 1:3� 108 ð18Þ

with a confidence coefficient R2 ¼ 99%. The predicted Nusseltnumbers from the above correlations are plotted against the

experimental Nusselt number in Fig. 10(a, b) for the two enclosuresrespectively. The solid lines present the perfect fit whereas thedashed lines present the error band width of �10% in Fig. 10(a) andare �5% in Fig. 9(b). Furthermore, the overall correlation coveringboth enclosures is obtained using the enclosure’s aspect ratio k asa parameter

Nu ¼1:426�Ra*

�0:119�1þ 44:097f� 6943:36f2

�k0:137;

3� 105� Ra* � 1:3� 108 ð19Þ

8a

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124122

with a confidence coefficient R2¼ 99%. This correlation is presentedin Fig. 10 with the experimental data and band width of �10%.

Fig. 11(a) shows the average Nusselt number developed from Eq.(17) for different values of the modified Rayleigh number for theshallow enclosure (k ¼ 0.0635). It is clear that for any Ra* as thenanoparticle volume fraction increases the Nusselt numberincreases over that of the base fluid (water) up to a specific valuethen it decreases; this specific value is detected from the currentexperimental data to be 0.6 > f > 0.51% (vol.). Therefore, thequalitative critical values of f z 0.6% which pointed out by thedownward arrow in Fig. 11(a) is the critical value of the volumefraction where beyond this value a degradation of the naturalconvection should be occurred. Fig. 11(b) shows similar behaviorfor the Nusselt numbers derived from Eq. (18) for the other

0 4 8 12 16 20T( C)

0.6

0.8

1.0

1.2

1.4

1.6

hf/h

b

0.85% m (0.21% Vol.)1.98% m (0.51% Vol.)2.95% m (0.75% Vol.)

a

o

0 5 10 15 20 25T( C)

0.92

0.96

1.00

1.04

1.08

1.12

hf/h

b

0.85% m (0.21% vol)1.98% m (0.51% vol)2.95% m (0.75% vol)

b

Fig. 12. Heat transfer coefficient ratio of nanofluid to its base fluid for varioustemperature differences across the enclosures (a) k ¼ 0.0635 and (b) k ¼ 0.127.

enclosure (k¼ 0.127). Observation of Fig.11 suggests that in order toget quantitative values of the Nu and f corresponding to themaximum Nusselt number and the critical values of f, one mustrepeat the experiment for different many concentrations to getpiecewise curves for various Ra*.

In order to quantify the natural convection heat transfer furtherfollowing [17], Fig. 12(a, b) presents the results of the average heattransfer coefficient ratio between the current Alumina nanofluidand the base fluid versus the average temperature difference acrossthe enclosures ðDT ¼ Th � TcÞ. This comparison of the base fluid

1E+5 1E+6Ra

2

3

4

5

6

7

Nu

Water (0.00%vol)

Leong et al. [26]Inaba [25]

15 %

1E+5 1E+6Ra

3

4

5

6

7

8

9

Nu

0.85% m (0.21%vol)

Ho et al. [7]10%

b

Fig. 13. Comparison between the current experimental results and those in the liter-ature, (a) with Inaba [25] and Leong et al. [26] for water 4 ¼ 0.0% vol. and (b) with Hoet al. [7] for 4 ¼ 0.21% vol.

M. Ali et al. / International Journal of Thermal Sciences 63 (2013) 115e124 123

shows that the enhancement of the heat transfer coefficient couldattain an increase of up to 40% for f ¼ 0.21% and an averagedegradation of about 20% for f ¼ 0.75% (vol.) as shown in Fig. 12(a)for the shallow enclosure (k ¼ 0.0635). However, on the otherenclosure (k ¼ 0.127) a maximum enhancement of only about 8%could be attained and this happened using a volume fractionmostlyless than 0.75% (vol.) and it degrades the heat transfer coefficient byabout 4% which mostly happened using f ¼ 0.75%. It could beconcluded that the aspect ratio of the enclosure plays a veryimportant role in enhancing the heat transfer coefficient ([5] and[11]) of the nanofluid over that of the base fluid.

In order to compare the present results with those in the liter-ature; Rayleigh number is calculated and used in Fig. 13(a, b). It canbe seen in Fig. 13(a) that the present results for the base fluidf ¼ 0.0% lie within the predication of Inaba [25] for air cavityheated from below. The dashed lines show an error band width of�15% where 92% of the data are inside this error band. Othercorrelation for Leong et al. [26] for a cubical air filled cavity is alsoshown and lies in the limit of the error band. These differencescould be attributed to the different aspect ratio and due to the sidewall effect. On the other hand, the correlation of Ho et al. [7] forvertical cavity heated from a side using their model II of viscosityand thermal conductivity for f ¼ 0.21% (vol.) is shown in Fig. 13(b)for qualitative comparison. An error band width of 10% is observedbetween the current experimental data and those of [7]. It shouldbe noted that, the differences between the current experimentalresults and those in Fig.13(b) is expected due to the different aspectratio and the heating boundary conditions and orientation associ-ated with [7].

6. Conclusions

Natural convection heat transfer using Alumina nanofluid ina vertical circular enclosure heated from below is studied for twogap aspect ratios k¼ 0.0635 and 0.127. Results show that increasingthe nanofluid concentration enhances the heat transfer coefficientover that of the base fluid for small volume fraction ratio f � 0.51%(vol.). However, for f > 0.51% it degrades the heat transfer coeffi-cient. The enhancement percentage of the heat transfer coefficientis aspect ratio dependent for example it increases by a maximum of40% for the shallow enclosure k ¼ 0.0635 and only by 8% fork ¼ 0.127 using the same volume fraction f ¼ 0.21%. Furthermore,using f¼ 0.75% degrades the heat transfer coefficient by about 20%for k ¼ 0.0635 and by 4% for k ¼ 0.127 from that of the base fluid.General correlations are obtained for the average Nusselt numbersverses the modified Rayleigh numbers using the volume concen-tration ratio as a parameter for each enclosure (Eqs. (17) and (18)).Finally, an overall correlation is obtained for both enclosures usingthe aspect ratio as a parameter (Eq. (19)).

Acknowledgement

This research is supported by King Abdullah Institute forNanotechnology at King Saud University under the project numberNano 1429/54. This support is highly appreciated andacknowledged.

Nomenclature

A area, m2

C specific heat, kJ/kg KD Enclosure inside diameter, m2

g acceleration due to gravity, m/s2

h heat transfer coefficient, W m�2 K�1

I current, Ampere

k thermal conductivity, W m�1 K�1

m mass, kgL enclosure height, mNu average Nusselt number, hL=kQtotal Electrical input power, WQcv convection heat transfer, Wqcv convection heat flux, ¼ Qcv/A, W/m2

R Thermal resistance, W/KRa* Modified Rayleigh number, gbqcL4n�1a�1k�1

Ra Rayleigh number, ¼ gbDTH3/anT temperature, KDT Th � Tct temperature, �CV voltage, voltvol. volumex distance along the diameter, m

Greek symbolsa thermal diffusivity, m2 s�1

b coefficient for thermal expansion, K�1

d Bakelite thickness, mk aspect ratio, (L/D)m dynamic viscosity, Pa sn kinematics viscosity, m2 s�1

r density, kg/m3

f volume concentration ratioc mass concentration ratio

SubscriptsBk Bakelite materialBk.b Bakelite surfaceBk.s Bakelite sideb base fluid (water)c coldexp experimental dataf nanofluidh hotp nanoparticlepred predicted dataN ambient condition

Superscriptse average quantity

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