Hamid Moradi,Bahamin Bazooyar *,Ahmad Moheb ,Seyed Gholamreza Etemad

1 Department of Chemical Engineering,Isfahan University of Technology,Isfahan 84156-83111,Iran

2 Ahvaz Faculty of Petroleum Engineering,Petroleum University of Technology,Ahvaz,P.O.Box 6198144471,Iran

Keywords:Natural convection heat transfer Nano fluid Optimization Cylinder orientation

ABSTRACT This study characterizes and optimizes natural convection heat transfer of two Newtonian Al2O3 and TiO2/water nanofluids in a cylindrical enclosure.Nusselt number(Nu)of nanofluids in relation to Rayleigh number(Ra)for different concentrations of nanofluids is investigated at different configurations and orientations of the enclosure.Results show that adding nanoparticles to water has a negligible or even adverse influence upon natural convection heat transfer of water:only a slight increase in natural convection heat transfer of Al2O3/water is observed,while natural convection heat transfer for TiO2/water nanofluid is inferior to that for the base fluid.Results also reveal that at low Ra,the likelihood of enhancement in natural convection heat transfer is more than at high Ra:at low Ra,inclination angle,aspect ratio of the enclosure and nanoparticle concentration influence natural convection heat transfer more pronouncedly than that in high Ra.

1.Introduction

During the past few years,the use of nanofluids as a conventional fluid to enhance heat transfer has attracted considerable attention.Improvement in forced convection regime of heat transfer has been widely proven by many researchers.However,it is still a hot debate among workers regarding the role of nanoparticles in natural convection heat transfer.

There are several researchers who employed numerical techniques to explore natural convection heat transfer of nanofluids in enclosures.The effect of nanoparticle shape on heat transfer enhancement by“dissolving”rod-like and spherical nanoparticles in water was numerically investigated by Kim et al.[1].The increase in the convective heat transfer with rod-like particles is more than spherical particles.Khanafer et al.[2]developed a model to study heat transfer enhancement of Cu/water nano fluid in a two-dimensional enclosure.They employed the finitevolume approach along with the alternating direction implicit procedure to solve the transport equations numerically.They reported that heat transfer rate rises significantly as the volume fraction of nanoparticles increases in the base fluid.Jou et al.[3]employed Khanafer's model to study natural convection heat transfer in a rectangular enclosure utilizing finite difference approach.They observed that increasing the buoyancy parameter and nanoparticle volume fraction increases the average heat transfer coefficient.Polidori et al.[4]theoretically investigated the natural convection flow and heat transfer of Al2O3/water nanofluid over a vertical semi-in finite plate.Results showed that the heat transfer enhancement of nanofluids depends on both nanofluid effective thermal conductivity and the proposed viscosity model.Hwang et al.[5]applied Jang and Choi'smodel[6]to predictthe effective thermal conductivity of Al2O3/water nanofluid in a rectangular cavity heated from below.They concluded that the ratio of heat transfer coefficient of nanofluid to that of base fluid is lessened as the size of nanoparticles increases.Ho et al.[7]aimed at identifying impacts of uncertainties of effective dynamic viscosity and thermal conductivity of nanofluid in natural convection heat transfer of a square enclosure.They concluded that the type of the viscosity model applied to calculate the viscosity of nanofluids has significant impact on heat transfer.Pakravan and Yaghoubi[8]simultaneously investigated the thermophoresis of nanoparticles and the Dufour effect on natural convection heat transfer of nanofluids.They reported that there is a decreasing linear relation between the heat transfer coefficients of nanofluids and the particle diameter as well as the volume fraction.Alloui et al.[9]carried out an analytical and numerical study of natural convection heat transfer in a shallow rectangular cavity filled with nanofluids.They reported that heat transfer of nanofluids reached a maximum that depends on the Rayleigh as well as nanoparticle volume fraction.Daungthongsuk and Wongwises[10]delved into the convective heat transfer coefficient of TiO2/water in a double-tube counter flow heat exchanger.They studied the influence of physical properties of nanofluid over heat transfer of the exchanger and managed to develop mathematical models to predict the physical properties of the nanofluid.Effects of inclination angle on natural convection heat transfer and fluid flow of Cu/water nanofluid in a two-dimensional enclosure by solving the governing equations using finite-volume technique was studied numerically by Abu-Nada and Oztop[11].They stated that the inclination angle of the enclosure can be an effective major parameter in natural convection heat transfer of the Cu/water nanofluid.In a study by Ghasemi and Aminossadati[12],the influence of Rayleigh number,inclination angle,and solid volume fraction upon natural convection heat transfer of a two-dimensional inclined enclosure filled with a CuO/water nanofluid was numerically studied.In this study,two opposite walls of the enclosure were insulated and the other two walls were kept at different temperatures.Results revealed that at a specific concentration of nano-particles and a specific inclination angle for the enclosure,natural convection heat transfer reached its maximum and the value of the maximum depended on the studied Rayleigh number.

Compared with extensive numerical and theoretical studies on natural convection heat transfer of nanofluids,limited experimental work has been conducted.In a pioneering work,Putra et al.[13]investigated natural convection heat transfer of Al2O3/water and Cu/water nanofluids through a horizontal cylinder,which was heated from one end and cooled from the other.They claimed that particle density,concentration,and the aspect ratio of the cylinder are effective parameters upon natural convection heat transfer.Wen and Ding[14]studied natural convection heat transfer of TiO2/water nanofluid between two disks.Experimental results showed that as particle concentration was increased,the natural convection heat transfer coefficient was decreased,which was in contradiction to the initial expectation.Nnanna[15]carried out experimental studies of heat transfer behavior of a buoyancy-driven Al2O3/water nanofluid in a two dimensional rectangular cavity which its vertical walls were heated partially and the horizontal walls were isolated.They managed to develop an empirical correlation for Nusselt number as a function of the volume fraction of the nanoparticles and Rayleigh number.They claimed that the heat transfer rate can be enhanced even by a small volume fraction of nanoparticles.

Experimental studies on the natural convection heat transfer of nanofluids are rare.Hence,the objective of this work is to experimentally investigate the effects of two common nanoparticles on the natural convection heat transfer of water in a cylindrical enclosure.This study will clarify whether or not nanoparticle has a positive consequence on natural convection heat transfer.The influence of the geometry and configuration of the cylindrical enclosure on natural convection heat transfer is also studied for better understanding of the natural convection heat transfer of nanofluids.

2.Material and Methods

2.1.Test samples

γ-Al2O3and TiO2nanoparticles(Nanostructured&Amorphous Materials Inc.,USA)were dispersed into the de-ionized water for nanofluids preparation.Five nanofluids samples were prepared with different volume concentrations of nanoparticles(0.1%,0.2%,0.5%,1%and 1.5%).The dispersion of nanoparticle into the water occurred by means of a mechanical mixer operated at 200 r·min?1.Afterwards,the mixture was located into an ultrasonic vibration apparatus for 240 min for better dispersion of nanoparticles into the base fluid.The behaviors of prepared samples(AL2O3/water[13]and TiO2/water[16])were highly Newtonian.The stability of the prepared nanofluids was frequently checked during experiments.Calculation of the density(by weighing a specific volume of each sample)of all the samples before and after each test(the difference was below 0.1%)showed that the samples were quite stable and no sedimentation of nanoparticles was observed throughout the experiment.

2.2.Description of experimental apparatus

Experimental setup is designed based on the work of Putra et al.[13].Five distinct sections(test cell,data acquisition,power,PC,thermostatic bath)of the experimental setup are shown in Fig.1.

Test cell is a vertical cylindrical enclosure with a diameter of 80 mm and a height of 250 mm that is made from PTFE(polytetra- fluoro-ethylene).The cylindrical enclosure was fully insulated for having a minimum heat loss during experiments so as to get results of better accuracy in the case of natural convection.The test cell was uniformly heated from bottom side by a heating system,which consisted of an aluminum circular plate and an electrical heater.The heater was located between the aluminum plate and a thick PTFE circular plate in order to provide constant heat flux.The PTFE plate is also an insulation.The upper cover of the cylindrical enclosure was mobile and could be moved along the cylinder for adjusting the height of the test cell.This makes it possible for us to investigate the effect of aspect ratio on natural convection heat transfer.Experimental setup also includes a thermostatic bath which provides and circulates cooling water to the upper cover of the chamber to adjust the upper surface temperature constant at 10°C.Heat fluxes were provided by a DC power supply and the power changed by setting the voltage of the heater.The experimental section also has a PC and data acquisition system to gather,process,and record data from our experiments.Detailed description of the cylindrical enclosure is shown in Fig.2.

Surface temperatures at the top and bottom plates of cylindrical enclosure were measured by virtue of six K-type thermocouples(three at each surface,accuracy of measurements:0.1°C).Surface temperature which was used in our calculations was the average of three temperatures measured by thermocouples.The inlet and the outlet temperatures of the water of the cooling chamber were also measured by thermocouples.A data acquisition system record measurements of thermocouples and sent them to a computer.Prepared samples(nano fluids)were cautiously added to the enclosure(test section)so that no air bubbles formed and interrupted experiments.

Experiments were all performed on days with exactly the same weather conditions(relative humidity and average temperature).They were repeatable within each series of tests on those days.Tests were also recorded and obtained at steady-state conditions in test cells(for heat transfer as indicated by a constant water outlet temperature value)that allowed good repeatability.Experiments were repeated three times.Results presented were the average of measurements in these three disparate tests.The uncertainty of tests was calculated from a combination of the experiment repetition error and the precision error of the thermocouples.

To investigate the performance of the setup apparatus,a benchmark experimentation was carried out with pure distillated water.At this stage,the variation of Nu(Nusselt number)in relation to Ra(Raleigh number)was experimentally verified at0°,30°,45°,60°and 90°inclination angles of the enclosure.At each specific inclination angle,Ra was increased by changing the heating power.By doing this,the temperature of the hot surface was changed,whereas the temperature of the cold surface was remained at a fixed value,the temperature difference in Ra and consequently Ra was varied.Note that other variables in Ra remained pretty constant during the experiment.Results for all inclination angles revealed that by increasing Ra, firstly,Nu increased dramatically and then showed a much less intensification from itself(Fig.3).

This observation is in agreement with the result of all previous studies.For instance,Putra et al.[13]carried out an experiment to investigate natural convection heat transfer of pure water by exploring the relationship of Nu with Ra.Results in their study demonstrated that at first Nu increased significantly with Ra,then its trend became milder on higher Ra.Wan and Ding[14]also proclaimed that in natural convection heat transfer of pure water Nu is an increasing function of Ra.

Fig.1.Schematic diagram of the experimental setup[13].

2.3.Calculations

To begin with,physical and rheological properties of nanofluids were calculated.Density and thermal capacities of the nanofluids were defined by the Pak and Cho equations[17].Viscosity was defined by the Wang equation[18]and the thermal conductivity was defined by the Hamilton and Crosser[19]equation as follows:

where ρ,μ,Cp,and K denote density,viscosity,heat capacity,and thermal conductivity,respectively.The subscripts p,bf and nf refer to particles,base fluid,and nanofluid,respectively.

The temperatures of the lower and the upper surfaces of the cold and the hot plates were calculated by the following equations:

where q represented the heat flux measured by the heat flux meter mounted on the bottom surface,t and kAlare the thickness and thermal conductivity of the aluminum plates,respectively.Moreover,the heat flux was calculated by

where V and I represented voltage(recorded by power supply)and amperage(recorded by amplifier),respectively.

Finally,for the heat transfer coefficient,Nu and Ra values were formulated as follows:

Fig.2.Parts of the cylindrical test enclosure.

where L was the distance between the hot and the cold surface.The parameters βnf,?nfand αnfwere the thermal expansion coefficient,kinematic viscosity and thermal diffusivity of nanofluids,respectively.The following equation was used to calculate their values[17]:

Fig.3.Nu versus Ra for pure water at different inclination angles.

3.Results and Discussion

The influence of Al2O3and TiO2nanoparticle volume concentrations on natural convection heat transfer is illustrated in Figs.4 and 5.

The trend of Nu ofAl2O3/water and TiO2/water nanofluids in relation to Ra is shown at constant inclination angles in these figures.It can be readily seen from Fig.4 that only Al2O3nanoparticle can enhance the natural convection heat transfer within the enclosure.A mild improvement in natural convection heat transfer of Al2O3/water nanofluid can be observed by increasing the nanoparticle volume concentration from 0 to 0.2%(maximum heat transfer occurred at 0.2%).At inclination angles 0°,30°,45°,60°,and 90°,Nu of nanofluid with 0.2%(by volume)Al2O3nanoparticles are on average 6.42%,6.76%,6.24%,6.33%,and 6.38%higher than that of pure water.When the volume concentration of Al2O3in the nanofluid is 0.2%,any increase in the amount of nanoparticle has an adverse influence on the natural convection heat transfer.The Nu value of Al2O3/water with 1%and 1.5%volume concentration becomes even lower than that of pure water(base fluid).For example,at inclination angles 0°,30°,45°,60°,and 90°,Nu of 1%(by volume)of Al2O3/water are roughly 4.41%,4.58%,5.90%,6.88%,and 6.99%lower than that of the base fluid,respectively.Putra et al.[13]stated that heat transfer of CuO2/water and Al2O3/water nanofluids passed through a maximum both at 1%volume concentration.

Fig.5 confirms that natural convection heat transfer can deteriorate by adding nanoparticles(TiO2nanoparticle)in water.It shows that whatever the inclination angle is,TiO2nanoparticle cannot improve natural convection heat transfer.For example,at inclination angle 30°,Nu of TiO2/water nanofluid with volume concentrations of 0.1%,0.2%,0.5%,1%and 1.5%is nearly 1.88%,6.28%,38.84%,47.35%and 51.42%,respectively lower than that of the base fluid.

Rheological(such as density and viscosity)and thermal properties(conductivity coefficient)of nano fluids are highly influenced by the existence of nanoparticles[20].Since both Al2O3and TiO2are made from metals,they both lead to incontrovertible enhancementin thermal conductivity of base fluid.However,they can also adversely influence natural convection heat transfer because they increase the viscosity and density of nanofluids.The fact that natural convection heat transfer for Al2O3/water nanofluid firstly increases and then decreases shows these two contrary effects of nanoparticles on natural convection heat transfer.For TiO2nanoparticles,thatthere is no enhancementin natural convection shows that the adverse in fluence of TiO2on natural convection heat transfer(by rheological properties)is stronger than the positive role of nanoparticles for heat transfer.Table 1 gives the properties of Al2O3and TiO2nanoparticles.It can be inferred from the table that TiO2/water nanofluid had a lower thermal conductivity and higher viscosity and density compared to Al2O3/water nanofluid.This can partly explain the adverse influence of TiO2nanoparticle on natural convection heat transfer.Investigating the influence of adding nanoparticles to fluids is not easy.Khadangi et al.[21]also reported that TiO2/water nano- fluid has a lower thermal conductivity compared to Al2O3/water nanofluid,giving rise to the absence of improvement in natural convection heat transfer of this nano- fluid.Hojjat et al.[22]proposed a model based on neural network for the prediction of thermal conductivity of TiO2/water,CuO/water and Al2O3/water nano- fluids.Their experimental data showed that TiO2/water has the lowest thermal conductivity.

The influence of inclination angle at different nanoparticle concentrations on natural convection heat transfer is demonstrated in Figs.6 and 7.

Fig.4.Nu versus Ra for Al2O3/water nanofluid for showing the effect of nanoparticle concentration.

It is apparent that for both nanofluids,inclination angles 30°,0°,45°,60°,and 90°are the best to worst orientations for natural convection heat transfer within the enclosure.It can also be said that the influence of inclination angle on natural convection heat transfer of Al2O3/water nanofluid is more pronounced at lower Ra(relevant to lower heat flux)than at Ra(higher heat flux).For instance,at Ra=1.3×108natural convection heat transfer for 30°inclined enclosure filled with pure water and 0.1%,0.2%,0.5%,1%and 1.5%(by volume)Al2O3nanoparticles is respectively 2.49%,1.28%,0,1.03%,and 0.59%more than that for 0°inclined enclosure,while at Ra=3.7×108the figure is 0.89%,0.78%,0.33%,0.35%,and 0.5%.To the contrary,numerical simulation proves that at high Ra value,inclination angle is more effective in natural convection heat transfer of nanofluids than at low Ra[12].

Likewise,inclination angle has exactly the same influence on natural convection heat transfer of TiO2/water nanofluid(Fig.7).

This means that 30°is the best and 90°is the worst angles for natural convection heat transfer of TiO2/water nanofluid.However,the influence of inclination angle seems to be stronger on natural convection heat transfer of TiO2/water than on that of Al2O3/water.For example,Nu in the 30°inclined enclosure filled with water and TiO2nanoparticle volume concentrations 0.1%,0.2%,0.5%,1%,and 1.5%on average increases by 2.33%,1.22%,1.38%,1.05%,and 1.04%relative to that in 0°,while the figure for Al2O3/water is 1.15%,1.04%,0.21%,0.54%,and 0.55%.Figs.6 and 7 also show that 30°and 90°inclined enclosures are respectively the best and worst orientations for natural convection heat transfer of nanofluids.With three disparate experiments,the uncertainty of Nu was below 0.5%.Numerical studies also confirm that natural convection heat transfer in nanofluids becomes maximum at 30°inclination angle[11].Inclination angle of 90°is also theoretically shown to be the worst orientation for natural convection heat transfer of nanofluid[12].

Fig.5.Nu versus Ra for TiO2/water nanofluid for showing the effect of nanoparticle concentration.

Fig.8 depicts the trends of Nu in relation to Ra for three aspect ratios(0.5,1 and 1.5)of 30°inclined enclosure filled with nanofluids(both with volume concentration of 0.2%nanoparticles).

Table 1 Physical properties of nanoparticles and the base fluid

The influence of aspect ratio upon heat transfer is obvious in this graph.By glancing through the figure,it can be conferred that increasing the length of the enclosure relative to its diameter enhances considerably the natural convection heat transfer.For instance,the average Nusselt numbers of Al2O3/water and TiO2/water nanofluids at the aspect ratio of 1.5 are approximately 3.76 and 3.43 folds higher than the corresponding values at the aspect ratio of 0.5.Note that the maximum and minimum aspect ratios that can be adjusted for the enclosure are 1.5 and 0.5,respectively.Consequently,the aspect ratio of 1.5 is the best.The influence of aspect ratio was also theoretically and experimentally investigated on natural convection heat transfer of nanofluids by other researchers[13].They show that the more the proportion of length to diameter of cylindrical enclosure becomes,the more natural convection heat transfer within the enclosure improves.

Fig.6.Nu versus Ra for Al2O3/water nanofluid for showing the effect of inclination angle.

4.Conclusions

This paper intends to optimize the natural convection heat transfer of Newtonian nanofluids in a cylindrical enclosure.The influence of Al2O3and TiO2nanoparticles concentrations is examined at different positions,configurations and orientations of the enclosure.This study shows that the influence of nanoparticles is not satisfactory for natural convection heat transfer.Whatever the configuration and orientation of enclosure are,Nusselt numbers of both nanofluids increase dramatically at low Raleigh numbers and then become constant at high Ra.Nu within the enclosure for Al2O3/water nanofluid at 0.2%nanoparticle concentration is higher than that for other concentrations of this nanoparticle.This study shows that the influence of nanoparticles and geometry of the cylindrical enclosure on natural convection heat transfer is stronger in low Ra.

Nomenclature

A area of the aluminum plate,m2

CPspecific heat,J·kg?1·K?1

dPnanoparticle diameter,m

g gravitational acceleration,m·s?2

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

I amperage recorded by amplifier,A

k thermal conductivity,W·m?1·K?1

L height of cavity,m

Fig.7.Nu versus Ra for TiO2/water nanofluid for showing the effect of inclination angle.

Nu Nusselt number(=hL/k)

q heat flux,W·m?2

R aspect ratio

Ra Rayleigh number,(=gβΔTx3/νk)

T temperature,K

t thickness of aluminum plate,m

V voltage recorded by power supply,V

α thermal diffusivity,m2·s?1

β isobaric coefficient of volumetric thermal expansion,K?1

θ inclination angle,(°)

μ dynamic viscosity,kg·m?1·s?1

υ kinematic viscosity,m2·s?1

ρ density,kg·m?3

φ nanoparticle volume fraction

Subscripts

bf base fluid

CD lower surface of cold plate

CU upper surface of cold plate

HD lower surface of hot plate

HU upper surface of hot plate

nf nano fluids

p particle

Fig.8.Nu versus Ra for nano fluids at different aspect ratios.