International Communications in Heat and Mass Transfer 36 (2009) 731–738

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International Communications in Heat and Mass Transfer

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Experimental and numerical study of the natural convection from a heatedhorizontal cylinder☆

Ş. Özgür Atayılmaz ⁎, İsmail TekeDepartment of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey

☆ Communicated by W.J. Minkowycz.⁎ Corresponding author.

E-mail address: atayil@yildiz.edu.tr (Ş.Ö. Atayılmaz)

0735-1933/$ – see front matter © 2009 Elsevier Ltd. Aldoi:10.1016/j.icheatmasstransfer.2009.03.017

a b s t r a c t

a r t i c l e i n f o

Available online 21 April 2009

Keywords:Natural convectionHeat transferHorizontal cylinderCFD

Natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically.Experimental study had taken place in different environmental temperature in a conditioned room whichcan be maintained at a stable required value and inside a sufficiently designed test cabin. The environmentaland cylinder surface temperatures varied between 10 °C–40 °C and 20 °C–60 °C respectively. In theexperimental study, two cylinders having different diameters of 4.8 mm–9.45 mm are used and constant heatflux was applied. On the basis of the experimental data, a correlation for the average Nusselt number over thecylinder is proposed in the range of 7.4 101bRab3.4 103. The proposed correlation is compared with the wellknown correlations on natural convection heat transfer from a horizontal cylinder in the specified range ofRayleigh number, and it is shown that the results are in satisfactory agreement. The problem is alsoinvestigated numerically. The experimental data and the numerical results fall in ±20% band. The numericalresults obtained in this study are also compared with the results of Merkin. The characteristics of trend linesare similar.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Natural convection heat transfer from horizontal cylinder arefound in many technical applications such as heat exchangers, boilerdesign, air cooling systems for air conditioning. Wire-and-tube heatexchangers of the kind widely used in small refrigeration appliancesaremade of cylinders with outer diameter 4.8 mm. It is determined bymeans of the detailed literature researches that there is no experi-mental and numerical study including this diameter. In this study,natural convection heat transfer from a horizontal cylinder is studiedexperimentally and numerically using two different diameters(4.8 mm–9.45 mm) and one of them is preferred especially with4.8 mm outer diameter.

Natural convection heat transfer from a horizontal cylinder hasbeen studied numerically and experimentally for more than 50 yearsbut it is reported by the researchers [1,2] that the obtained results showhigh levels of deviation among each other due to various reasons.Morgan [1], after a wide literature research, proposed empiricalcorrelation equations for average Nusselt number and pointed out thatthe results of the experimental study show deviations ranging from3%to 36% according to the Rayleigh number. The discrepancy in theaverage Nusselt number between the well-known previous experi-mental studies in the literature was defined by one or some of thesefactors together; wrong designed test cabin, undersized measuring

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systems, heat conduction to the supports and the temperature mea-surement locations, distortion of the temperature and velocity fieldsby fluid movements. Fand and Brucker [2] compared the eightempirical and half-empirical correlations obtained from the pre-studies on natural convection around an infinitely long horizontalisothermal cylinder and created a new correlation by using theexperimental data in the range of 10−8bRab108 to 0.7bPrb104 in theliterature. And it was determined that the correlations do not agreeclosely with each other. They reported that there is approximately %50difference between averageNusselt numbers calculated fromChurchilland Chu's [7] and Raithby and Hollands' [9] equations for air at Ra=1.The difference can be calculated as 43% for higher Ra numbers(Ra=105 and Pr=0.7). Recently, Misumi et al. [3] investigated naturalconvectionflows around large horizontal cylinders experimentally anddiscussed the discrepancy on the average Nusselt numbers betweentheir results and the previous empirical correlations. They stated thatprevious empirical equations such asMcAdams [4] and Kutateladze [5]may not predict the Nusselt numbers correctly because of poordescriptions on the experimental apparatus and measurementtechniques. Besides Kitumura et al. [6] pointed out that some of theprevious researchers have derived the equations by averaging theexisting experimental data obtained by others. However, the datashow considerable scatters between the researchers, so that a simpleaverage of the data may cause the deviations against the real Nusseltnumbers.

Churchill and Chu [7] proposed a simple empirical expressionfor average Nusselt numbers over horizontal cylinder for all Rayleighand Prandtl numbers by using Churchill and Usagi's [8] model. This

Nomenclature

A heat transfer area, m2, A=πDLD cylinder diameter, mQe input electrical power, WQrad radiation heat loss, WQconv convection heat loss, WQcond conduction heat loss, WV heater voltage, VI heater current, AH heat transfer coefficient, W/m2KL length along cylinderGr Grashof numberRa Rayleigh number (Ra=GrPr)Pr Prandtl numberNuD,w local Nusselt numberK thermal conductivity, W/mkT temperature, (°C)Nu average Nusselt numberGe Gebhart numberw uncertainty2D two dimensionalXPS extruded polystyrene foamCFD computational fluid dynamicsLDA laser doppler anemometerDC direct current

SubscriptsW cylinder surfaces∞ ambientT top point of the cylinderb bottom point of the cylindernum numericalexp experimental

Greek lettersρ density, (kgm−3)v kinematic viscosity, (m2s−1)θ angle about cylinder centre from bottom of cylinderε emissivityσ Stephan-Boltzmann constantβ volumetric coefficient of thermal expansion (β=1/

(273+Tf))

732 Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 36 (2009) 731–738

expression can be applied for uniform heat flow, uniform walltemperature, mass transfer and simultaneous heat and mass transfer.Also simpler expressions were obtained for the limited conditions.Raithby andHollands [9] studied heat transfer over elliptic cylinders ofarbitrary eccentricity at a constant surface temperature, and proposedcorrelations for laminar and turbulent natural convection. Thin layeranalysis is developed by adding the thick boundary layer found at thelower Rayleigh numbers to the calculation. In the suggested correla-tion the temperature for the fluid properties is not specified. Fand et al.[10] developed Raithby and Hollands' [9] and evaluated fluid proper-ties at mean film reference temperature tf= t∞+ j(tw− t∞); j=0.5 intheir study. Fujii et al. [11] studied experimentally the free convectionfrom horizontal cylinder in water, spindle oil and mobeltherm oil anddefined a reference temperature: tj=t∞+ j(tw−t∞); 0≤ j≤1. Mean filmreference temperature was a special occasion of reference temperature,where tf and tj became equal for j=0.5. Thermo physical propertieswere evaluated at the mean film temperature in the present study.

The wake formation formed over the heated cylindrical surface atnatural convection and the effect of this phenomenon to the heattransfer on the surface are within the context of pre-made researches.

Pera and Gebhart [12] aimed to study the characteristic of the flowover the cylinder's surface caused by thermal effects and visualize thewake formation over cylindrical surfaces experimentally. They paidattention to the obscurity about the behavior in a separated region orin the region of wake formation. Development of a vertical boundarylayer flow adjacent to each of the two vertical side surfaces of theinverted U shaped cylindrical surface heated in distilled water wasvisualized. The flows, along the curved sections, were interacted andjoined together to rise in a plume above the curved surface.

Kuehn and Goldstein [13] numerically integrated the Navier Stokesand energy equations by using the finite-difference over-relaxationmethod for an isothermal horizontal circular cylinder in the range10°≤Ra≤107. Streamlines and isotherms were computed at differentvalues of the Rayleigh numbers. The temperature distributioncalculated at θ=90° and θ=180° for Ra=105, Pr=0.7 and theyhave been compared with the experimental results and it isascertained that the values for θ=90° are in good agreement. In thepreceding studies it is clearly demonstrated that the first effects of theseparation into a plume flow are seen for values of θ between 120° and150°. Thereafter, the flow and temperature fields depart completelyfrom the boundary layer forms. Such effect increases at larger θ [14].Kuehn and Goldstein [13] indicated that the boundary layer formula-tions for θN130° was not a sufficient approach for heat transfer. Morerecently, Reymond et al. [15] studied natural convection heat transferfrom a horizontal cylinder bounded with water and indicated thataround the circumference of a cylinder, the average Nusselt numberdistribution show a maximum at the bottom of the cylinder (θ=0°)and as the boundary layer developing it decreases towards the top(θ=180°).

Merkin [16] described a method of solving the full partialdifferential equations for the natural convection boundary layer overcylinders of general rounded cross-sectional formwhich could be usedto give reliable results over the whole of the cylinder; the particularexample considered there was of a circular cylinder. Muntasser andMulligan [17] used the local non-similarity method and gave localsolutions for different values of the Prandtl number. The change ofnatural convection along the radius of the horizontal cylinder wasstudied and the results were given from lower stagnation point(θ=0°) to the θ=150°. For different Prandtl numbers NuD,w/GrD,w1/4

were calculated by using the 1st degree and the 2nd degree similaritymethod at different angles and the results of arithmetic mean (Nu/Gr1/4) were given. It was said that the results from the first degreewere in good agreement with Merkin's finite difference equation untilθ=120°, and the deviations do not go beyond %1.87, but after θN120°the deviations increase and they reached %30 at 150°. In their studythe difference between the 1st and the 2nd degree results were so lowthat could be neglected. Farouk and Guceri [18] conducted somenumerical analysis of the heat transfer around a single cylinder. Theydemonstrated that heat transfer increases to its maximum at thebottom and decreases towards the top of the cylinder. According totheir analysis heat transfer decreases with increasing thermalboundary layer thickness. The model is capable of predicting theheat transfer from an isothermal cylinder and also considers a cylinderwith non-uniform wall temperature. It demonstrated that the plumewill shift to the cylinder's side with larger temperature gradients.

It is stated that there are many theoretical and experimentalstudies on natural convection heat transfer from horizontal cylinder.Generally the wide dispersion in the published experimental resultswas attributed to distortion of the temperature and velocity fields bybulk fluid movements, the use of under sized test cabin or existence ofthe temperature measurement system and supports. In the presentstudy, the test cabinwas constructed at proper dimensions and all thesurfaces except the top were made impermeable to minimize thesefactors. Different from the other experimental studies made in the air,all the experiments were performed in the conditioned room to keepthe environmental temperature constant during the experiments and

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to have experimental runs at different environmental temperatures. Inaddition, sensitive measuring devices were used to minimize themeasuring errors. The cylinders weremade of coppermaterial and thewall thickness was made as thick as possible (1 mm) to maintainuniform temperature distribution on the surfaces of the horizontaltest cylinders. Besides two pieces of insulatingmaterial made of XPS isplaced on the cylinder's endpoints to minimize the end losses (heatconduction to the supports).

Despite the contribution of published numerical studies, CFDanalysis was not used for natural convection heat transfer from ahorizontal cylinder. In the numerical part of this study, CFD package(FLUENT [21]) was used for the 2D heat transfer analysis.

2. Experimental investigation

2.1. Experimental apparatus and conditioned room

The experiments were performed in the conditioned room in orderto provide the desired environmental temperature and the naturalconvection conditions. In the room with the dimensions of4000 mm×4900 mm×2550 mm the environment temperaturebetween 5 and 50 °C and the relative humidity between 20% and95% can be adjusted to the required value. Ambient environment

Fig.1. Schematic diagram of the experimental apparatus: (1) conditioned room; (2) test cabin(5) insulating material made of XPS; (6) thermocouples on cylinder surface(14 pieces); (7)(11) DC power supply; (12) Power meter.

should be quiescent since the experiments will be made under theconditions of natural convection. As the result of the velocitymeasurements made with the hot-wire calibrated with LDA fromthe different points in the room it is determined that air velocity variesbetween 0 and 0.25m/s. A test cabinwas constructed from hard boardwhich has four lateral surfaces and floor with the dimensions of800 mmx1250 mmx1300 mm. A gap on the closed surfaces in theprotection cabin with only its top open can cause a stack effect andthus an unwanted bulk fluid movement will affect the temperatureand velocity fields. This effect leads to disturbance of the naturalconvection conditions. Hence, it is checked that there is no gap on theclosed surfaces. It is determined that the required quiescent environ-ment was provided as the result of velocity measurements madeinside the test cabin.

A schematic drawing of the experimental apparatus that consistsof twelve parts is shown in Fig. 1. The two test cylinders made fromcopper material at 1 m length and with diameters of 4.8 mm and9.45 mm have been prepared. Silicone covered cylindrical resistantwires, are centered not to leave any air space and close fitted inside thetest cylinder, to maintain the required uniform surface temperature.The diameter and the resistance value of the wires used for the firstand the second cylinder were 0.35 mm–11.3 Ω and 0.75 mm–3.4 Ωrespectively.

; (3) test cylinder (replacements of thermocouples); (4) silicone covered resistant wire;thermocouples in environment(2 pieces); (8) humidity sensor; (9) dataloger; (10) PC;

734 Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 36 (2009) 731–738

To provide the uniform surface temperature in the axial direction,test cylinders were made from copper and the wall thickness is madeas thick as possible (1 mm). In axial direction 11 notches were formedwith 10 cm space on the surface. Thermocouples can be partly buriedin these notches. In order to determine radial temperature distribu-tion three more notches were formed in radial direction with 90°. Ttype thermocouples with diameter of 0.3 mm calibrated withsensitive reference thermometer were used. The average surfacetemperature is determined with the thermocouples brazed to thenotches. Replacement of thermocouples on test cylinder is shown inFig. 1. Also to minimize the end losses, two pieces of insulatingmaterial made of XPS is placed on the cylinder's endpoints.

Thework station connected to the data acquisition unit of the roomis used for data collection. By means of HP VEE based softwareprogram, the all instant experimental data and required average valuescan be observed graphically. The program was developed on demandand brought into use. The mentioned features help to determine thesteady state condition and making analysis after experiment.

The cylinder was connected to a DC power supply with 10 A–60 Vvalue to give the required electrical power. Although the adjustablevoltage and current values given by the power supply can be read fromthe indicators on the device, a power meter with a resolution of±0.1 W is used to measure the input power accurately.

It is stated that the differences between the experimental dataobtained from the pre-studies on heat transfer in horizontal cylinderunder conditions of natural convection are caused by choosing theinsufficient heatmeasuring systemor designed test cabin. Tominimizethe errors mentioned in the pre-studies highly sensitive measuringtools were used, the test cabin volume was well determined and theexperiments were made in the conditioned room to keep theenvironmental temperature stable at the required values.

2.2. Experimental procedure

Natural convection heat transfer from a horizontal cylinder isstudied experimentally by using two cylinders with differentdiameters, on different uniform wall temperature and environmentaltemperature. The steps of experimental study are listed in order:

• The conditioned room temperature was set to provide the requiredenvironmental temperature in the test cabin. The environmentaltemperatures varied between T∞=10 °C and 40 °C. A quiescentenvironment was created and this was checked with hot wireanemometer inside the test cabin.

• Input electric power was sensitively regulated by DC power supplyfor the desired surface temperature. Eleven pieces of thermocouplesin the axial direction and two thermocouples in the test cabin is usedfor measuring the surface and environment temperatures respec-tively. It is possible to see the variation of these values graphicallywith the HP VEE based data collection program. The steady statecondition is considered when variation of all temperatures andespecially the average temperatures stay in the range of ±0.1–0.2 °Cfor 20 min. For each experiment steady state condition is realizedalmost 5 h later.

• An approximate uniform wall temperature boundary condition wasenabled by using highly conductive and thick (1 mm) coppercylinder. Maximum variation of the temperatures is 4% betweeneleven pieces of thermocouples in the axial direction. Beside this thesurface temperature has been observed under steady state conditioncircumferentially. For the range of measurements presented thesurface temperature of the second cylinder (4.8 mm) was observedto vary by less than 0.29 °C circumferentially. These low temperaturedifferences for both two cylinders can be clearly seen from Fig. 5.

• The experiments repeated by increasing the surface temperature by10 °C for each experiment up to 60 °C.

2.3. Data reduction

The dimensional analysis generally shows that natural convec-tion heat transfer from horizontal cylinders depends on Nusseltand Rayleigh numbers. So that, the aim of this study is to deter-mine the average Nusselt number for the horizontal cylinder as afunction of Rayleigh number Nu=f(Ra). In the experiment facility,sensitively measured input electrical power defined by Eq. (1)gives the total natural convection heat transfer from the horizontalcylinder.

Q e = VxI ð1Þ

Under steady state conditions the energy equation for thehorizontal test cylinder based on the 1st law of thermodynamics isexpressed as below:

Q e = Q conv + Q rad + Q cond ð2Þ

Since two pieces of insulating material made of XPS is placed onthe endpoints of the cylinder the conduction heat loss is neglected. Forthat reason, heat transfer from the horizontal cylinder surface byconvection can be calculated as:

Q conv = Q e − Q rad ð3Þ

Heat transfer from the horizontal cylinder surface by radiation canbe represented by:

Q rad =Ebw − Eb∞

1 − ewAwew

+ 1AwFw∞

+ 1 − e∞A∞e∞

ð4Þ

Ebw = σ :T4w ð5Þ

Eb∞ = σ :T4∞ ð6Þ

The emissivity of horizontal cylinder surface εw should bedetermined accurately to calculate the heat transfer by radiationfrom Eq. (4). Therefore the surface temperature of the heatedhorizontal cylinder is measured with T type thermocouple thatcalibrated with reference thermometer and thermal camera simulta-neously. Thermal camera's emissivity value is adjusted till themeasured two temperatures become equal. As a result, emissivity isfound as 0.51 in this study. Also the obtained value is in the suggestedrange of Thermal camera's emissivity tables for oxidized copper.

The convection heat transfer which is the driving force of theplume can be represented by:

Q conv = hA Tw − T∞ð Þ ð7Þ

Nusselt number is defined as:

Nu = hD= k ð8Þ

The air thermo physical properties (k, v) in non-dimensionalparameters were evaluated at the mean film temperature [Tf=(Tw+T∞)/2].

2.4. Uncertainty analysis

The accuracy of the experimental study can be affected by theerrors which may arise during the experiments for different reasons.These errors may be appeared in two ways. The first one is caused bythe researchers and the rest is the measurement error which consistsof two components; a random error and a systematic error. A randomerror reflects degree of randomness in any real life processes, whereasa systematic error is usually associated with a specific experimental

Table 1Thermal boundary conditions and test cylinder diameters.

Experiment no. Cylinder diameter (mm) Temperatures (°C)

T∞ TW

1 4.8 11.24 20.682 11.27 30.693 11.31 40.524 11.37 50.245 11.36 60.586 20.82 30.137 20.84 40.418 20.81 50.069 30.19 40.1110 30.29 50.3611 30.31 60.1912 39.95 50.4713 40.02 60.6814 49.51 60.7715 9.45 9.56 30.3516 9.72 40.1417 9.59 50.3618 9.81 60.519 20.26 30.1520 20.25 40.3821 20.15 50.2922 20.23 60.3623 30.57 40.2224 30.73 50.1525 30.54 60.8126 40.29 50.0127 40.27 60.09

Fig. 2. The solution grid (a) of the 2Dmodel of the cylinder in the test cabin (b) betweenthe cylinder's outer surface and the virtual circle [19].

735Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 36 (2009) 731–738

set-up and/or procedure. A random error is evaluated using statisticalmethods, while a systematic error can be reduced or eliminated bymeans of calibration. Error analysis is the determination of thesystematic and random errors and the introduction of the effects onthe experimental results. Also, the error analysis must be accom-plished before choosing the range of measurement devices in order tominimize the uncertainty of the results. On the other hand,determining the most important parameter will also contribute tominimize the uncertainty of the results by measuring it moreaccurately.

Amongst many error analysis methods, uncertainty analysismethod which is firstly proposed by Kline and McClintock [20] ismost widely used one for experimental studies. In this experimentalstudy, the uncertainty analysis method which is more sensitivecompared to others is used.

If the independent variables that cause errors in experiments arechosen as, input electrical power, eleven local cylinder surfacetemperatures and the environment temperatures that measuredfrom two points, the uncertainty of Nusselt number can be definedas follows.

Uncertainty analysis is not necessary for radiation heat transferbecause it is calculated theoretically and the errors neglected onlength measurements;

wh = F½ 1A: Tw−T∞ð ÞwQT

� �2+

−Q conv

A: Tw−T∞ð Þ2 wT0

� �2

+Q conv

A: Tw−T∞ð Þ2 wT∞

� �2�1=2ð9Þ

wNu = FDkwh

� �2� �1=2ð10Þ

As the result of the calculations made the maximum uncertainty isfound as 2.56% for heat transfer coefficient (Nusselt number).

3. Numerical analysis and model

In the numerical study FLUENT, CFD package was used. Thispackage uses a technique based on control volume theory to convertthe governing equations to algebraic equations so they can be solvednumerically. The control volume technique works by performing theintegration of the governing equations about each control volume, andthen generates discretization of the equations which conserve eachquantity based on control volume [21].

The GAMBIT mesh generator associated with the solver has beenused to plot and mesh the 2D model of the cylinder in the test cabinbased on the dimensions in the experimental study. For simplegeometries, quad/hexmeshes can provide high-quality solutions withfewer cells than a comparable tri/tet mesh. Since the surface of thetest cabin is planar and the surface of the cylinder is circular it wasseen that solution grids didn't overlap. To apply quad/hex meshesdecomposition is applied and it's divided to six pieces. The solutiongrid created is shown in Fig. 2a. The phenomenon in the boundarylayer around the horizontal cylinder surface is more important andcomplicated than rest of the solution domain. Hence, a virtual circlewas created outside the cylinder surface covering the boundary layerarea and structured computational cells were created with a fine

Fig. 4. Experimental average Nusselt number for the horizontal cylinder (a) comparisonwith the previous studies [1,2,7] (b) comparison in ±20% band.

Fig. 3. Experimental and numerical average Nusselt numbers for both two horizontalcylinders (a) comparison of data and trend lines (b) comparison in ±20% band.

736 Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 36 (2009) 731–738

mesh. The solution grid created between the cylinder's outer surfaceand the virtual circle is shown in Fig. 2b.

Boundary conditions can be defined in four different types inFLUENT: Constant heat flux, constant temperature, convection-radiation and convection. In this study, the constant temperatureboundary condition is applied, the lateral and bottom surface of testcabin and the surface of horizontal test cylinder are defined as walltype boundary condition; upper surface of the test cabin is defined aspressure-inlet type boundary condition. The temperature of the lateraland bottom surface of the box is taken as equal to the environmentaltemperature and measured environmental temperature from experi-ments is used. The average surface temperature measured in theexperimental study is used for the horizontal cylinder surfacetemperature. The thermal boundary conditions used in the study isgiven on the Table 1.

Segregated solutionmethod is used for the solution. The governingequations are solved consecutively in this method. In order to obtain aconverged solution, several iterations of the solution loop mustbe performed because the governing equations are non-linear (andcoupled).

The standard laminar viscous flow model was used. Hence thepurpose of the present study is to determine the convective heattransfer coefficient over the surface, radiation heat transfer at the

surfaces was not considered. For pressure-velocity coupling discritiza-tion the SIMPLE (Semi-Implicit Method for Pressure Linked Equa-tions) algorithm has been used. For continuity and momentum theresidual values were taken 10−3 and for energy 10−6.

4. Results and discussion

4.1. Experimental results

On the basis of the experimental data gathered, Rayleigh andaverage Nusselt numbers were calculated. Several researchers haveproposed commonly used correlations for the average Nusseltnumbers as a function of the Prandtl and Rayleigh numbers. For thisreason the new correlation was proposed as Nu=cRan in the range of7.4 101bRab3.4 103, (Pr=0.7)

Nu = 0:954 Ra0:168 ð11Þ

The experimental data and the correlations developed were givenin Fig. 3a.

The results of Morgen[1], Churchill and Chu [7], Fand andBrucker [2] are also presented in comparison with experimental

Fig. 5. The maximum temperature difference around the circumference of a cylinder(Tt− Tb) versus (Tw− T∞) for different cylinder diameters.

737Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 36 (2009) 731–738

data in Fig. 4a. The correlations that are used for comparison can beseen as follows:

Nu = 0:85 Ra0:188 102b Ra b 104 1½ � ð12Þ

Nu1=2 = 0:6 + 0:387 Ra= 1 + 0:559=Prð Þ9=16h i16=9� �1=6

Ra V 1012 7½ �

ð13Þ

Nu = ½ 0:4Pr0:0433Ra0:25� �

+ 0:503Pr0:0334Ra0:0816� �

+0:95Ge0:122

Pr0:06Ra0:0511

!� 108b Ra b 108 2½ �

ð14Þ

Average Nusselt number increases with increasing Rayleighnumber as expected. It is shown for validation of experimental dataand characteristics of this similar trend can be seen in pre studies atthe same time. Our new correlation is very close to the comparativecorrelation in literature that is given by Morgen[1]. The deviation ofexperimental average Nusselt number and previous studies [1,2,7]stay in the range ±20% and is seen in Fig. 4b. The max deviation is

Fig. 6. Comparison of the numerical correlation and the Merkin's suggested correlation.

seen between our experimental result and Churchill and Chu's [7]empirical correlation and that could be attributed to the wide range(Ra≤1012) of this correlation.

As a result of high thermal conductivity and the thickness of thecopper, the cylinders approximate a uniform wall temperatureboundary condition during experiments. The surface temperaturehas been observed under steady state condition circumferentially. Itwas emphasized that, the maximum temperature difference is seenbetween the top (θ=180°) and the bottom (θ=0°) of the cylinder. It isfound that the temperature difference between the top and thebottom (Tt−Tb) of the cylinder varies between 0.017 °C–0.29 °Cand 0.45 °C–1.69 °C for the first (4.8 mm) and the second cylinder(9.45 mm). For the range of measurements presented, the maxi-mum temperature difference around the circumference of a cylinder(Tt−Tb) versus (Tw−T∞) for different cylinder diameters can be seenin Fig. 5.

4.2. Numerical results

The surface heat transfer coefficient and the Nusselt number werecalculated using the total heat transfer rate obtained from the result of

Fig. 7. Results and flow view of numerical solution (a) the temperature distributioninside the test cabin (b) the temperature distribution on the heated horizontal cylindersurface inside the test cabin.

738 Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 36 (2009) 731–738

numerical solution. Nusselt and Rayleigh values calculated by usingthe experimental data and the values obtained from the result ofnumerical solution and the comparison of the correlations proposedaccording to these values are given in the Fig. 3a. The deviation valuesbetween experimental and numerical Nusselt numbers stay in therange ±20% is seen in the Fig. 3b.

Also the results of numerical solution were compared with theresults of Merkin [16] who studied natural convection heat transferfrom horizontal cylinder by using finite difference method. LocalNusselt numbers were given as NuD,w=f(GrD,w) in that study [16].Merkin's results were numerically integrated between 0° and 180° andan equation was created as Nu=f(Gr) in order to compare with thenumerical solutions of present study. Average Nusselt numbers weredetermined according to Grashof numbers that calculated by using theexperimental data. Numerical trend line created by using thenumerical solution results and the trend line of calculations' resultsmade according to the Merkin's correlation seem to have similarcharacter in Fig. 6.

As a result of numerical solution the temperature distributioninside the model was also drawn. The volume inside the test cabin(800 mmx1250 mmx1300 mm) is much bigger than the horizontalcylinder and therefore it is seen that the heated cylinder has noeffect on the temperature distribution inside the test cabin. Here, asan example, the results of the 17th experiment (T∞=9.59 °C,Tw=50.36 °C) were given in Fig. 7a. The phenomenon in theboundary layer around the horizontal cylinder surface is moreimportant and complicated than rest of the solution domain. Thusthe wake formation and the temperature distribution in the maininterested area is shown closer in Fig. 7b.

5. Conclusion

Natural convection heat transfer from a horizontal cylinder wasexperimentally and numerically investigated. Accurate and repeatableexperiments were carried out using sensitive measuring devices in aconditioned room. CFD analysis were performed as numerical solutionin the study and there is no another work using CFD program for thedetermination of natural convection from a horizontal cylinder withthe parameters of study. For that reason, this work is expected tocontribute to literature.

The following results were obtained:

(a) Nusselt numbers increase with increasing Rayleigh numbers inthis study.

(b) Characteristics of trend lines according to the numericaland experimental studies for the determination of averageNusselt numbers are found consistent in figures. Also results ofnumerical and experimental studies on the average Nusseltnumbers are found to be in good agreement.

(c) Comparison of average Nusselt numbers were done using thecorrelations of Morgen [1], Churchill and Chu [7], Fand andBrucker [2] according to the different experimental conditionsand test cylinders. Morgen's [1] correlation was the mostpredictive one due to its similar Rayleigh range with this study.In addition to this, majority of data belong to other correlationswere seen to fall into the 20% deviation line.

(d) A new correlation was proposed on the determination ofaverage Nusselt numbers for the range of 7.4 101bRab3.4 103

for air.(e) Wake formation and temperature distribution over the horizon-

tal cylinder were obtained by CFD analysis and shown in figureswhichhaveneverbeen seen in the literature before. In addition tothis, temperature and velocity fields were checked not to beaffected by the heated test cylinder in the test cabin, this resultshowed that the test cabin's size was designed properly.

Acknowledgments

The authors are grateful to Arcelik A.Ş. the leading refrigeratorcompany of Turkey for the usage of measurement devices and con-ditioned room.

References

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[3] T. Misumi, K. Suzuki, K. Kitamura, Fluid flow and heat transfer of naturalconvection around large horizontal cylinders: experiments with air, Heat Transfer,Asian Research 32 (2003) 293–305.

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