Experimental investigation on free convection from a horizontal cylinder beneath an adiabatic ceiling

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Experimental Thermal and Fluid Science 32 (2007) 614–623

Experimental investigation on free convection from ahorizontal cylinder beneath an adiabatic ceiling

M. Ashjaee a, A.H. Eshtiaghi b,*, M. Yaghoubi b, T. Yousefi c

a Mechanical Engineering Department, University of Tehran, Tehran, Iranb School of Engineering, Shiraz University, Shiraz, Iran

c Mechanical Engineering Department, Razi University, Kermanshah, Iran

Received 24 April 2007; received in revised form 25 July 2007; accepted 25 July 2007

Abstract

Steady two-dimensional free convection heat transfer from a horizontal, isothermal cylinder located underneath an adiabatic ceiling isstudied experimentally using a Mach–Zehnder interferometer. Effects of the ratio of cylinder spacing from the adiabatic ceiling to itsdiameter (L/D) on heat transfer from the cylinder are investigated for various Rayleigh numbers. Experiments are performed forL/D = 0.1, 0.3, 0.5, 0.7, 1.0, 1.5 and 2.4, and the Rayleigh number ranging from 1000 to 40,000. For each experiment thermal and flowfields are illustrated. Results indicate that the adiabatic ceiling has no influence on free convection heat transfer from the cylinder forL/D P 1.5. But by reducing this ratio from 1.5 to 0.5, Nusselt number decreases considerably. For close spacing of (L/D < 0.5), averageNusselt number again increases due to the vortex formation at the top of the cylinder where its effect is present as a sharp increase in themagnitude of local Nusselt number around circumferential position 130 6 h 6 180. Flow visualization by smoke is done to exhibit theexistence and the location of the vortices. A correlation based on the experimental data for the average Nusselt number of the cylinder asa function of Ra and L/D is presented in the aforementioned ranges.� 2007 Elsevier Inc. All rights reserved.

1. Introduction

Free convection heat transfer from a horizontal, iso-thermal cylinder suspended under an adiabatic ceilinghas been a subject for many researchers due to its vari-ous applications in different industries. In HVAC indus-tries, pipes of carrying hot fluid are often suspended onhangers below an overlying surface. Also electronic cool-ing of cylindrical components which is mounted below acircuit board is another application. An understanding ofthe influence of ceiling or blocking surface on free con-vection heat transfer from a heated cylinder which is dif-ferent from a single cylinder in a free environment isimportant.

0894-1777/$ - see front matter � 2007 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2007.07.004

* Corresponding author.E-mail address: [email protected] (A.H. Eshtiaghi).

In Fig. 1, a sketch of the model geometry is shown. Along cylinder of diameter (D) and length (l) is located belowan adiabatic ceiling. The ceiling dimension is (l · W) inwhich W is chosen to be 20 times the cylinder diameter.It is considered to be sufficiently wide in order to reducethe influence of W on heat transfer from the cylinder.The cylinder is heated to a temperature (Ts) and is locatedin air with ambient temperature (T1). The ceiling is madefrom very low conductive material and can be assumed asan adiabatic surface.

All modes of free convention from a horizontal cylin-der in a quiescent, infinite fluid have been studied exten-sively and well established correlations are available inthe literature [1–5]. The effect of adiabatic confining wallson the heat transfer coefficient from a circular cylinderhas been studied by some researchers [6–10]. Howeverinformation about heated cylinder below an adiabaticceiling is rare.

mailto:[email protected]

Nomenclature

C Gladstone–Dale coefficientD cylinder diameter (m)g gravitational acceleration (m/s2)h heat transfer coefficient (W/m2 K)�h average heat transfer coefficient (W/m2 K)k thermal conductivity of air (W/m K)L cylinder-to-ceiling distance (m)l cylinder length (m)M parameter in Eq. (5)Nu Nusselt numberNu average Nusselt numberNu modified Nusselt numberP pressure (Pa)r radius (m)R gas constant (J/kg K)Ra Rayleigh number based on the cylinder diameterT temperature (K)t end cap thickness (m)

U uncertainty function Eq. (5)W ceiling width (m)x parameter in Eq. (5)

Greek symbols

e fringe shiftg modified ceiling spacing, Eq. (9)k laser wave length (m)X heater electrical resistance (X)h angle from stagnation point (�)

Subscripts

1 ambient conditionref reference conditionf film conditionmin minimum conditionopt optimum conditions at the cylinder surface

M. Ashjaee et al. / Experimental Thermal and Fluid Science 32 (2007) 614–623 615

One of the closely related studies belongs to Saito et al.[11]. In their studies, the effect of a relatively narrow alumi-num covered Bakelite plate (0.94 6W/D 6 3.7) above ahorizontal heated cylinder is investigated at Grashof num-ber ranging from 2.1 · 106 to 3.2 · 106. They found that theoverall convection heat transfer rate from the cylinder wasminimum, when it was placed at a distance of L/D � 0.12below the ceiling. At such position, the average Nusseltnumber was about 11% lower than that of a single cylinderin an infinite medium.

Koizumi and Hosokawa [12] used flow visualization todelineate the flow regime around an isothermal cylinderlocated below a wide isothermal or an adiabatic ceiling.Experiments were performed in air for Rayleigh numberranging from 4.8 · 104 to 1 · 107. Three flow patterns werefound for isothermal ceiling, which dependent primarily onRayleigh number and dimensionless cylinder-to-ceilingspacing (L/D). At low Rayleigh number (approximatelyRa 6 105), steady two-dimensional flow was found to existfor all values of (L/D). At moderate and high Rayleigh

Fig. 1. Model

numbers, unsteady three-dimensional flow was observedfor some low values of (L/D) and the plume was observedto oscillate laterally at high values of (L/D). Local heattransfer data for the cylinder were presented for both typeof ceilings at Ra = 1.3 · 106 and L/D = 0.05, 0.2.

Using a Mach–Zehnder interferometer and a finite ele-ment based code; Lawrence et al. [13] studied the free con-vection heat transfer rate from a heated cylinderunderneath a wide isothermal ceiling. Experiments wereperformed in air for Rayleigh number ranging from 103

to 105 and 0.1 6 L/D 6 5.0. It was found that for cylin-der-to-ceiling spacing greater than about one diameter,the ceiling has almost no influence on heat transfer. Forvery close cylinder-to-ceiling spacing, average Nusseltnumber increased substantially because of conductioneffects. However, for 103

6 Ra 6 105 and L/D > 0.25, effectof the ceiling on the numerically predicted overall heattransfer rate was less than 10%. In the numerical studiesof Correa et al. [14], a finite difference code was used todelineate free convection temperature field around an

geometry.

616 M. Ashjaee et al. / Experimental Thermal and Fluid Science 32 (2007) 614–623

isothermal horizontal cylinder placed under an adiabaticceiling. Numerical solution has been obtained for a Prandtlnumber of Pr = 0.7 and a Rayleigh number range of1026 Ra 6 105. Their results demonstrate that the ceiling

has no effect on heat transfer rate for L/D > 2. By reducingcylinder-to-ceiling spacing less than half of the cylinderdiameter, heat transfer rate decreases to 30% in compari-son with a horizontal cylinder in a quiescent, infinite med-ium. By using a perfect adiabatic ceiling, the local Nusseltnumber around cylinder is different from those obtained byKoizumi and Hosokawa [12] for small cylinder-to-ceilingspacing.

The objective of the current study is to investigate localand average free convection heat transfer from a horizontalisothermal cylinder located below a wide adiabatic ceilingat different spacing (L/D) and Rayleigh numbers experi-mentally using a Mach–Zehnder interferometer as well asflow visualization of flow field by smoke test. Experimentsare performed in air for the spacing 0 6 L/D 6 2.4 and theRayleigh number range of between 1000 6 Ra 6 40,000.For practical consideration, a new correlation for the aver-age Nusselt number as a function of (L/D) and (Ra) hasbeen proposed which is very useful due its vast applicationin different industry. It should be added that all numericaland experimental studies [12–14] have not reported the vor-tex formation due to the induced secondary flow created byhot air plume at L/D 6 0.3, and therefore its effect on localheat transfer. The lack of this observation necessitates car-rying specific experiments to study and find local values ofconvection coefficient on the cylinder parallel with the flowvisualization by smoke test, in order to verify the vortexformation.

2. Experimental setup

2.1. Experimental apparatus

A Mach–Zehnder interferometer is used to observe thetemperature field around an electrically heated cylinderwhich is located below an adiabatic ceiling. In order toobtain the ranges of 1000 6 Ra 6 40,000, hollow alumi-num cylinders of 10, 19.5 and 22 mm O.D. are used forthe range of Rayleigh number 1000 6 Ra 6 3000,5500 6 Ra 6 14,500, and 15,000 6 Ra 6 40,000, respec-tively. In order to eliminate 3D effect, the length of eachcylinder is chosen as sixteen times its diameter. A thinspiral rod of Ni–Cr with ohmic resistance of Xtot = 160 X

Fig. 2. Schematic of the

is inserted at the core of cylinder as a heater. To increasethe thermal conductance between the tube and the heater,the hollow tube is filled with magnesium oxide powder.After reaching the steady state condition, the uniformityof the surface temperature is validated experimentally.The surface temperature of the tube is measured at 12 dif-ferent locations both in the circumferential and axial direc-tions with a calibrated hand held digital thermometer. Thedifference between the readings did not exceed 0.2 �C.

Two wooden caps with thermal conductance of (0.05 W/(m K)) [20] are mounted at the bases of the cylinder to min-imize the thermal end effects. The cylinder is placedbetween two optical windows as shroud wall for elimina-tion of any velocity end effect. A sketch of the cylinder isshown in Fig. 2. To measure the cylinder surface tempera-ture, two K-type thermocouples are inserted axially in theholes which are drilled in its wall. Surface of the cylinderare highly polished to achieve very fine surface smoothnessand minimize radiation heat transfer.

A two layer adiabatic ceiling is constructed frommedium-density fiberboard (MDF) [21] and Polystyrene[22] sheet with dimensions of 800 mm length, 170–200 mm width and 36 mm in thickness for the shortcylinder and 800 mm length, 360 mm width and 36 mm inthickness for the long one. The ceiling length to cylinderdiameter ratios are more than 40 and this makes the flowfield independent of ceiling length [13].

The electrical power supplied to the heaters is controlledby a variable transformer to obtain different cylinder sur-face temperatures. For measuring ambient and referencetemperatures, K-type thermocouples are used. Ambienttemperature thermocouple junction is placed 40 cm belowthe cylinder and reference temperature junction is placedright out of the cylinder’s thermal boundary layer.

All temperatures are monitored in a PC by a calibrated‘‘TESTO 177’’ four channel data logger. All the thermo-couples are calibrated in an isothermal bath to an accuracyof ±0.1 �C against a precision calibration thermometer,traceable to national standards. The pressure and relativehumidity of the laboratory are also recorded during allthe experiments.

To obtain different cylinder surface temperature andtherefore a constant Rayleigh number, it took about60 min to achieve the steady state condition. Three linearpositioners are used to alter altitude of three points onthe ceiling surface. By altering altitude of these points,the desired cylinder-to-ceiling spacing and ceiling parallel-

cylinder structure.


ism with the laser beam are achievable. To hold the cylin-ders parallel with the laser beam, two steel rods areattached to the wooden end caps. The rods are connectedto special positioners that could be adjusted to providethe cylinder vertical and horizontal movements as illus-trated in Fig. 3.

To eliminate laboratory air disturbance effects on thetest section, entire interferometer setup and the test sectionare enclosed within a large, open top Plexiglas box ofdimensions 2 · 1.5 · 4 m.

2.2. Interferometer and flow visualization

A 10 cm diameter beam Mach–Zehnder Interferometer(MZI) is used to measure the temperature field in the air

Fig. 3. Experiment setup.

Fig. 4. Schema

surrounding the cylinder. Schematic of the MZI used inthe experiment is shown in Fig. 4. A basic MZI is com-posed of a light source, two beam splitters (BS1 and BS2)and two mirrors (M1 and M2). Classic MZI utilizes semi-transparent layers as beam splitting elements. The parallelbeam, which is most commonly used, is split into a measur-ing and a reference beam at the beam splitter BS1.

Measuring beam passes through the test section and ref-erence beam passes through undisturbed medium. Finallythe reference and measuring beams recombine at beamsplitter BS2 and form interference fringes. When measuringand reference beams are parallel upon recombination, infi-nite fringe mode forms. In this mode, the constructive anddestructive interference fringes indicate the isotherms. So,local temperature gradient at the cylinder surface can becalculated. A 30 mW Helium–Neon laser with the wave-length k = 632.8 nm is used as a light source.

In a classic MZI, all the optical components are parallel.To obtain a wider beam during experiments, the laser beamis incident upon the optical components at 30� in compar-ison to 45� which is for a classical MZI. To reduce aberra-tion, the beam that passes through BS2 is reflected bymirror M3. This reflection process makes the beam to tra-vel a longer way and focus at the focal point of the lenswhich is placed in front of the CCD camera. By placingthe CCD at focal point of the lens, very clear image isachievable. Further information about MZI is availablein the literature [18,19]. All the interferograms are capturedby an ‘‘ARTCAM-320P’’ camera, connected to a PC, andby using video recorder software, interferograms are cap-tured online.

To visualize the free convection flow field around thecylinder, a vertical smoke sheet, perpendicular to the cylin-

tic of MZI.

Fig. 5. Local Nusselt number for individual cylinder.


der axis, is produced by using a smoke tube. Sulphuric acidaerosol generated by a Drager smoke tube. The smoke isthen introduced from bottom of the cylinder. The 30 mWHelium–Neon laser is used to visualize the created smokesheet. Shadow of smoke streaks in the laser beam illus-trated the flow pattern in two dimensions. These patternsare captured by an ‘‘ARTCAM-320P’’ CCD camera.

2.3. Data reduction

In order to obtain local Nusselt number around the cyl-inder, it is very important to recognize the cylinder sur-face. However, specific temperature differences betweenthe cylinder surface and the ambient are chosen in away to result in a constructive fringe which is attachedto the cylinder surface. To ascertain experiment repeat-ability, three interferograms are recorded for each Ray-leigh number.

The temperature of each fringe in the cylinder thermalboundary layer is calculated by method demonstrated byHauf and Grigull [18]. A code has been developed byMATLAB software to calculate the temperature of eachfringe as well as its distance from the cylinder surface at19 different radial directions for each recorded interfero-gram. By extrapolating the temperature distribution curveto the cylinder surface temperature, the gradient at the cyl-inder surface are calculated. Due to symmetry of the tem-perature field, data reduction is only made for half of thecylinder.

The local air temperature gradient at the cylinder sur-face is calculated as follow:

dTdr

��rs

¼ dTde

��rs

� dedr

��rs

; ð1Þ

where T is temperature; r is radii parameter and e is thefringe shift value relative to the cylinder surface. ThendTde

��rs

can be calculated from the following equation [18,19]:

dTde

��rs

¼ 6ClP1kRT 2ref

ð3ClP1 � 2kRT refeÞ2rs

: ð2Þ

In Eq. (2), P1 is ambient pressure, R is the gas constant forair, l is the cylinder length along the laser beam, k is thewavelength of laser, C is Gladstone–Dale constant, Tref isreference fringe temperature and rs is radius of the cylinder.Eq. (2) is based on an ideal gas and Lorenz–Lorenz rela-tions [18].

Local Nusselt number can be calculated from thefollowing:

Nuh ¼�ks

dTdr

��r¼rs

D

ðT s � T1Þkf

; ð3Þ

where ks and kf are the thermal conductivity of airevaluated at the surface temperature (Ts) and at thefilm temperature, Tf = (Ts + T1)/2, respectively. Theaverage Nusselt number is calculated from the follow-ing:

�h ¼ 1=pZ p

0

hhdh; Nu ¼ �hD=kf : ð4Þ

In order to validate the experiments and the data reduc-tion method, a heated cylinder is tested in an infinite med-ium for Ra = 1000. The results are compared with theprevious works [1,2] which is shown in Fig. 5. Excellentagreement between the current experimental results andthe previous works exist.

2.4. Uncertainty analysis

Usually in optical methods, light distortion errors existbecause light beam passes through non ideal optical com-ponents. Total uncertainty U comprises of uncertaintiesof many parameters, which influence on the experiment[15]. For a value of M, whose results depend on uncorre-lated input estimates x1,x2, . . .xN, the standard uncertaintyof the measurement is obtained by appropriately combin-ing the standard uncertainties of these input estimates.The combined standard uncertainty of the estimate M

denoted by U is calculated from the following equations[16,17]:

M ¼ f ðx1; x2; . . . xN Þ;

U 2ðMÞ ¼XN

i¼1

ofoxi

� �2

U 2ðxiÞ;ð5Þ

where f is the function of M in terms of input, estimatesx1,x2, . . .xN, and each U(xi) is a standard uncertainty of in-puts. Relation between local Nusselt number and fringeshift (e) is presented by Eqs. (2) and (3).

By applying Eqs. (3)–(5) average Nusselt number uncer-tainty is

Table 1Values for the parameters of Eq. (6)

Parameter xi dxioNuhoxi

dxiNuh

(%)

Tw 309.65–388.55* K 0.1 K 0.8–0.66T1 297.75–297.75 K 0.1 K 0.8–0.66P1 87,000–87,100 Pa 100 Pa 0.12–0.09l 16–360 mm 0.025 mm 0.008–0.006D 10–22 mm 0.025 mm 0.12–0.1Dr 0.63–1.5** mm 0.027 mm 4.42–1.35

0.35–1.9 mm 5.9–1.1

* Values of parameters for Ra = 40,000.** 0.63 and 1.5 are radial distance differences for h = 0�, 180�,

respectively.

Fig. 6. Interferograms of (a) Ra = 15,000, (b) Ra = 25,000 and (c)Ra = 40,000.


dNu ¼ oNuoT1

dT1

� �2

þ oNuoT w

dT w

� �2

þ oNuoP1

dP1

� �2"

þ oNuol

dl� �2

þ oNuoD

dD� �2

þ oNuoT ref

dT ref

� �

þ oNuoðDrÞ dðDrÞ� �2

#12

: ð6Þ

In Eq. (6), standard uncertainties in the gas constant, theGladstone–Dale constant, the fringe shift and the laserwave length have been neglected. Table 1 lists the experi-mental values of the parameters in Eq. (3) and the associ-ated uncertainties for L/D = 1, Ra = 1000 and 40,000and D = 10, 22 mm.

Uncertainties of the parameters T1, Tw and P1 can beestimated from the measurement devices precision anduncertainties of the parameters l and D from the measure-ment process. The uncertainty of the parameter Dr, theincrement in radial distance from the cylinder surface, isrelated to the precision of reading the digitized interfero-grams. From Table 1, it can be seen that the latter is thedominant source of error. The uncertainties in the averageNusselt numbers for specified Rayleigh numbers and geo-metrical parameters are 3.64% and 4.75%, respectively.Using this analysis, uncertainties in the measured localNusselt numbers have been estimated to be 3.6 ± 1.5%for Ra = 1000 and 4.95 ± 2.6% for Ra = 40,000.

3. Results and discussion

Effects of horizontal heated cylinder spacing from anadiabatic ceiling and the Rayleigh number on free convec-tion heat transfer have been investigated experimentally.The experiments are carried out for the spacing to cylinderdiameter ratios of L/D = 0, 0.1, 0.3, 0.5, 0.7, 1.0, 1.5, 2.0and 2.4 for the Rayleigh number range of 1000 6 Ra 6

40,000.Fig. 6 indicates the infinite fringe interferograms for the

Rayleigh numbers of 15,000, 25,000 and 40,000 with L/Dratios of 0.0, 0.1, 0.3, 0.5, 0.7, 1.0 and 1.5, respectively.All the interferograms for the range of 0.5 6 L/D 6 2.4indicate that air plume from the heated cylinder will rise


around h = 180� and hits the adiabatic ceiling. Then it getsdivided to two streams and flow towards the left and rightof the cylinder beneath the ceiling with a symmetrical flowpattern. This symmetry also exists for the cases ofL/D = 0.3, 0.1 and 0.0, but the air plume gets suppressedfrom rising vertically at h = 180� by the damping effect ofthe ceiling which is due to its small distance from the cylin-der. This causes that the plume to flow towards the left andright beneath the ceiling which happens at angles of abouth = 110, 130 and 150 for the L/D = 0.0, 0.1 and 0.3,respectively.

Fig. 7 represents the variation of the average Nusseltnumber of the heated cylinder with respect to L/D ratiofor different Rayleigh numbers. As it can be observed,the average Nusselt number is approximately constantbetween 1.5 6 L/D 61 for all the Rayleigh numbers,i.e., the free convection heat transfer from the cylinder doesnot indicate any decrease compared to its value in an infi-nite medium till a distance of L/D = 1.5 from the ceiling.

The ceiling’s damping effect on free convection heattransfer from the cylinder starts from L/D = 1.5 andincreases by taking the cylinder closer to the ceiling tillaround L/D = 0.5 for all the Rayleigh numbers. Below thispoint, the average Nusselt number again starts to increaseeven by decreasing the spacing between the cylinder andthe ceiling. This does not imply that the ceiling dampingeffect on heat transfer vanishes. But formation of vorticesat the top of the cylinder and their enhancement effect onthe local heat transfer, overcome the damping effect ofthe ceiling on heat transfer. Therefore, an increase of aver-age Nusselt number for L/D < 0.5 is observed as shown inFig. 8. The flow pattern and the vortices around the cylin-der are found by the smoke test for the cases of L/D = 0.0,0.1, 0.3, 0.5, 0.7, 1.0 and 1.5, and Ra = 14,500 which areshown in Fig. 8.

Fig. 7. Average Nusselt number versus L/D.

For L/D = 0.0, 0.1 and 0.3, vortex flow can be observedat the top of the cylinder between h = 130� and 180�. ForL/D = 0.5 and 0.7, vortex flow exists at h � 170�, but vor-tices do not have any impact on the cylinder surface. Forthe values of L/D = 1.0, a very weak vortex flow can beobserved above the cylinder, but it is too weak to propelthe smoke particles. By increasing the L/D ratio to 1.5, vor-tex flow is not observed at the top of the cylinder.

To investigate the effect of these vortices on heat trans-fer, the value of local convection coefficient has been plot-ted versus � for the Rayleigh numbers of 14,500 and40,000 and different values of (L/D) which are shown inFigs. 9a and b, respectively. For L/D = 0.1 and Ra =14,500, Fig. 9a indicates the formation of a stronger vortexflow, and therefore its impact at the top of the cylinderwhich causes a sharper increase of local convection coeffi-cient between 120� 6 h 6 180� compared to the case ofL/D = 0.3. A smaller rate of increase of local Nusselt num-ber is observed for L/D = 0.3 and the affected location ofvortex flow on the cylinder is shifted towards its upperpart around 140� 6 h 6 180�. By increasing the Rayleighnumber from 14,500 to 40,000, one can observe a shift ofimpact of vortices on the cylinder, where this shift is about10� for L/D = 0.1 and 5� for L/D = 0.3.

Average Nusselt number versus Rayleigh number hasbeen illustrated in Fig. 10 for different cylinder spacing.Also in Fig. 10 the result of Morgan [3] for a cylinder inan infinite medium is presented for comparison. By com-paring the case of L/D = 1.5 with L/D =1, it can beobserved that the ceiling does not have any effect on therate of heat transfer from the cylinder for L/D P 1.5 atall the Rayleigh numbers.

3.1. Correlation

Results of the experimental investigation are used todevelop a general equation which gives the variation ofthe Nusselt number in terms of the Rayleigh number and(L/D) ratio as following:

Nu ¼ 1� 0:2357� exp � g� 0:8921

0:9955

� �2 !

; R2 ¼ 0:9061;

ð7Þ

where

Nu ¼ Nu

Nu1ð7aÞ

and the value of Nu1 from the work of Morgan [3] is

Nu1 ¼0:85� Ra0:1888 102 < Ra < 104;

0:48� Ra0:25 104 < Ra < 107

�� ð8Þ

and

g ¼ LD

� �1:215

Ra0:141 � 0:2

!0:52

: ð9Þ

Fig. 8. Combined smoke test indicating flow patterns with the thermal field for various L/D.


For the limit of (L/D)!1 (cylinder in an infinite med-ium), Eq. (7) reduces to unity. Fig. 11 represents the corre-lation given by Eq. (7) graphically along with all theexperimental measurements.

The standard deviation for the curve fitting of Eq. (7) isabout ±4.7% with the maximum and minimum errors of9.31% and 2.61%, respectively. The values of the gopt alsohave been obtained from the correlation Eq. (7) by differen-tiating it with respect to g as it follows:

oNuog¼ 0; ð10Þ

which results in the equation

LD

� �opt

¼ 1:0024

Ra0:1161: ð11Þ

The values of the (L/D)opt, which are for the occurrenceof minimum heat transfer from the cylinder are shown inFig. 8. A relation for the minimum Nusselt number,Numin, at the optimum wall spacing, (L/D)opt, can beobtained for different Rayleigh numbers by substitutionof Eq. (11) into Eq. (7) which results in

Numin ¼ 0:7643� Nu1: ð12Þ

Fig. 10. Average Nusselt number versus Rayleigh number.

Fig. 11. Correlation of Nusselt number based on experimental data.

Fig. 9. Local Nusselt number around cylinder for (a) Ra = 14,500 and (b)Ra = 40,000.


A comparison of minimum and the infinite mediumvalue of Nusselt number from Eq. (12) and Eq. (8) revealsa maximum decrease of 23.4% in the heat transfer from thecylinder under an adiabatic ceiling. The experimental dataindicates an average of 19.1% reduction.

4. Conclusion

Laminar free convection from an isothermal horizontalheated cylinder beneath an adiabatic ceiling is studiedexperimentally in air. Experiments are carried out usingMach–Zehnder interferometer for different cylinder spac-ing and Rayleigh numbers. The experimental data showthat the average Nusselt number increases with increasingRayleigh number for all the cylinder spacing. At each Ray-

leigh number, there exists an optimum spacing which min-imizes the heat transfer from the cylinder. All theexperimental results are presented with a single correlationwhich gives the average Nusselt number as a function ofRayleigh number and (L/D) ratio. Also our experimentaldata indicate an average of 19.1% decrease in the valueof Nusselt number at the optimum wall spacing withrespect to the cylinder in an infinite medium.

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[20] M.B. Bever, Encyclopedia of Materials Science and Engineering, vol.7, Pergamon Press, Oxford, UK, 1986.

[21] Australian wood panels association incorporated, Data sheet 8,Standard medium density fiberboard, May 2004.

[22] Engineering plastics, Engineering material handbook, ASM Interna-tional, 2, p. 196.

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Experimental investigation on free convection from a horizontal cylinder beneath an adiabatic ceiling