International Journal of Heat and Mass Transfer 55 (2012) 1154–1163

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International Journal of Heat and Mass Transfer

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Experimental study of conjugate heat transfer within a bottom heated verticalconcentric cylindrical enclosure

Asif Hussain Malik a,⇑, M.S.I Alvi a, Shahab Khushnood a, F.M. Mahfouz a, M.K.K. Ghauri a, Ajmal Shah b

a Department of Mechanical Engineering, University of Engineering and Technology, Taxila, Pakistanb Department of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan

a r t i c l e i n f o

Article history:Received 3 May 2011Received in revised form 22 September2011Accepted 22 September 2011Available online 22 October 2011

Keywords:Conjugate heat transferCylindrical enclosureBottom disc temperatureInner cylinder materialsOuter cylinder diameterThermal conductivity

0017-9310/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2011.09.055

⇑ Corresponding author. Tel.: +92 51 4493400.E-mail address: asifhussainmalik@yahoo.com (A.H

a b s t r a c t

In this research work an experimental study of conjugate heat transfer within an air filled bottom-heatedvertical enclosure is conducted. The enclosure consists of two concentric cylinders with inner cylinderbeing shorter and open at the top. The study is important with respect to the centrifuge machine usedin the process industry. Eighteen different experiments are performed by varying the bottom disc centraltemperature between 353 and 433 K, using three different materials (aluminum, mild steel and stainlesssteel) of the inner cylinder and two different diameter outer cylinders of mild steel. This study unfolds thetemperature, material and geometric effects of bottom disc, inner cylinder and outer cylinder respectivelyon thermal convection in the enclosure. Generally, a uniform temperature is required in such enclosures.A more uniform axial and radial temperature is observed in the enclosure by using aluminum inner cyl-inder within a temperature range of 353–433 K of the bottom disc and using two different diameter outercylinders. It is observed that the maximum temperature in the enclosure is lowest for aluminum innercylinder and higher for mild steel and highest for stainless steel. The heat balance and non-dimensionalanalysis of the enclosure are carried out and discussed critically.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction with the same heat flux at the top surface and the bottom surface

The study of conjugate heat transfer i.e., combination of all orany of the two modes of heat transfer taking place simultaneously,through the cylindrical enclosures has been under investigation forthe last fifty years. The conjugate heat transfer in the cylindricalenclosures has a broad spectrum of engineering applications likein process industries, building technology, solar collectors, centri-fuge machines, heat exchangers, material processing, storagetanks, furnace designs, nuclear designs, etc. However, the studyof bottom heated non-conventional cylindrical enclosure (two con-centric cylinders) is important with respect to the segregation ofchemicals in the centrifuge machines. In these machines heat isadded to the enclosure through the bottom due to electrical motorlosses and production of heat due to rotation of inner cylinderwhich affects the process of segregation. It is common practice tosimulate the addition of such heat losses to the enclosure througha bottom heated disc.

The past researchers have conducted the study of variousmodes of heat transfer through different enclosures. Lemembreand Petit [1] numerically investigated the two-dimensional lami-nar natural convection heat transfer in cylindrical enclosures of lat-erally heated walls at uniform heat flux. The enclosure is cooled

ll rights reserved.

. Malik).

is insulated. They have studied the temperature profiles along theaxial direction. Baïri [2], Franke and Hutson [3], Roschina et al. [4],Raghavarao and Sanyasiraju [5], Sharma et al. [6] numericallyinvestigated the convection heat transfer in the cylindrical enclo-sures with thermo-physical fluid properties assumed to be con-stant except the density variation which varies according toBoussinesq approximation.

The experimental and numerical study of natural convection intwo-dimensional Newtonian and incompressible fluid-filled enclo-sures with different temperatures on the two vertical walls is pre-sented by Kim and Viskanta [7], Das et al. [8], and Vargas et al. [9].They have concluded that heat conduction reduces the average tem-perature difference across the enclosure but also produces partialstabilization of the flow and decreases natural convection heattransfer. Kee et al. [10] presented the experimental and numericalstudy of steady natural convection of a heat generating tritium gasin a two-dimensional closed vertical cylinders and spheres withtheir bounding isothermal walls and demonstrated the experimen-tal and analytical agreement for the local temperatures over a rangeof Grashof number. Newport et al. [11] experimentally investigatedthe thermal interaction in the two-dimensional isothermal cylinderlocated in a water-cooled isothermal cubical enclosure. They havegiven a considerable insight into the nature of the enclosure heattransfer. Keyhani et al. [12] experimentally investigated the increasein free convection heat transfer in a vertical annulus with inner

Fig. 2. Sectioned view of the enclosure showing all temperature sensors.

A.H. Malik et al. / International Journal of Heat and Mass Transfer 55 (2012) 1154–1163 1155

cylinder at constant surface heat flux and outer cylinder at constanttemperature. The flow field is strongly dependent on the Rayleighnumber (Ra) and the enclosure geometry, while the Prandtl numberand the radius ratio have less effect on the flow regime. Lipkea andSpringer [13] experimentally investigated heat transfer throughgases (argon, helium and neon) between vertical concentric cylin-ders with axial conduction in a cylinder by providing heat sourcesat different places. The characteristic recirculation speed insidethe enclosure is introduced and analyzed. In their study steady strat-ified temperature distributions are compared with the model simu-lations of the RMIX++ code. Bohn and Anderson [14] experimentallyinvestigated the heat transfer between parallel and perpendicularvertical walls in a three-dimensional water-filled cubical enclosurewith adiabatic top and bottom and isothermal sides and discussedmany aspects of natural convection heat transfer. Kuznetsov andSheremet [15] numerically analyzed laminar two-dimensional con-jugate convective-conductive heat transfer in the enclosure. Theyhave studied the effects of Grashof numbers, buoyancy ratio, andtransient factor on flow modes, heat and mass transfer. Liaqat andBaytas [16] numerically analyzed the laminar two-dimensional con-jugate natural convection in an enclosure. They have shown a signif-icant change in the buoyancy flow parameters as compared toconventional non-conjugate investigations. The conjugate naturalconvection in a liquid sodium filled cylindrical enclosure with inter-nal volumetric heat source is studied by Sharma et al. [6]. The lateralwalls of the enclosure are isothermal, while the top and bottomwalls are adiabatic. They have presented the transient features ofconfined turbulent natural convection due to time varying genera-tion of heat in the volumetric source and shown that the intensityof heat source exponentially decays with time. The laminar, three-dimensional natural convection in the air-filled vertical annularspace formed by a square rod enclosed within a cylinder is studiedby Glakpe et al. [17]. They have studied the effects of thermal radi-ation exchange between the walls of an enclosure. Paroncini et al.[18], Aydin and Yang [19] have investigated the natural convectionheat transfer of air in a two-dimensional enclosure with localizedheating from bottom and symmetrical cooling from the sides. Theyhave concluded that for small Rayleigh number, the heat transfer isprimarily by conduction across the fluid layer, while for highRayleigh number, the heat transfer is primarily by convection andthe effect of conduction vanishes.

In this research paper, the conjugate heat transfer within a bot-tom heated vertical concentric cylindrical enclosure has beeninvestigated experimentally. In spite of the above mentioned re-search, the effects of bottom disc temperature, inner cylinder

Fig. 1. Experimental model.

materials and outer cylinder diameters on thermal convection inthe enclosure has not been studied so far to the best of our knowl-edge. Experimental model has been designed to conduct the exper-iments using two different configurations with three differentmaterials of the inner cylinders and bottom disc and three differentbottom disc temperatures (353, 393 and 433 K) at the upper cen-tral location of the disc. This study provides a tool to adjust thecooling system as per requirements, gives insight of different con-figurations and inner cylinder materials and promotes the under-standing of the conjugate heat transfer. This gives an openguidance for the future and leaves open fields for studying on dif-ferent materials and geometries.

2. Experimental setup

The actual experimental setup is shown in Fig. 1, which consistsof cylindrical enclosure, electric heater, foundation box, tempera-ture sensors, data acquisition system and computer etc. In totaleighteen experiments are performed by changing the bottom disctemperature, inner cylinder material and outer cylinder diameter.The different parts of the experimental setup are discussed below.

2.1. Cylindrical enclosure

The enclosure consists of two concentric cylinders filled with airand a circular disc at the bottom. The cylinders are placed in thevertical direction as shown in Fig. 2. The details of the bottom discand the two vertical cylinders are given below.

2.1.1. Bottom discIn the centrifuge machines electrical losses and production of

heat due to rotation of inner cylinder take place, which affect the

Table 1Geometric specifications of the cylindrical enclosure.

Parts ofgeometry

Material Diameter(m)

Thickness(m)

Height(m)

Bottomdisc

Aluminum, mild steel,stainless steel

0.138 0.004 –

Innercylinder

Aluminum, mild steel,stainless steel

0.146 0.005 1.480

Outercylinder

Mild steel O1 = 0.256,O2 = 0.300

0.010 1.540

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process inside the enclosure. In this experimental model, theselosses are simulated by heating the bottom disc at the bottom ofthe enclosure by an electric heater. N-type thermocouple, havingaccuracy of ±0.75%, is mounted to the upper central location ofthe disc as shown in Fig. 2. The temperature at the center of thedisc is controlled by a temperature controller ‘CAL Series 9900’and a contactor (solid state rely), having accuracies of ±0.25% and±0.5%, respectively. Temperature of the disc central point is varied

Table 2Bottom disc experimental temperature distribution.

Radial distance, m 0

Outer cylinder, O1 Tc = 353 K Aluminum 353Mild steel 353Stainless steel 353

Tc = 393 K Aluminum 393Mild steel 393Stainless steel 393

Tc = 433 K Aluminum 433Mild steel 433Stainless steel 433

Outer cylinder, O2 Tc = 353 K Aluminum 353Mild steel 353Stainless steel 353

Tc = 393 K Aluminum 393Mild steel 393Stainless steel 393

Tc = 433 K Aluminum 433Mild steel 433Stainless steel 433

Fig. 3. Axial temperature distributions of (a and b) aluminum inner cylinder with K1 = 87inner cylinder with K3 = 611.52.

within the range of 353–433 K during different experiments. Therest of the thermocouples used in the experiment are all PT-100type, having accuracy of ±0.3%. The uncertainty in the reading ofN-type thermocouple is estimated to be less than 1.5% and thatof PT-100 sensors less than 1.1%, including the effect of the scatterof observed experimental data. In each experiment the disc and in-ner cylinder used are of the same material. Bottom disc is shown inFig. 2 and its materials along with dimensions are given in Table 1.

0.014 0.028 0.042 0.056 0.069

351 350 349 348 347351 349 348 346 343348 346 344 341 340391 388 387 385 384391 390 388 384 381391 388 381 376 374431 430 429 427 425432 430 428 427 425427 424 421 513 410

351 348 346 344 343352 350 349 348 346350 348 346 345 344389 386 385 384 383391 390 389 388 386391 386 381 377 375430 428 427 425 422430 428 427 426 424431 428 420 413 407

02.47, (c and d) mild steel inner cylinder with K2 = 1775.77, (e and f) stainless steel

Table 3Temperature sensors distribution in the enclosure.

Inner cylinder Outer cylinder Axis Disc Ambienttemperature

Innerwall

Outerwall

Innerwall

Outerwall

14 14 14 14 14 11 1

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In each experiment the bottom disc act as an isothermal boundaryand its temperatures for all eighteen experiments are tabulated inTable 2.

2.1.2. Inner cylinderIn centrifuge machines which are used in chemical, sugar, phar-

maceutical, textile and dyestuff industries the heat losses added tothe enclosure affect the processes occurring in the inner cylinder.For example in the centrifuge hydro extractor, chemical centrifugeand top driven bottom discharge centrifuge machine the segrega-tion of chemicals takes place in the inner cylinder. Therefore, thethermal behavior and material of the inner cylinder plays animportant role in centrifuge machines. Generally, the temperaturewithin the centrifuge machines, used in the above mentionedindustries, reaches up to 473 K. Ideally, the design of centrifugegeometry should be such that a uniform temperature is achievedalong the wall of the inner cylinder. Due to this reason, the effectof temperature, material and outer cylinder geometry on the innercylinder is studied. Heat is transferred from disc to the air insidethe inner cylinder through convection and radiation and conduc-tion takes place through the wall of the inner cylinder. Three inner

Fig. 4. Axial temperature distributions of outer cylinder with (a and b) aluminum inner cand f) stainless steel inner cylinder with K3 = 611.52.

cylinders of same dimensions and different materials (aluminum,mild steel and stainless steel) are used in these experiments as tab-ulated in Table 1. Three inner cylinders of aluminum, mild steeland stainless steel have thermal conductivities (K) of 222, 45.3and 13.4 W m�1 K�1 and thermal conductivity ratios (K1, K2, K3)of 8702.47, 1775.77 and 611.52, respectively.

2.1.3. Outer cylinderTwo outer mild steel cylinders (O1,O2), of different diameters

having aspect ratios (A1,A2) of 6.016 and 5.133 and radius ratios(RR1,RR2) of 1.753 and 2.055, respectively are used in these exper-iments to study the effect of outer cylinder diameter on the conju-gate heat transfer occurring within the enclosure. The details ofouter cylinders (O1,O2) are given in Table 1.

2.2. Electric heater

A coil type electric heater of 500 W is placed below the bottomdisc in a bucket inside the foundation box. The heater is capable ofmaintaining temperatures up to 1116 K and features rapid coolingand heating due to low mass construction. The heating of the electricheater is controlled by a contactor (solid states rely). The contactor isguided by temperature controller which is connected to the thermo-couple placed at the central point of the upper surface of disc.

2.3. Other accessories

The bottom of the enclosure, except the disc, is insulated with alayer of ceramic wool placed between two sheets of Teflon. The topcover is also insulated by a thick layer of ceramic wool.

ylinder with K1 = 8702.47, (c and d) mild steel inner cylinder with K2 = 1775.77, (e

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In total 82 thermocouples are used to monitor the temperatureat different locations within the enclosure as tabulated in Table 3.The distribution of these temperature sensors is shown in Fig. 2.First row of the temperature sensors is mounted at an axial dis-tance of 5 mm from the bottom disc. The successive rows are then116 mm apart except the last row. In the last row the sensors areplaced at the end of their respective locations. One thermocoupleis hanged in the open environment to sense the ambient tempera-ture. The thermocouples are connected to ATmega based dataacquisition systems of 64 channels. The steady state is assumedwhen the temperatures inside the enclosure remained unchangedfor fifteen minutes as mentioned by Niu et al. [20].

2.4. Heat balance

The heat enters the enclosure through bottom disc and leaves itthrough the wall of the outer cylinder. In steady state, the heat enter-ing the enclosure must be equal to the heat lost from it. The heat islost from the wall of outer cylinder to the surrounding through nat-ural convection. The ambient temperature and pressure are 299 Kand 0.934 kg cm�2, respectively, while the natural convection heattransfer coefficient at the outer cylinder is assumed 10 W m�2 K�1

as mentioned by Sukhatme [21] Prandtl number, thermal conductiv-ity and dynamic viscosity of air are 0.71, 0.0255 W m�1 K�1 and1.8949E�05 Pa-s, respectively. The heat enters the enclosure,mainly, through convection. Therefore, neglecting radiations theheat transfer coefficient for the enclosure can be calculated fromheat balance. The heat transfer coefficient for the enclosure calcu-lated from this heat balance is varying from 21.5 to 39.9 W m�2 K�1

for the experiments performed in this work. Cengel [22] shows some

Fig. 5. Radial Temperature distributions of aluminum inner cylinder, K1 = 8702.47

examples in which the heat transfer coefficient varies in this range.This shows that the quantity of heat lost from the enclosure is equalto the heat added to the enclosure provided the heat transfer coeffi-cient varying in the range of 21.5–39.9 W m�2 K�1.

3. Results and discussion

The study of heat transfer within the cylindrical enclosure isimportant because of its numerous applications in the processindustry. Lipkea and Springer [13] have experimentally investi-gated heat transfer through gases (argon, helium and neon) be-tween vertical concentric cylinders with axial conduction in acylinder by providing heat sources at different places. Lemembreand Petit [1] have presented the laminar natural convection in a ver-tical cylinder by insulating its bottom and heating laterally at uni-form heat flux density and cooling at the same heat flux at the topsurface and plotted axial temperature profiles. Although, a lot of re-search work has been done in this area during the last 4–5 decades,but still there are certain areas which are not explored fully. In thispaper the effect of different parameters (bottom disc temperatures,bottom disc and inner cylinder materials and outer cylinder diam-eters) on the conjugate heat transfer within an air filled vertical con-centric cylindrical enclosure (Fig. 2) is studied experimentally. Thisstudy will help in understanding the heat transfer phenomenonwithin the bottom heated cylindrical enclosure and the effects ofdifferent materials and geometric configurations on it.

3.1. Axial thermal behavior

Amara et al. [23] studied temperature profiles in the axial direc-tion by applying lateral heat flux density in the vertical cylindrical

at an axial distance of (a and b) 5 mm, (c and d) 700 mm, (e and f) 1396 mm.

A.H. Malik et al. / International Journal of Heat and Mass Transfer 55 (2012) 1154–1163 1159

enclosure. In this research paper the axial temperature profiles ofinner and outer cylinders are studied by heating the bottom discof the enclosure by an electric heater. Inner cylinder is the mostimportant part of the experimental model. It is directly affectedby the hot bottom disc and heat is transferred to the wall of thiscylinder through convection and radiation heat transfer. Ideally,uniform temperature along the wall of inner cylinder is requiredin the centrifuge machines which are used in the process industriesfor segregation of different chemicals. Design of the centrifugegeometry should be such that the conditions within the inner cyl-inder should approach the above mentioned ideal conditions. Dueto this reason, the effect of temperature, material and outer cylin-der geometry on the inner cylinder is studied. Fig. 3 shows the ax-ial temperature profile of inner cylinder. Fig. 3(a) and (b) shows thetemperature profile of inner cylinder (inner side) of aluminum atthree different bottom disc temperatures (353, 393, 433 K) andtwo different configurations of the outer cylinder (O1 and O2).Fig. 3(c) and (d) and Fig. 3(e) and (f) shows the same graphs forthe mild steel and stainless steel materials respectively.

The temperature profiles of aluminum at different bottom disctemperatures (353–433 K) for two different outer cylinders O1and O2 in Fig. 3(a) and (b) are almost similar. The reason may bethat the thermal conductivity of aluminum is very high and heattransfer phenomenon is controlled mainly by thermal conductivityrather than diameter of outer cylinder. Because of this reason thetemperature profile does not change by changing the outer cylin-der diameter. The temperature profiles of mild steel and stainlesssteel at different bottom disc temperatures for two different outercylinders O1 and O2 are shown in Fig. 3(c) and (d) and Fig. 3(e) and(f), respectively. These figures show that the temperature of the in-ner cylinder wall increases for mild steel and even more for stain-less steel as compared to aluminum. The reason is obvious that the

Fig. 6. Radial temperature distributions of mild steel inner cylinder, K2 = 1775.77,

thermal conductivity of mild steel is lower than aluminum andhigher than stainless steel. Fig. 3(c) and (e) show that the temper-ature spread near the bottom disc for a temperature range of thebottom disc (353–433 K) is more as compared to Fig. 3(d) and (f),respectively. The thermal conductivities of mild steel and stainlesssteel are lower than aluminum. Therefore, it is argued that, thethermal conductivity and the outer cylinder diameter are boththe controlling parameters for the heat transfer mechanism ratherthan only the thermal conductivity in mild steel and stainless steel.Because of the lower thermal conductivity of stainless steel ascompared to mild steel the same trend can be seen between themas well. Thus it is observed that a more uniform temperature is ob-tained at the inner side of aluminum cylinder over a range of bot-tom disc temperatures (353–433 K) and outer cylinder diameters(O1,O2) as compared to mild steel and stainless steel and the sameis true for mild steel as compared to stainless steel. Another impor-tant observation is that stainless steel is more sensitive to outercylinder diameter as compared to mild steel and aluminum isnon sensitive to the range of outer cylinder diameters (O1–O2)used. The axial temperature profile at the outer side of the outercylinder wall is shown in Fig. 4.

3.2. Radial thermal behavior

In this research work heat is transferred from the hot bottomdisc to the inner enclosure in the axial as well as radial directionthrough radiation and convection. The convection heat transfer oc-curs in the outer enclosure and conduction heat transfer in thewalls of inner and outer cylinders. This study depicts the effectsof different materials (inner cylinder and bottom disc) and config-urations on radial heat transfer at the three different axial locations(5, 700, 1396 mm) measured from bottom disc.

at an axial distance of (a and b) 5 mm, (c and d) 700 mm, (e and f) 1396 mm.

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Fig. 5(a)–(f) shows the radial temperature profiles of two differ-ent geometric configurations with outer cylinders O1 and O2,respectively. Both configurations use the inner cylinder of alumi-num material and the bottom disc temperature varies over a rangeof 353–433 K (Fig. 5). Fig. 5(a) and (b) show the temperature pro-files at an axial location of 5 mm for the two different outer cylin-ders (O1,O2). Due to high thermal conductivity of the innercylinder of aluminum material the temperature at the axis and in-ner and outer sides of inner cylindrical wall are almost same for thetwo different outer cylinders used in the experiment. However, thespread in temperature at the outer cylinder is more in Fig. 5(a) ascompared to Fig. 5(b) over a range of bottom disc temperatures(353–433 K), the reason is that the outer cylinder has a low ther-mal conductivity and the heat transfer mechanism is controlledby outer cylinder diameter in this region. Fig. 5(c) and (d) andFig. 5(e) and (f) show the same plots as Fig. 5(a) and (b) but at axiallocations of 700 and 1396 mm, respectively. Radial response at ax-ial locations of 700 and 1396 mm are almost similar to that at5 mm. However, the spread in temperature at the outer cylinderis not more prominent possibly, because of the low temperaturegradient from the ambient at these two axial locations.

The radial temperature profiles using mild steel and stainlesssteel inner cylinders at three axial locations (5, 700, 1396 mm)for different bottom disc temperatures (353–433 K) for two differ-ent outer cylinders O1 and O2 are shown in Fig. 6(a)–(f) andFig. 7(a)–(f), respectively. The radial temperature at the axis andinner and outer sides of inner cylinder wall for mild steel at allthree axial locations (Fig. 6(a)–(f)) is higher than aluminum(Fig. 5(a)–(f)) and lower than stainless steel (Fig. 7(a)–(f)) becauseof their different thermal conductivities. However, by using differ-ent outer cylinders (O1,O2), the behavior of temperature at the

Fig. 7. Radial Temperature distributions of stainless steel inner cylinder, K3 = 611.52

outer radial positions in Fig. 6(a)–(f) and Fig. 7(a)–(f) is similar tothat in Fig. 5(a)–(f) because of the strong dependence of heat trans-fer mechanism on the diameter of the outer cylinder and using thesame material (mild steel) for the outer cylinder in all theexperiments.

3.3. Non-dimensional analysis

Nusselt number (Nu) is a dimensionless parameter to expressthe heat transfer coefficient in convection heat transfer study. Inthis study the local Nu is calculated by the relation given in Eq.(1) and also used by Refs. [18,19] for heat transfer study.

NuðzÞ ¼ �@h@r

����

r¼0ð1Þ

where, Nu(Z) is local Nusselt number, r is radial component in theenclosure and

h ¼ T � Tc

Th � Tc; ð2Þ

where, T is the variable temperature, Th is temperature of hot sur-face and Tc is temperature of cool surface all measured in Kelvin.

The local Nusselt number is plotted on a semi-log scale againstthe non-dimensional axial distance of the inner cylinder as shownin Fig. 8 for both geometric configurations used in the experiments.The non-dimensional diameter e of the heat source (bottom disc) is0.54 for configuration with outer cylinder O1 and 0.46 for configu-ration with outer cylinder O2. The Nu is high near the heat source(disc) and decreases with height of the cylinder for all the experi-ments (Fig. 8). The decrease in Nu is very steep near the bottom ofthe cylinder as compared to the rest of the cylinder height. Simi-

at an axial distance of (a and b) 5 mm, (c and d) 700 mm, (e and f) 1396 mm.

Fig. 8. Axial local Nusselt number distributions of (a and b) aluminum inner cylinder with K1 = 8702.47, (c and d) mild steel inner cylinder with K2 = 1775.77, (e and f)stainless steel inner cylinder with K3 = 611.52.

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larly, the decrease in Nu is steep in the middle section of the innercylinder for e = 0.54 (Fig. 8(a), (c) and (e)) as compared to e = 0.46(Fig. 8(b), (d) and (f)).The same trend of Nu verses dimensionlessdistance is observed by Paroncini et al. [18], Aydin and Yang[19], El-Shaarawi and Sarhan [24].

Another important dimensionless parameter is the Rayleighnumber which is calculated by the relation given below:

Ra ¼ gbDTD3

av ; ð3Þ

where Ra is Rayleigh number, DT is temperature difference mea-sured in Kelvin, D is enclosure diameter measured in meter, g isacceleration due to gravity measured in m s�2, a is thermal diffusiv-ity measured in m2 s�1, b is coefficient of thermal expansion and v iskinematic viscosity measured in m2 s�1. The same relation is usedby Kim and Viskanta [7], Adachi and Imai [25], Amoura et al. [26],Sankar and Venkatachalappa [27] for heat transfer calculations.

The variation of local Nu verses Ra, at the inner cylinder wall, isplotted in Fig. 9 for both geometric configurations used in theexperiments. The non-dimensional diameter e of the heat source(bottom disc) is 0.54 for configuration with outer cylinder O1and 0.46 for configuration with cylinder O2. The Nu increases withRa for constant e. Comparing Fig. 9(a), (c) and (e) with Fig. 9(b), (d)and (f) it can be seen that the Nu increases with increasing e keep-ing Ra constant. The same behavior is observed by Paroncini et al.[18], Aydin and Yang [19] for the same type of heat transfer prob-lem. For both the configurations, high Ra is achieved with stainlesssteel inner cylinder as compared to mild steel, keeping the disctemperature constant. The same is true with mild steel and alumi-num inner cylinders.

4. Conclusions

In this work the phenomena of conjugate heat transfer, within abottom heated vertical concentric cylindrical enclosure, is studiedexperimentally. The axial (inner side of inner cylinder) and the ra-dial (at an axial distance from the bottom disc 5, 700, 1396 mm)behavior of the enclosure is studied by varying bottom disc tem-perature (353–433 K), inner cylinder material (aluminum, mildsteel, stainless steel) and outer cylinder diameter (O1,O2). In totaleighteen different experiments are performed. As a result of theseexperiments following conclusions are made:

(1) A more uniform axial temperature is obtained at the innerwall of aluminum cylinder over a range of bottom disc tem-peratures (353–433 K) and outer cylinder diameters (O1,O2)as compared to mild steel and stainless steel. The same istrue for mild steel as compared to stainless steel.

(2) Inner cylinder of stainless steel is more sensitive to outercylinder diameter as compared to mild steel. Here, the ther-mal conductivity and the outer cylinder diameter are boththe controlling parameters for the heat transfer mechanismrather than only the thermal conductivity. Aluminum is non-sensitive to the outer cylinder diameters (O1,O2).

(3) In mild steel and stainless steel inner cylinders the temper-ature spread near the bottom disc in the temperature rangeof the bottom disc (353–433 K) decreases with increasingouter cylinder diameters.

(4) The radial temperatures towards the interior of the enclo-sure and the inner cylinder of aluminum material are inde-pendent of outer cylinder diameter, while towards theexterior it is dependent on it due to its mild steel material.

Fig. 9. Axial local Nusselt number distributions with Rayleigh number of (a and b) aluminum inner cylinder with K1 = 8702.47, (c and d) mild steel inner cylinder withK2 = 1775.77, (e and f) stainless steel inner cylinder with K3 = 611.52.

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(5) The decrease in Nu is very steep near the bottom of the cyl-inder as compared to the rest of the cylinder height. Simi-larly, the decrease in Nu is steep in the middle section ofthe inner cylinder for e = 0.54 as compared to e = 0.46.

(6) The Nu increases with Ra for constant e and increases withincreasing e keeping Ra constant.

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