Experimental Study of Natural Convection Cooling of Vertical Cylinders with Inclined Plate Fins

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1 energies Article Experimental Study Natural Convection Cooling Vertical Cylinders Inclined Plate Fins Jong Bum Lee, Hyun Jung Kim and Dong-Kwon Kim * Department Mechanical Engineering, Ajou University, Suwon , Korea; eamice@ajou.ac.kr (J.B.L.); hyunkim@ajou.ac.kr (H.J.K.) * Correspondence: dkim@ajou.ac.kr; Tel.: Academic Editors: Vincent Lemort and Samuel Gendebien Received: 12 April 2016; Accepted: 17 May 2016; Published: 24 May 2016 Abstract: In this paper, natural convection rom vertical cylinders s is investigated experimentally or use in cooling electronic equipment. Extensive experimental investigations are perormed or various inclination angles, numbers, and base temperatures. From experimental data, a correlation or estimating Nusselt number is proposed. The correlation is applicable when Rayleigh number, inclination angle, and number are in ranges 100, ,000, 30 90, and 9 36, respectively. Using correlation, a contour map depicting rmal as a unction number and thickness is presented. Finally, optimal rmal s cylinders s and conventional radial s are compared. It is ound optimal rmal cylinder s is 30% lower than cylinder radial s. Keywords: nusselt number; natural convection; 1. Introduction Heat dissipation rom electronic devices increases considerably continuous needs or high perormance, cost eective, and miniaturized electronic devices [1 3]. The high power dissipation rom electronic device raises junction temperature device, which adversely inluences overall perormance and durability device. One example is a light-emitting diode (LED), eiciency which is signiicantly reduced as junction temperature increases due to an increase in nonradiative recombinations through deect states and an increase in leakage carriers rom quantum well [4,5]. Thereore, rmal management electronic devices is important to maintain ir perormance and durability [6,7]. Various cooling techniques or rmal management have been suggested; among se, natural convective sinks have proven to be appropriate because ir outstanding simplicity, reliability, and low cost [8]. Many studies have ocused on natural convective sinks, as reviewed in Martynenko and Khramtsov [9] and in Raithby and Hollands [10]. In particular, many previous researchers investigated natural convection rom cylindrical sinks, which are cylindrical bodies s attached. These studies are motivated by act dissipation rom cylinder can be increased by using s. Sparrow and Bahrami investigated transer rom square vertical s attached to a horizontal tube by using naphthalene sublimation technique [11]. Chen and Chou also conducted an experimental study horizontal cylinders square vertical s [12]. Yildiz and Yüncü suggested a Nusselt number correlation or annular arrays mounted on a horizontal cylinder rom ir experimental data [13]. Hahne and Zhu also suggested a Nusselt number correlation or horizontal cylinders annular s rom measured transer coeicients [14]. Recently, vertical cylinders vertically oriented radial s, as shown in 1, are widely used or Energies 2016, 9, 391; doi: /en

2 Energies 2016, 9, Energies 2016, 9, coolingused LEDor lighting. cooling LED For lighting. natural For convection natural convection rom se rom cylinders se cylinders radial radial s, s, an empirical an correlation empirical estimating correlation or estimating Nusselt number Nusselt was number proposed was proposed by our group by our [15]. group [15]. Energies 2016, 9, used or cooling LED lighting. For natural convection rom se cylinders radial s, an empirical correlation or estimating Nusselt number was proposed by our group [15]. 1. Cylindrical 1. sink radial radial s. s. Heat transer through s is currently considerable interest. Takeishi et al. investigated Heat convective transer through transer rectangular s is currently ducts considerable pin s. interest. They showed Takeishi etducts al. investigated convective pin transer s have inhigher rectangular rmal 1. Cylindrical perormance ducts sink compared radial pin to those s. s. They normal showed pin s because ducts pin low spressure have higher loss and rmal extended perormance area compared pin tosuraces those [16]. normal Hagote and pindahake s because investigated Heat transer transer through rom vertical s is s currently considerable s interest. under Takeishi natural et convection. al. investigated They convective low pressure demonstrated loss transer and average in rectangular extended transer ducts area coeicient is maximized pin s. suraces They when showed [16]. inclination Hagote ducts and angle Dahake is investigated 60 [17]. pin From s transer se have studies, higher rom vertical rmal s we can expect perormance compared rmal perormance to those s under normal natural vertical pin cylinders s convection. because They demonstrated radial low pressure s ( average loss and 1) will be extended transer urr area enhanced coeicient by employing ispin maximized suraces when [16]. Hagote s inclination and as shown Dahake in angle is 60 [17]. investigated From2. It se is mainly studies, transer because rom we can vertical expect surace s area rmal vertical perormance cylinder s under natural vertical convection. s cylinders is greater They radial demonstrated compared s to ( 1) radial average will be urr s transer when enhanced coeicient space by reserved is employing maximized or when sink is inclination ixed, s i.e., angle as shown is in 60 [17]. sink length From 2. It is mainly L se and because studies, height we H can are expect surace ixed. area However, rmal to vertical perormance best cylinder our knowledge, vertical cylinders s natural is greater radial compared convection to rom s ( vertical 1) radial cylinders will be s urr when enhanced by space s employing reserved has not been orexperimentally s as sinkinvestigated shown in is ixed, i.e., yet. As 2. a It result, is mainly re because is no reliable experimental surace area data by vertical which cylinder one can obtain Nusselt s is numbers, greater sink compared length L and height H are ixed. However, to best our knowledge, natural and re to is no way to radial obtain s rmal when space reserved vertical or cylinders sink is ixed, i.e., s convection sink rom vertical cylinders s has not been experimentally investigated quantitatively. length L and Thereore, height degree H are ixed. improvement However, in to perormance best our knowledge, cylinders natural yet. Asconvection a result, s compared re rom vertical is no to reliable cylinders cylinders experimental conventional data s by which radial has not one been s, can experimentally and obtain conditions investigated Nusselt under numbers, and re yet. which As is this a no result, improvement wayre to obtain is no is reliable achieved, rmal experimental are not clear. data by which vertical one can cylinders obtain Nusselt numbers, s and re is no way to obtain rmal vertical cylinders s quantitatively. Thereore, degree improvement in perormance cylinders quantitatively. Thereore, degree improvement in perormance cylinders s compared to cylinders conventional radial s, and conditions under s compared to cylinders conventional radial s, and conditions under which which this improvement this improvement is achieved, is achieved, are are not not clear. clear. (a) (b) 2. Cylindrical sink s. (a) schematic diagram; (b) top view. (a) (b) 2. Cylindrical sink s. (a) schematic diagram; (b) top view. 2. Cylindrical sink s. (a) schematic diagram; (b) top view.

3 Energies 2016, 9, The purpose this study is to investigate natural convection cooling vertical cylinders s. Extensive experiments or various inclination angles, numbers, and base temperatures were conducted. From se results, a Nusselt number correlation is suggested. Using correlation, a contour map depicting rmal as a unction number and thickness is presented. Finally, rmal s cylinders s and conventional radial s are compared. 2. Experimental Investigation The rmal s natural convective sinks s were measured or various inclination angles, numbers, and base temperatures. Schematic diagrams sinks are presented in 2a, and dimensions sinks are listed in Table 1. Eleven dierent sinks were used to cover a wide range inclination angles and numbers. In Table 1, sink large number (N 36) and large inclination angle (α 90 ) was excluded because adjacent s touch and bend each or in this sink because space required or a single was insuicient or this case. An annular cylinder base and s or sinks were made aluminum alloys 6061 (k 167 K) and 5052 (k 138 K), respectively. Table 1. Geometric coniguration tested sinks. Number N α ( ) H (mm) D (mm) L (mm) T (mm) Heat sink 1 9 Heat sink 2 12 Heat sink 3 18 Heat sink 4 36 Heat sink 5 9 Heat sink 6 12 Heat sink 7 18 Heat sink 8 36 Heat sink 9 9 Heat sink Heat sink The sinks were assembled by intererence itting s and base. Then, a cartridge er was inserted into inner hole base ( 3a). A rmal interace material (TC 5080; Dow Corning: Auburn, MI, USA) was used to minimize contact rmal between sink base and er. The supporting cylindrical blocks, length which was 200 were made Telon to minimize loss rom top and bottom sides base ( 3b,c). Power was supplied to er rom a power supply (E3633A; Agilent Technologies: Santa Clara, CA, USA) in range 2 45 W. To calculate actual transer rate to sink, loss through supporting blocks (q loss,1 + q loss,2 in 3b) was measured and subtracted rom electric power supplied to er (Appendix A). To measure base temperature, our T-type rmocouples were circumerentially attached to cylinder ( 3d) A data acquisition unit (34970A DAQ; Agilent Technology) was used to acquire signals rom rmocouples and convert m into temperature data. The temperatures were measured until change in temperature was smaller than 0.1 C in a 2 min period. The experiments were perormed in an isolated and quiescent room.

4 Energies 2016, 9, Energies 2016, 9, (a) (b) (c) (d) 3. Experimental setup. (a) photograph sink assembly; (b) schematic diagram 3. Experimental setup. (a) photograph a sink assembly; (b) schematic diagram experimental apparatus; (c) photograph experimental apparatus; (d) positions rmocouples. experimental apparatus; (c) photograph experimental apparatus; (d) positions rmocouples. 3. Results and Discussion 3. Results and Discussion The dierence between sink base temperature (Tw) and ambient temperature (Tamb) The or various dierence inclination between angles (α), sink numbers base temperature (N), and inputs (T w ) and (q) is shown ambient in Table temperature 2 and (T amb ) or various 4. From inclination se experimental angles (α), data, numbers rmal (N), and inputs (q) sink iscan shown be calculated in Table as 2 and 4. From se experimental data, rmal Tw T sink can be calculated as amb Rth (1) q R th T w T amb (1) q Table 2. Thermal s and Nusselt numbers calculated rom experimental data. Table 2. Thermal s and Nusselt numbers calculated rom experimental data. Number α ( ) N q (W) Tw Tamb (K) Rth (K/W) NuDh Number α ( ) N 2.15 ± ± ± ± 0.78 q (W) T w T 4.94 ± ± 1.3 amb (K) R 4.04 ± th (K/W) Nu ± 0.71 Dh ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

5 Energies 2016, 9, Table 2. Cont. Number α ( ) N q (W) T w T amb (K) R th (K/W) Nu Dh In Equation (1), rmal R th is deed as dierence between sink base temperature and ambient temperature per unit transer rate. The calculated rmal values are listed in Table 2. The uncertainties calculated rmal s are also listed. As shown in Table 2 and 4, rmal perormance sink is minimized when α 60 and N 36. According to 3 in [15], rmal conventional radial sink is also minimized when N 36. In 5, minimal s measured rom sink (α 60, N 36) in present study are compared those rom radial sink (N 36) in [15]. 5 shows sink has rmal s up to 10% lower than those radial sink.

6 Energies 2016, 9, Energies 2016, 9, Energies compared 2016, 9, 391 those rom radial sink (N 36) in [15]. 5 shows 6 15 compared sink those has rom rmal radial s up to 10% sink lower (N than 36) in those [15]. radial 5 shows sink. sink has rmal s up to 10% lower than those radial sink. 4. Temperature dierences or various numbers, inclination angles, and inputs. 4. Temperature dierences or various numbers, inclination angles, and inputs. 4. Temperature dierences or various numbers, inclination angles, and inputs. 5. Comparison experimental data or minimal s between sink and 5. radial Comparison sink experimental (H 30 data N or 36). minimal s between sink 5. Comparison experimental data or minimal s between sink and radial sink (H 30 N 36). and On radial basis sink (H model, 30 rmal N 36). can be calculated as ollows: On basis model, rmal can be calculated as ollows: 1 On basis model, rmal Rth (2) h( NA1 can be calculated as ollows: R Ab) th (2) h( NA1 Ab) where η, h, A, and Ab are eiciency, R th transer coeicient, surace area, and unned (2) hpηna ` A b q where surace η, area, h, A, respectively. and Ab are eiciency, transer coeicient, surace area, and unned where surace η, h, A area, respectively., and A b are eiciency, transer hp coeicient, surace hp area, and unned surace area, respectively. tanh H 0.5 h ks ( hpksac) khp s Ac khp tanh H s Ac 0.5 h ks ( hpk (3) ha sac) ˆb ks A ˆ Nb c ks A c hp hp hp hp (3) ha 1 h ks tanh H 1 khp s Ac khp η phpk sa c q 0.5 tanh k s A c H ` h k s A c k s ˆ hnb k s A ha s tanh ˆb c H (3) ks A hp 1 ` h c ks A hp k s A c k s tanh kc s A c H h Nu Dh k {D h (4) A b πdl NLt (5) A 2H L ` 2H t ` Lt (6)

7 Energies 2016, 9, Here, A c and p are cross-sectional area and perimeter, respectively. The height H is given as a unction α, D, and H: H A c Lt (7) p 2L ` 2t (8) b D 2 cos 2 α{4 ` H 2 ` HD Dcosα{2 (9) D h is hydraulic diameter channel between two adjacent s, i.e., yellow region in 2b, and can be calculated rom area A ch and wetted perimeter p ch channel: D h 4A 4 πph ` D{2q 2 {N πpd{2q 2 {N H ch t p ch 2H ` 2πR{N t The Nusselt number Nu Dh can be calculated rom Equations (2) (10) once rmal is obtained rom experimental data. The calculated Nusselt numbers are listed in Table 2. In present study, Nusselt number correlation, which match best experimental data, is developed. In case sinks vertical s under natural convection, Nusselt number correlations were generally developed as unctions a Rayleigh number Ra Dh. For example, Welling and Woodridge [8] suggested a Nusselt number correlation or rectangular vertical s on lat surace in orm Nu Dh pra Dh q (11) where Rayleigh number Ra Dh is deed as (10) Ra Dh gβ pt w T amb qd 4 h ν α L (12) Similarly, Karagiozis et al. [18] used average spacing as hydraulic diameter, and suggested a correlation or triangular vertical s on lat surace in orm Equation (11). In present study, to relect eect inclination angle on transer coeicient, Equation (11) is modiied as Nu Dh pra Dh, αq (13) Here, g, β, ν, and α are gravitational acceleration, volume expansion coeicient luid, kinematic viscosity luid, and rmal diusivity luid, respectively. We tested various unctional orms or unction in Equation (13), and ally ound unctional orm Nu Dh C 1 ` C 2 lnpra Dh q ` pc 3 ` C 4 α ` C 5 α 2 qlnpra Dh q 2 (14) is matched best experimental data. The best empirical coeicients or predicting Nusselt numbers are determined using a least-squares it on experimental data: C , C , C , C , C (15) Finally, correlation Nusselt number or vertical cylinders s under natural convection is given as Nu Dh lnpra Dh q ` p0.120 ` α α 2 qlnpra Dh q 2 (16)

8 Energies 2016, 9, Finally, correlation Nusselt number or vertical cylinders s Energies 2016, 9, under natural convection is given as Nu ln( Ra ) ( ) ln( Ra ) (16) Dh Dh Dh In 6, Nusselt numbers calculated rom Equation (16) are compared those obtained rom experimental In 6, data or Nusselt various numbers Rayleigh calculated numbers. rom Equation 6 (16) shows are compared Nusselt those number correlation obtained is in rom good experimental agreement data or various experimental Rayleigh numbers. data in a 6 10% shows error. This Nusselt correlation is valid number in correlation ranges 100,000 is in good < Ra agreement Dh < 600,000, 9 < experimental N < 36, anddata 30 in < α < a 90, ± 10% in error. which This correlation is valid in ranges 100,000 < RaDh < 600,000, 9 < N < 36, and 30 < α < 90, in which experimental data were obtained. In addition, though correlation is developed only or experimental data were obtained. In addition, though correlation is developed only or sinks, this correlation can predict Nusselt numbers radial sinks (α 0) in sinks, this correlation can predict Nusselt numbers radial sinks a 30% error (Appendix B). (α 0) in a ± 30% error (Appendix B). 6. Nusselt numbers calculated using proposed correlation and those rom experimental data. 6. Nusselt numbers calculated using proposed correlation and those rom experimental data. The rmal s sinks are predicted using proposed correlations and are The compared rmal s experimental data sinks s are7 predicted and 8. The using results rom proposed correlation correlations match and are compared experimental data experimental well in data a ±15% in s error. s 7 and7 8. and The8 results present rom rmal correlation s match or experimental various data numbers well in and inclination a 15% error. angles, s respectively. 7 and 8 present rmal s or various numbers and inclination angles, respectively. Energies 2016, 9, Thermal s or various numbers. 7. Thermal s or various numbers.

9 Energies 2016, 9, Thermal s or various numbers Thermal Thermal s or various inclination inclination angles. angles. In In 7, as 7, as number number increases, increases, rmal rmal decreases. decreases. It is mainly It is mainly because because surace area increases as as number number increases. increases. As As shown shown in in 8, 8, rmal rmal is minimized is minimized when when inclination angleis is Thermal sink sink inclination angle angle is is smaller than 30, 30, because surace area area is greater. is greater. The The sink inclination angle angle 60 has60 slightly has smaller slightly rmal smaller rmal compared compared to to 90. It 90. is because It is because amount amount transer transer suppression suppression caused bycaused boundary by boundary layer layer overlap decreases an increase an increase in -to- -to- spacing spacing [15] and [15] -to- and spacing -to- spacing sink sink inclination inclination angle 60 angle is larger 60 is than larger than 90. Next, 90. a contour Next, a map contour map depicts rmal as a unction number and thickness by using proposed depicts rmal as a unction number and thickness by using proposed correlation is presented in 9. This contour map covers range 9 < N < 36, in which correlation is presented in 9. This contour map covers range 9 < N < 36, in which experimental data were obtained. The contour map shows rmal decreases as experimental number data decreases. were This obtained. is because, The as contour number map shows increases, eective rmal surace area, ηna decreases as + A b, number decreases. This is because, as number increases, eective surace area, ηna sink increases rapidly ( 10a), while transer coeicient h decreases slowly + Ab, ( 10b). At sink maximum increases rapidly number ( (N 36, 10a), alongwhile line AA in transer 9), coeicient rmal h decreases slowly is minimized ( 10b). at a At certain maximum thickness. This number is because, (N when 36, along N 36, asline AA thickness in increases, 9), rmal transer is minimized coeicient at ha decreases certain ( thickness. 10b), whereas This is because, eiciency when N and 36, eective as surace thickness area (ηna + A b ) increase ( 10a). Finally, 9 shows a rmal 1.06 K/W can be achieved by optimizing number and thickness sink in range 9 < N < 36. For comparison, a contour map rmal s cylinders conventional radial s, which are calculated rom Nusselt number correlation [15], is presented in 11. It shows optimal rmal is 1.50 K/W or sink radial s.

10 are sinkoptimized radial in s, which s. range 9 < N < 36, are compared in 12. This igure clearly Finally, rmal s cylinders conventional shows rmal optimized s and sink radial inclination s, which are optimized in range 9 < N < 36, are compared in 12. This igure clearly angle 60 is 29.3% lower than optimized radial sink. Thereore, we can shows cylinders rmal optimized than sink inclination conclude s perorm better those cylinders radial angle 2016, 60 9,is % lower than optimized radial sink. Thereore, we Energies 10 can 15 s. conclude cylinders s perorm better than those cylinders radial s. 9. map or and thicknesses (H Contour Contour map rmal rmal or orvarious various numbers and thicknesses (H (H Contour map rmal various numbers numbers and thicknesses 30 5 C, D 6060 L L50 α 60, Tw60 T,amb 50 C, k K, k s 220 K, ν m2/s, D 50 α T T 50 k K, k 220 s ν K,m2/s, ambk D 60 L 50 α 60, Tw Tamb w 50 C, K, ks 220 K, 5 2/s, αν m β /K). 1.6 α 2.23 ˆ 10 m /s, β /K). α ˆ 5 10 m2/s,mβ /s, /K). (a) (a) 10. Cont.

11 Energies 2016, 9, Energies 2016, 9, Energies 2016, 9, (b) (b) 10. Contour maps (a) eective surace area and (b) transer coeicient or various various Contour Contourmaps maps(a)(a)eective eective surace area and transer coeicient surace area and (b)(b) transer coeicient or or various numbers and and thicknesses (H 30 60D 50 α 60, Tw, TTwamb T50 C, k C,0.026 numbers thicknesses 30 D 60 LL 50α 50 ambk numbers and thicknesses (H (H 30 D 60 50L 60,α Tw 60 Tamb 50 C, ν α 2 kk, K, K, ks ν220 K, ˆ 10 m /s, ˆ0.0033/K). 10 m /s, β /K). s m2/s, /s,2.23 k /s,α 5 m K, ks 220 K, ν mm/s, α ββ /K) Contour Contour map map rmal rmal cylinder cylinder conventional conventional radial radial s s or or various numbers and thicknesses or (H 30 D 60 L 50 T w Tamb 50 C, various numbers and thicknesses or (H 30 D 60 L 50 Tw Tamb 50 C, ContourK,map rmal 2αcylinder radial s or 5 2conventional kk K, K, ν m β m /K). 2/s, 2 /s, β /K) K,ksk 220 ν 1.6 ˆ 10 /s,m α m ˆ /s, 10 5 s various numbers and thicknesses or (H 30 D 60 L 50 Tw Tamb 50 C, k K, ks 220 K, ν m2/s, α m2/s, β /K). Finally, rmal s cylinders s and conventional radial s, which are optimized in range 9 < N < 36, are compared in 12. This igure clearly shows rmal optimized sink inclination

12 Energies 2016, 9, angle 60 is 29.3% lower than optimized radial sink. Thereore, we can conclude cylinders s perorm better than those cylinders radial s. Energies 2016, 9, Comparison rmal s between optimized sinks and 12. Comparison rmal s between optimized sinks optimized radial sink (9 < N < 36, t 2 H 30 D 60 L 50 Tw Tamb and optimized radial sink (9 < N < 36, t < 2 H 30 D 60 L C, k K, ks 220 K, ν m 2 /s, α m 2 /s, β /K). T w T amb 50 C, k K, k s 220 K, ν 1.6 ˆ 10 5 m 2 /s, α 2.23 ˆ 10 5 m 2 /s, β /K). 4. Conclusions 4. Conclusions In present paper, natural convection rom vertical cylinders s is investigated experimentally. Experimental investigations are perormed or various inclination In present paper, natural convection rom vertical cylinders s is angles, numbers, and base temperatures. Although its applicability is limited to certain speciic investigated experimentally. Experimental investigations are perormed or various inclination angles, ranges (100,000 < RaDh < 600,000, 9 < N < 36, and 30 < α < 90 ), suggested correlation enables easy numbers, and base temperatures. Although its applicability is limited to certain speciic ranges rmal perormance calculation. Using proposed correlation, a contour map depicting (100,000 < Ra Dh < 600,000, 9 < N < 36, and 30 < α < 90 ), suggested correlation enables easy rmal as a unction number and thickness is presented. Finally, optimal rmal perormance calculation. Using proposed correlation, a contour map depicting rmal rmal s cylinders s and conventional radial s are as a unction number and thickness is presented. Finally, optimal rmal compared. It is ound optimal rmal cylinder s is 30% s cylinders s and conventional radial s are compared. It is lower than cylinder radial s. Thereore, s have potential or ound optimal rmal cylinder s is 30% lower than use in cooling equipment in various rmal systems. cylinder radial s. Thereore, s have potential or use in cooling equipment Acknowledgments: in various This rmal research systems. was supported by Nano Material Technology Development Program through National Research Foundation Korea (NRF), unded by Ministry Science, ICT and Future Planning (NRF ). This work was supported by Human Resources Program in Energy Technology Appendix A. Measurement Heat Loss through Supporting Blocks Korea Institute Energy Technology Evaluation and Planning (KETEP), granted ancial resource rom Ministry The measurement Trade, Industry & Energy, lossrepublic is similar to Korea. (Project writtenno: in Reerence ). [15]. For measuring Author loss, Contributions: instead Jong Bum sink, Lee and a slim Dong-Kwon cylindrical Kim er conceived is sandwiched designed by experiments; supporting Sang blocks Woo as Lee shown perormed in experiments; A1. In this Hyun situation, Jung Kim all and Dong-Kwon produced Kim analyzed by er data; isdong-kwon released tokim surroundings wrote paper. through supporting blocks. Thereore, loss through supporting blocks (q Conlicts loss,1 + q loss,2 ) can be measured by measuring power supplied to er. In present study, Interest: The authors declare no conlict interest. loss was measured or various er temperatures and was used to calculate actual transer Appendix rate A. tomeasurement sink. Heat Loss through Supporting Blocks The measurement loss is similar to written in Reerence [15]. For measuring loss, instead sink, a slim cylindrical er is sandwiched by supporting blocks as shown in A1. In this situation, all produced by er is released to surroundings through supporting blocks. Thereore, loss through supporting blocks (qloss,1 + qloss,2) can be measured by measuring power supplied to er. In present study, loss was measured or various er temperatures and was used to calculate actual

13 Energies 2016, 9, Energies 2016, 9, A1. A1. Schematic Schematic diagram diagram experimental experimental setup setup or or loss loss measurement. measurement. Appendix Appendix B. Comparison B. Comparison Nusselt Nusselt Numbers or Radial Radial Heat Heat Sinks Sinks Calculated Calculated Using Using Proposed Proposed Correlation and and Those rom Experimental Data In In B1, B1, Nusselt Nusselt numbers calculated rom rom correlation (Equation (16)) are compared those obtained thoserom obtained experimental rom experimental data or data radial or radial sinks presented sinks Reerence presented[15]. in As shown Reerence in [15]. B1, As shown correlation in can B1, predict correlation Nusselt can predict numbers Nusselt numbers radial radial sinks in sinks in a 30% error, despite act correlation is developed only or a ±30% error, despite act correlation is developed only or sinks. For sinks. For predicting Nusselt numbers or both sinks and radial predicting Nusselt numbers or both sinks and radial sinks, sinks, we developed an alternative correlation as ollows: we developed an alternative correlation as ollows: Nu Dh lnpra Dh q ` 0.19lnpRa Dh q 2 NuD h ln( RaDh ) 0. 19ln( Ra 2 (B1) Dh ) (B1) In B2, Nusselt numbers calculated rom correlation (Equation (B1)) are compared In thoseb2, obtained Nusselt rom experimental numbers calculated data or rom radial correlation (Equation sinks and(b1)) are compared those sinks. obtained As shown rom inexperimental B2, data correlation or can radial predict Nusselt sinks numbers and radial sinks. As shown sinksin and B2, correlation sinks can in predict a 15% Nusselt error. Thereore, numbers we suggest radial use sinks Equation and (16) or accurate prediction sinks in Nusselt a ±15% numbers error. Thereore, we suggest sinks use Equation (30 < (16) α < or 90 ), and accurate Equation prediction (B1) can benusselt used ornumbers prediction or Nusselt numbers sinks or both (30 < α < 90 ), and Equation radial (B1) sinks can and be used or prediction s sinks. Nusselt numbers or both radial sinks and s sinks.

14 Energies 2016, 9, Energies 2016, 9, Energies 2016, 9, B1. or B1. Nusselt numbers or radial sinks calculated using proposed correlation and those rom experimental data [15]. rom experimental data [15]. B2. Nusselt numbers calculated using alternative correlation and those rom experimental data. B2. Nusselt numbers calculated using alternative correlation and those rom experimental data. B2. Nusselt numbers calculated using alternative correlation and those rom experimental data. Reerences Reerences Acknowledgments: 1. Oktay, S.; Hannemann, This research R.J.; Bar-Cohen, was supported A. High byheat Nano rom Material Small Package. Technology Mech. Development Eng. 1986, 108, Program through 1. Oktay, 2. Bar-Cohen, National S.; Hannemann, A. Thermal Research R.J.; Management Foundation Bar-Cohen, A. Korea High Electric (NRF), Heat rom Components unded a Small by Package. Dielectric Ministry Mech. Liquids. Science, Eng. 1986, JSME ICT108, Int. and J. Future Fluids Planning 2. Bar-Cohen, (NRF ). A. Thermal Management This work was supported Electric Components by Human Resources Dielectric Program Liquids. in Energy JSME Technology Int. J. Fluids Therm. Eng. 1993, 36, Therm. Korea Eng. Institute 1993, 36, Energy Technology Evaluation and Planning (KETEP), granted ancial resource rom 3. Ministry Pop, E. Energy Trade, dissipation Industry & and Energy, transport Republic in nanoscale Korea. devices. (ProjectNano No.: Res , , ) Pop, E. Energy dissipation and transport in nanoscale devices. Nano Res. 2010, 3, Author 4. Park, J.; Shin, M.; Lee, C.C. Measurement temperature priles on visible light-emitting diodes by use 4. Park, Contributions: J.; Shin, M.; Lee, Jong C.C. Bum Measurement Lee and Dong-Kwon temperature Kim priles conceived visible and light-emitting designed diodes experiments; by use Sang Woo nematic Leeliquid perormed crystal and experiments; an inrared laser. Hyun Opt. Jung Lett. 2004, Kim 29, and Dong-Kwon Kim analyzed data; Dong-Kwon a nematic liquid crystal and an inrared laser. Opt. Lett. 2004, 29, Luo, X.; Kim Liu, wrote S. microjet paper. array cooling system or rmal management high-brightness LEDs. IEEE 5. Luo, X.; Liu, S. A microjet array cooling system or rmal management high-brightness LEDs. IEEE Conlicts Trans. Adv. Interest: Packag. The2007, authors 30, declare no conlict interest. Trans. Adv. Packag. 2007, 30, Incropera, F.P. Convection Heat Transer in Electronic Equipment Cooling. J. Heat Trans. 1988, 110, Incropera, F.P. Convection Heat Transer in Electronic Equipment Cooling. J. Heat Trans. 1988, 110, Nakayama, W. Thermal Management Electronic Equipment: Review Technology and Research 7. Nakayama, W. Thermal Management Electronic Equipment: A Review Technology and Research Topics. Appl. Mech. Rev. 1986, 39, Topics. Appl. Mech. Rev. 1986, 39,

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