- Email: [email protected]
Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs
International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs Seung-Jae Park a, Daeseok Jang a,b, Kwan-Soo Lee a,⇑ a b
School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Korea Atomic Energy Research Institute, 111 Daedeok-daero 989 beon-gil, Yuseong-gu, Daejeon 34057, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 July 2016 Received in revised form 18 August 2016 Accepted 18 August 2016 Available online xxxx Keywords: Heat sink Natural convection Orientation effect LED
a b s t r a c t An inclined cross-cut cylindrical heat sink was investigated in an attempt to improve the energy conversion and management of LED light bulbs. The thermo-flow characteristics were studied to enhance the cooling performance of a cylindrical heat sink, which is the cooling apparatus used for LED light bulbs. In the inclined cross-cut heat sink, the natural convection flow with an incidence angle had a flow path length that was more stretched in comparison to the flow path length of a straight cross-cut heat sink. Accordingly, the heat transfer rate between the air and fins was increased. When the fins had an inclined angle of 25–30°, the thermal resistance was the smallest. However, when the inclined angle increased to greater than 50°, only the blocking effect was increased and the flow path length was not stretched. Hence, cooling performance was decreased with inclined angles greater than 50°. A correlation predicting the degree of improvement in cooling performance relative to a baseline straight cross-cut heat sink was suggested as a function of heat sink design variables and the installation angle of the heat sink. Finally, a contour map was developed, which can be used to select the optimum heat sink type, with respect to the installation angle of the heat sink and the inclined angle of the fins. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The latest trend in light-emitting diode (LED) lighting is a move toward increased energy efficiency and eco-friendliness. Accordingly, there is a growing demand for the development of high energy-efficient lighting to reduce greenhouse gas (GHG) emissions [1]. Because lighting is responsible for 20% of the overall energy consumption of buildings, the replacement of conventional lighting with lighting that is highly energy efficient is required [2]. The production and import of conventional incandescent lamps is globally prohibited because of the low efficiency of incandescent lamps. Alternative light sources include compact fluorescent lamps (CFLs) and halogen lamps. The presence of harmful substances, such as mercury, in CFLs reduces the demand for CFLs. The EU energy committee announced the implementation of increased energy efficiency standards in 2016, one result of which is the further prohibition of halogen lamps. Therefore, eco-friendly, energyefficient LED bulbs are rapidly replacing conventional light bulbs [3]. When the heat dissipation performance of LED light bulbs is insufficient, the light emission efficiency of LED chips is decreased
⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee).
and the lifetime is reduced [4–6]. Therefore, research related to enhancing the cooling performance of LED light bulbs is required. A heat sink is used as a cooling system for LED lighting due to the low cost and semi-permanent life time [6]. Recently, the power consumption and heat generation rate of LED lightings have had to increase in order for the lightings to emit brighter light. Therefore, many researchers have attempted to increase the natural convective and radiative heat transfer rate from the heat sinks to improve both efficiency and performance in LED lighting. Costa et al. [7] improved the thermal performance of a radial heat sink by changing the number, length, height, and thickness of the fins. Jang et al. [8] optimized the thermal performance and the mass of a heat sink by varying the design factors of the fin. The installation angle of LED lighting can vary depending on its purpose. Thus, not only the thermal performance, but also the orientation effect, which changes the thermal performance of the heat sink depending on its installation angle, should be considered in designing a heat sink for LED lighting. Tari et al. [9] numerically analyzed the orientation effect and suggested a correlation equation for a plate fin heat sink. Shen et al. [10] investigated the impact of the number of plate fins on the orientation effect for LED lighting. Huang et al. [11] experimentally studied the effects of the installation angle on a square pin-fin heat sink and compared the performance with that of seven other types of heat sinks. Li et al. [12] developed a correlation
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
2
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Nomenclature C D F g H k L l N n P Q_ q_ RTH Ra s T t u v
specific heat [J/(kg K)] diameter of heat sink [mm] body force vector per unit volume gravity acceleration [m/s2] fin height [mm] thermal conductivity [W/(m K)] height of heat sink base [mm] length [mm] number of fin arrays normal direction vector pressure [Pa] heat transfer rate [W] heat flux [W/m2] thermal resistance [°C/W] Rayleigh number surface temperature [K] thickness of fin [mm] velocity [m/s] velocity vector [m/s]
equation to describe the orientation effect of a radial heat sink with a concentric ring. All of these aforementioned studies, however, focus investigation on heat sinks that have horizontal circular or square bases. LED light bulbs, which are the focus of this study, generally use cylindrical heat sinks that have fins on cylindrical bases. The thermo-flow characteristics of a cylindrical heat sink differ from the thermos-flow characteristics of a circular or square heat sink. Therefore, it is difficult to apply the results from former studies to a cylindrical heat sink. Recently, An et al. [13] experimentally investigated the effects of geometric factors on the plate fins of cylindrical heat sinks and proposed a correlation equation. Jang et al. [14,15] analyzed the orientation effect of a plate fin cylindrical heat sink numerically and suggested a straight crosscut cylindrical heat sink, which is shown to improve the orientation effect. In the case of a straight cross-cut cylindrical heat sink, the blocking effect from fins is reduced, which weakens the orientation effect. The cylindrical heat sinks in the aforementioned studies contain plate or straight cross-cut fins. Therefore, research on the thermal performance and orientation effects of an inclined cross-cut cylindrical heat sink that considers the inclined angle of the fin is required. In the present study, we investigate an inclined cross-cut heat sink in an attempt to improve the cooling performance of cylindrical heat sinks for LED light bulbs. Flow characteristics and thermal resistance with respect to the inclined angle of the cross-cut fins, are investigated. A correlation, which is able to predict the degree of improvement in the cooling performance of an inclined crosscut heat sink in comparison to a straight cross-cut heat sink, is suggested as a function of heat sink design variables, the installation angle of the heat sink, and the Rayleigh number. Finally, a contour map that can be used to select the optimum heat sink type with respect to the installation angle of the heat sink and the inclined angle of the fins is developed.
Greek symbols n heat transfer augmentation factor, b
c r q e
h /
RInclined cross-cut RStraight cross-cut 1
coefficient of volume expansion [K ] operating angle range Stefan–Boltzmann constant [W/m2K4] density [kg/m3] emissivity installation angle of heat sink [°] inclined angle of fin [°]
Subscripts avg average f unit fin film film temperature L average over the heat sink length i inner in in o outer out out 1 ambient
cross-cut fins. The cross-cut fins are aligned radially at uniform angle intervals. Unlike straight cross-cut fins [15], inclined crosscut fins are tilted at an inclined angle (/), with the middle of the heat sink at the center. The computational domain and installation angle of the heat sink (h) used for the numerical analysis of the cylindrical heat sink are indicated in Fig. 1(b). To generate an independent computational domain from the installation angle of the heat sink, we created a spherical control volume that is centered at the middle of the heat sink. The heat sink is symmetrical; thus, only half of the heat sink and the air region were considered as the computational domain. The assumptions for the numerical analysis are as follows: (1) The flow is three-dimensional, steady state, and laminar. (2) The density of air is calculated by the ideal gas law. (3) The surface of the heat sink is gray and diffuse. The governing equations for the numerical analysis are as follows: Continuity equation:
r ðqv Þ ¼ 0
ð1Þ
Momentum equation:
qðv rÞv ¼ rP þ lr2 m þ F ðfor z-direction F ¼ qgÞ
ð2Þ
Energy equation:
qC v rT ¼ r ðkrTÞ
ð3Þ
The boundary conditions are indicated in Table 1. Radiation heat transfer was calculated by using the discrete transfer radiation model (DTRM) [16–18], which is applicable for the symmetrical condition. 2.2. Numerical procedure
2. Mathematical modeling 2.1. Numerical model Fig. 1 shows the inclined cross-cut heat sink considered in this study. The heat sink consists of a cylindrical base and inclined
The SIMPLE algorithm was selected to combine the pressure and velocity of the flow field. The convective terms of the governing equations were discretized using a second-order upwind scheme to improve the accuracy of the numerical result. In the iterative calculation, we concluded that the dependent variables
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
3
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
independency, we tested between 650,000 and 2,300,000 grid points and selected 1,303,688 nodes as the reference mesh when the temperature variation was less than 0.5%.
3. Experiment and validation An experiment was performed to validate the numerical model. The geometric parameters of the tested heat sink were N = 12, / = 45°, L = 50 mm, H = 30 mm, lf = 10 mm, Di = 20 mm, Do = 60 mm, and t = 2 mm (Fig. 1). The heat sink was made of aluminum alloy 6061. A black anodizing surface treatment was applied to the heat sink, and its emissivity was 0.9. The emissivity of the heat sink was calculated using a thermal infrared camera. The test section of the experimental apparatus is shown in Fig. 2. To minimize the thermal contact resistance, thermal grease was used at the contact surface between the heat sink and the cartridge heater. To calculate the heat loss through the top and bottom directions of the heat sink, a 20-mm layer of polystyrene (k = 0.2 W/m°C) was used. The heat loss from the supporting blocks, which were installed on the upper and bottom sides of the heat sink, was calculated based on Fourier’s heat conduction law. To prevent heat loss from the side surfaces of the supporting blocks, insulators were equipped at the sides of the supporting blocks. The average temperature of the heat sink was measured using thermocouples at eight test points on the heat sink. The thermal resistance was used as the performance index of the heat sink, which is defined as follows:
(a) Isometric view
Symmetric plane
RTH ¼
T avg;heatsink T 1 Q_ supply Q_ loss
ð4Þ
In the experiment, the maximum uncertainty of the thermal resistance was estimated to be 6.7%. Fig. 3 shows the numerical and experimental results. The maximum error was 7.1%; thus, the numerical analysis accurately predicted the experimental results.
4. Results and discussion
(b) Computational domain Fig. 1. Schematic diagram of cross-cut cylindrical heat sink.
converged when the maximum values of their relative errors were less than 105. The radius of the computational region was varied between two and four times the radius of the heat sink ðH þ Do =2Þ while accounting for the heat sink temperature convergence and CPU time. Consequently, we determined the radius of the spherical control volume to be three times the radius of the heat sink with a temperature variation of less than 0.5%. To determine the grid
The flow characteristics and thermal resistance of straight and inclined cross-cut heat sinks were compared. Through this analysis, the effects of fin shape on cooling performance were investigated. Based on these results, a correlation that can predict the degree of improvement in the cooling performance of an inclined cross-cut heat sink relative to that of a straight cross-cut heat sink was suggested as a function of the heat sink design variables, the installation angle of the heat sink, and the Rayleigh number. Finally, a contour map was developed that can be used to select the optimum heat sink type in terms of the installation angle of the heat sink and the inclined angle of the fins.
Table 1 Boundary conditions for the computational domain. Wall
Momentum equation
Energy equation
Fluid domain Outer face
Pressure inlet/pressure outlet condition
T inlet ¼ T outlet;backflow ¼ T 1
Solid domain Heat sink base
ui = 0
Symmetric face
ui = 0
solid ksolid @T@n ¼ q_ heat sink base @T solid ¼ 0 @n section wall
Interface between fluid and solid domains Interface ui = 0
T fluid;w ¼ T solid;w ; R fluid solid kfluid @T@n þ q_ out ¼ ksolid @T@n þ q_ in q_ in ¼ sn>0 Iin s ndX; q_ out ¼ ð1 ew Þq_ in þ ew rT 4w w
w
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
4
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Fig. 2. Experimental setup.
effect still existed to some extent due to the horizontally positioned cross-cut fins. Therefore, the contribution of the back side of the cross-cut fins to the overall heat transfer was diminished. In the case of the inclined cross-cut heat sink with h = 90°, the blocking effect was reduced due to the fact that the inclined cross-cut fins enabled the air to smoothly flow over both sides of the fins, thereby contributing to the overall heat transfer. The ranges of the operating angle of the straight and inclined cross-cut fins with respect to the installation angle of the heat sink are illustrated in Fig. 5. The operating angle range of the reference model (/ = 45°) is presented by way of example. The operating angle range is the difference in the angle between the fin direction and the flow direction; it is also the angle that the rising flow experiences when the flow meets the fins. In the case of a straight crosscut fin, the heat sink installation angle can vary from h = 0° to 90°, and at the same time, the operating angle ranges from c = 0° to 90°. In the case of the inclined cross-cut fin, although the installation angle can change from h = 0° to 90°, it was determined that the operating angle actually experienced ranged from c = 45° to 45°, which improved the flow path throughout the installation angle range. 4.2. Cooling performance of the inclined cross-cut cylindrical heat sink
Fig. 3. Validation result (q_ ¼ 6000 W=m2 , T1 = 24 °C).
4.1. Flow characteristics of the inclined cross-cut cylindrical heat sink In the case of h = 0° and 90°, the path lines of the straight and inclined cross-cut cylindrical heat sinks are shown in Fig. 4. The geometric parameters and operating conditions of the reference model were the same as those in a previous study [15], i.e., N = 12, L = 50 mm, H = 30 mm, lf = 10 mm, Di = 20 mm, Do = 60 mm, t = 2 mm, e = 0.84, q_ ¼ 5000 W=m2 , and T1 = 26 °C. The only difference in the reference model was the inclined angle of the fin (/ = 45°). In the case of the straight cross-cut heat sink with h = 0°, the flow direction was coincident with the fin direction. Alternatively, in the case of the inclined cross-cut fin with h = 0°, the air flow through the lower side of the heat sink changed direction due to the inclined angle of the fin (/). As a result, the natural convection flow was affected by the inclined fin angle (/), and thus, had a longer flow path in comparison to the flow path of the straight cross-cut heat sink case. In the case of the straight cross-cut heat sink with h = 90°, the cooling performance was improved by allowing air to flow through the spaces between the cross-cut fins [15]. However, the blocking
Fig. 6(a) shows the variation of thermal resistance in the cylindrical heat sink with cross-cut fins inclined at an angle of /, when the heat sink is installed vertically (h = 0°). According to our findings, as the inclined angle of the fins increased, the thermal resistance was decreased relative to the thermal resistance of the straight cross-cut fin (/ = 0°). This was because the flow path length was stretched due to the fact that the inflow direction changed according to the fin direction. Minimum thermal resistance appeared at / = 25–30°. For inclined angles (/) greater than approximately 50°, however, the thermal resistance increased with increasing / in comparison to the thermal resistance of the straight cross-cut heat sink (/ = 0°). This is because the fins of the inclined cross-cut heat sink began to lean toward the horizontal line, and as a result, the blocking effect was enhanced, i.e., the cooling performance declined, resulting in an increase in the thermal resistance of heat sink. Fig. 6(b) shows the variation of thermal resistance according to the inclined angle of the fins (/) and the installation angle of the heat sink (h). Optimum cooling performance occurred at h = 20– 30° and / = 30°. For the inclined cross-cut fins with / = 30°, the thermal resistance was decreased by 10% in comparison to that of the straight cross-cut fin (/ = 0°). In the case of the inclined cross-cut cylindrical heat sink, the flow path was stretched throughout the entire range of installation angles, which increased the heat transfer rate between the air and the fins. 4.3. Heat transfer augmentation factor (n) To compare the cooling performance of the straight and inclined cross-cut fins, a heat transfer augmentation factor (n) is suggested. This factor is defined as the ratio of the thermal resistance of the inclined cross-cut heat sink to the thermal resistance of the straight cross-cut heat sink.
n¼
RTH;inclined cross-cut RTH;straight cross-cut
ð5Þ
The heat transfer augmentation factor (n) is the degree of improvement in the cooling performance when the straight cross-cut fin is replaced by the inclined cross-cut fin. If n > 1, then it is better to select the straight cross-cut heat sink; conversely, if n < 1, then it is better to select the inclined cross-cut heat sink.
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
5
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
0
(a)
( Fr ont view )
( b)
90
(Front view)
Straight cross-cut heat sink 0 ) (
Inclined cross-cut heat sink 45 ) (
Fig. 4. Path lines around a cylindrical heat sink for various installation angles (Q_ ¼ 5000 W=m2 , T1 = 26 °C).
Straight cross-cut fin
Inclined cross-cut fin
0
45
0 0
Operating angle range
90
Operating angle range lf lf
90
Buoyancy flow
Buoyancy flow
Fig. 5. Operating angle range in cross-cut heat sinks.
Fig. 7 shows the heat transfer augmentation factor according to the unit fin length (lf) at / = 30°, which was the optimum inclined angle of the fins in the reference model. In the case of lf = 10 mm, the thermal resistance was decreased by 10% with the use of the inclined cross-cut fins. In the case of lf = 2 mm, the thermal resistance was reduced by 5% with the use of the inclined cross-cut fins. This occurred because the effect of inclined angle (/) on the cooling performance was greater for longer unit fin lengths (lf). Overall, the most significant observed improvement in cooling performance was obtained by using the inclined cross-cut heat sink with a range of h = 50–60°. Over the entire h range, the heat transfer augmentation factor was less than 1; thus, the use of the inclined cross-cut heat sink is recommended to improve the cooling performance. 4.4. Correlation The results of this study lead us to suggest a correlation to predict the heat transfer augmentation factor as a function of the
cross-cut heat sink geometry parameters and installation angle. The design parameters of the cylindrical heat sink (N, lf, and /) and installation angle (h) were selected as the variables of the design of experiment (DOE). Using the full factorial design (FFD, three levels of N and lf and four levels of / and h), we selected a total of 144 design points. We selected a design range that can be manufactured and applied to actual commercial LED bulbs. The correlation form was based on the form in a previous study [15], which investigated the heat transfer augmentation factor in consideration of fin geometry. The heat transfer augmentation factor correlation obtained through a regression analysis of the design points is as follows:
ðc1 þc2 hþc3 h2 þc4 h3 Þ ðc5 þc6 hþc7 h2 þc8 h3 Þ n ¼ RaL N
ðc9 þc10 hþc11 h2 þc12 h3 Þ ðc13 þc14 hþc15 h2 þc16 h3 Þ lc / L
ð6Þ
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
6
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Fig. 7. Effect of the fin unit length on the augmentation factor.
(a) Effect of the inclined fin angle
(b) Effect of the installation angle
Fig. 8. Comparison of the augmentation factor between the numerical analysis and the correlation (t = 2 mm, 0° 6 h 6 90°, 0° 6 / 6 45°, 12 6 N 6 36, 0.04 6 lf/L 6 0.33, 4.4 104 6 RaL 6 3.5 106).
Fig. 6. Parametric study.
The coefficient of determination (R2) of the correlation is 0.96. The applicable range of the correlation is t = 2 mm, 0° 6 h 6 90°, 0° 6 / 6 90°, 12 6 N 6 36, 0.04 6 lf/L 6 0.33, and 4.4 104 6 RaL 6 3.5 106. The distributed discrete data in Fig. 8 shows the results of numerical analysis and the predicted values according to the correlation. The data are close to the thick diagonal line, which
where, gb T 1 ÞL3 ðT RaL ¼ film avg;heatsink . mfilm afilm h = 1 + h/90° (h: Installation angle of heat sink [°]). = 1 + //45° (/: Inclined angle of fin [°]). /
c1 ¼ 2:80 103 ; 3
c2 ¼ 1:69 104 ;
3
c5 ¼ 1:70 10 ;
c6 ¼ 0;
c9 ¼ 0;
c10 ¼ 9:83 103 ; 4
c3 ¼ 8:50 105 ; c7 ¼ 1:02 10 ;
c4 ¼ 0 c8 ¼ 1:18 103
c11 ¼ 1:07 102 ; c12 ¼ 7:01 104
4
c13 ¼ 3:95 10 ; c14 ¼ 786 10 ; c15 ¼ 4:56 103 ; c16 ¼ 10:05 103
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
7
improvement of cooling performance achieved by using an inclined cross-cut heat sink was the most significant at h = 50– 60°. Over the entire installation angle range, the heat transfer augmentation factor was less than 1. Thus, the use of an inclined crosscut heat sink was recommended for every installation angle. A correlation that predicts the degree of improvement in the cooling performance relative to a straight cross-cut heat sink was suggested as a function of the heat sink design variables and the installation angle of the heat sink. Finally, a contour map to select the optimum heat sink type with respect to the installation angle of the heat sink and the inclined angle of the fins was developed. Conflicts of interest We declare no conflict of interest in this paper. Acknowledgements This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (Nos. 20162010103830, 20164010200860). References Fig. 9. Contour map for heat sink selection.
demonstrates that the correlation predicted the results of numerical analysis well. 4.5. Contour map With the suggested correlation, we have developed a contour map to determine the optimum heat sink type. If the external design parameters of the heat sink are established, then the correlation n(N, lf, h, /) becomes n(h, /). The contour map compares the cooling performance of straight and inclined cross-cut heat sinks by using the heat transfer augmentation factor as a function of the installation angle (h) and the inclined angle (/). As an example, the heat transfer augmentation factor of the reference shape is indicated in Fig. 9. As shown in Fig. 9, the augmentation factor was less than 1 regardless of the installation angle; thus, the inclined cross-cut heat sink is recommended for every installation angle. Moreover, an inclined angle of 25–30° is recommended for most of the design range. Therefore, by using the contour map developed herein, the optimum fin shape for a given design condition can be determined. 5. Conclusion The present study investigated an inclined cross-cut cylindrical heat sink in an attempt to improve the cooling performance of cylindrical heat sinks, which is the cooling apparatus used for LED light bulbs. In the case of a straight cross-cut fin from h = 0° to 90°, the operating angle range is also between c = 0° and 90°. Using the inclined cross-cut fin, although the installation angle range from h = 0° to 90°, the actual operating angle range is from c = 0° to 45°. This led to an improved flow path in the overall installation angle range. For the inclined cross-cut heat sink, the natural convection flow with an incidence angle had a flow path that was stretched in length compared to the flow path of the straight cross-cut heat sink; accordingly, the flow efficiency was improved. At an inclined fin angle of 25–30°, the thermal resistance was the smallest. However, at inclined angles greater than 50°, only the blocking effect was increased, and the flow path length was not stretched; hence, the cooling performance declined. Overall, the
[1] E. Mills, A. Jacobson, From carbon to light: a new framework for estimating greenhouse gas emissions reductions from replacing fuel-based lighting with LED systems, Energy Effic. 4 (2011) 523–546. [2] A. De Almeida, B. Santos, B. Paolo, M. Quicheron, Solid state lighting review – potential and challenges in Europe, Renewable Sustainable Energy Rev. 34 (2014) 30–48. [3] I.L. Azevedo, M.G. Morgan, F. Morgan, The transition to solid-state lighting, Proc. IEEE 97 (2009) 481–510. [4] F. Salata, A. de Lieto Vollaro, A. Ferraro, An economic perspective on the reliability of lighting systems in building with highly efficient energy: a case study, Energy Convers. Manage. 84 (2014) 623–632. [5] J. Wang, X.J. Zhao, Y.X. Cai, C. Zhang, W.W. Bao, Experimental study on the thermal management of high-power LED headlight cooling device integrated with thermoelectric cooler package, Energy Convers. Manage. 101 (2015) 532– 540. [6] S.J. Park, D. Jang, S.J. Yook, K.S. Lee, Optimization of a chimney design for cooling efficiency of a radial heat sink in a LED downlight, Energy Convers. Manage. 114 (2016) 180–187. [7] V.A.F. Costa, A.M.G. Lopes, Improved radial heat sink for led lamp cooling, Appl. Therm. Eng. 70 (2014) 131–138. [8] D. Jang, S.H. Yu, K.S. Lee, Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications, Int. J. Heat Mass Transfer 55 (2012) 515– 521. [9] I. Tari, M. Mehrtash, Natural convection heat transfer from inclined plate-fin heat sinks, Int. J. Heat Mass Transfer 56 (2013) 574–593. [10] Q. Shen, D. Sun, Y. Xu, T. Jin, X. Zhao, Orientation effects on natural convection heat dissipation of rectangular fin heat sinks mounted on LEDs, Int. J. Heat Mass Transfer 75 (2014) 462–469. [11] R.-T. Huang, W.-J. Shew, C.-C. Wang, Orientation effect of natural convective performance of square pin fin heat sinks, Int. J. Heat Mass Transfer 51 (2008) 2368–2376. [12] B. Li, C. Byon, Orientation effects on thermal performance of radial heat sinks with a concentric ring subject to natural convection, Int. J. Heat Mass Transfer 90 (2015) 102–108. [13] B.H. An, H.J. Kim, D. Kim, Nusselt number correlation for natural convection from vertical cylinders with vertically oriented plate fins, Exp. Thermal Fluid Sci. 41 (2012) 59–66. [14] D. Jang, S.J. Park, S.J. Yook, K.S. Lee, The orientation effect for cylindrical heat sinks with application to LED light bulbs, Int. J. Heat Mass Transfer 71 (2014) 496–502. [15] D. Jang, D.R. Kim, K.S. Lee, Correlation of cross-cut cylindrical heat sink to improve the orientation effect of LED light bulbs, Int. J. Heat Mass Transfer 84 (2015) 821–826. [16] M.G. Carvalho, T. Faris, P. Fontes, Predicting radiative heat transfer in absorbing, emitting and scattering media using the discrete transfer method, in: W.A. Fiveland et al. (Eds.), Fundamentals of Radiation Heat Transfer, ASME HTD 160, 1991, pp. 17–26. [17] S.H. Yu, D. Jang, K.S. Lee, Effect of radiation in a radial heat sink under natural convection, Int. J. Heat Mass Transfer 55 (2012) 505–509. [18] D. Jang, S.J. Yook, K.S. Lee, Optimum design of a radial heat sink with a finheight profile for high-power LED lighting applications, Appl. Energy 116 (2014) 260–268.
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs Seung-Jae Park a, Daeseok Jang a,b, Kwan-Soo Lee a,⇑ a b
School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Korea Atomic Energy Research Institute, 111 Daedeok-daero 989 beon-gil, Yuseong-gu, Daejeon 34057, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 July 2016 Received in revised form 18 August 2016 Accepted 18 August 2016 Available online xxxx Keywords: Heat sink Natural convection Orientation effect LED
a b s t r a c t An inclined cross-cut cylindrical heat sink was investigated in an attempt to improve the energy conversion and management of LED light bulbs. The thermo-flow characteristics were studied to enhance the cooling performance of a cylindrical heat sink, which is the cooling apparatus used for LED light bulbs. In the inclined cross-cut heat sink, the natural convection flow with an incidence angle had a flow path length that was more stretched in comparison to the flow path length of a straight cross-cut heat sink. Accordingly, the heat transfer rate between the air and fins was increased. When the fins had an inclined angle of 25–30°, the thermal resistance was the smallest. However, when the inclined angle increased to greater than 50°, only the blocking effect was increased and the flow path length was not stretched. Hence, cooling performance was decreased with inclined angles greater than 50°. A correlation predicting the degree of improvement in cooling performance relative to a baseline straight cross-cut heat sink was suggested as a function of heat sink design variables and the installation angle of the heat sink. Finally, a contour map was developed, which can be used to select the optimum heat sink type, with respect to the installation angle of the heat sink and the inclined angle of the fins. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction The latest trend in light-emitting diode (LED) lighting is a move toward increased energy efficiency and eco-friendliness. Accordingly, there is a growing demand for the development of high energy-efficient lighting to reduce greenhouse gas (GHG) emissions [1]. Because lighting is responsible for 20% of the overall energy consumption of buildings, the replacement of conventional lighting with lighting that is highly energy efficient is required [2]. The production and import of conventional incandescent lamps is globally prohibited because of the low efficiency of incandescent lamps. Alternative light sources include compact fluorescent lamps (CFLs) and halogen lamps. The presence of harmful substances, such as mercury, in CFLs reduces the demand for CFLs. The EU energy committee announced the implementation of increased energy efficiency standards in 2016, one result of which is the further prohibition of halogen lamps. Therefore, eco-friendly, energyefficient LED bulbs are rapidly replacing conventional light bulbs [3]. When the heat dissipation performance of LED light bulbs is insufficient, the light emission efficiency of LED chips is decreased
⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee).
and the lifetime is reduced [4–6]. Therefore, research related to enhancing the cooling performance of LED light bulbs is required. A heat sink is used as a cooling system for LED lighting due to the low cost and semi-permanent life time [6]. Recently, the power consumption and heat generation rate of LED lightings have had to increase in order for the lightings to emit brighter light. Therefore, many researchers have attempted to increase the natural convective and radiative heat transfer rate from the heat sinks to improve both efficiency and performance in LED lighting. Costa et al. [7] improved the thermal performance of a radial heat sink by changing the number, length, height, and thickness of the fins. Jang et al. [8] optimized the thermal performance and the mass of a heat sink by varying the design factors of the fin. The installation angle of LED lighting can vary depending on its purpose. Thus, not only the thermal performance, but also the orientation effect, which changes the thermal performance of the heat sink depending on its installation angle, should be considered in designing a heat sink for LED lighting. Tari et al. [9] numerically analyzed the orientation effect and suggested a correlation equation for a plate fin heat sink. Shen et al. [10] investigated the impact of the number of plate fins on the orientation effect for LED lighting. Huang et al. [11] experimentally studied the effects of the installation angle on a square pin-fin heat sink and compared the performance with that of seven other types of heat sinks. Li et al. [12] developed a correlation
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
2
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Nomenclature C D F g H k L l N n P Q_ q_ RTH Ra s T t u v
specific heat [J/(kg K)] diameter of heat sink [mm] body force vector per unit volume gravity acceleration [m/s2] fin height [mm] thermal conductivity [W/(m K)] height of heat sink base [mm] length [mm] number of fin arrays normal direction vector pressure [Pa] heat transfer rate [W] heat flux [W/m2] thermal resistance [°C/W] Rayleigh number surface temperature [K] thickness of fin [mm] velocity [m/s] velocity vector [m/s]
equation to describe the orientation effect of a radial heat sink with a concentric ring. All of these aforementioned studies, however, focus investigation on heat sinks that have horizontal circular or square bases. LED light bulbs, which are the focus of this study, generally use cylindrical heat sinks that have fins on cylindrical bases. The thermo-flow characteristics of a cylindrical heat sink differ from the thermos-flow characteristics of a circular or square heat sink. Therefore, it is difficult to apply the results from former studies to a cylindrical heat sink. Recently, An et al. [13] experimentally investigated the effects of geometric factors on the plate fins of cylindrical heat sinks and proposed a correlation equation. Jang et al. [14,15] analyzed the orientation effect of a plate fin cylindrical heat sink numerically and suggested a straight crosscut cylindrical heat sink, which is shown to improve the orientation effect. In the case of a straight cross-cut cylindrical heat sink, the blocking effect from fins is reduced, which weakens the orientation effect. The cylindrical heat sinks in the aforementioned studies contain plate or straight cross-cut fins. Therefore, research on the thermal performance and orientation effects of an inclined cross-cut cylindrical heat sink that considers the inclined angle of the fin is required. In the present study, we investigate an inclined cross-cut heat sink in an attempt to improve the cooling performance of cylindrical heat sinks for LED light bulbs. Flow characteristics and thermal resistance with respect to the inclined angle of the cross-cut fins, are investigated. A correlation, which is able to predict the degree of improvement in the cooling performance of an inclined crosscut heat sink in comparison to a straight cross-cut heat sink, is suggested as a function of heat sink design variables, the installation angle of the heat sink, and the Rayleigh number. Finally, a contour map that can be used to select the optimum heat sink type with respect to the installation angle of the heat sink and the inclined angle of the fins is developed.
Greek symbols n heat transfer augmentation factor, b
c r q e
h /
RInclined cross-cut RStraight cross-cut 1
coefficient of volume expansion [K ] operating angle range Stefan–Boltzmann constant [W/m2K4] density [kg/m3] emissivity installation angle of heat sink [°] inclined angle of fin [°]
Subscripts avg average f unit fin film film temperature L average over the heat sink length i inner in in o outer out out 1 ambient
cross-cut fins. The cross-cut fins are aligned radially at uniform angle intervals. Unlike straight cross-cut fins [15], inclined crosscut fins are tilted at an inclined angle (/), with the middle of the heat sink at the center. The computational domain and installation angle of the heat sink (h) used for the numerical analysis of the cylindrical heat sink are indicated in Fig. 1(b). To generate an independent computational domain from the installation angle of the heat sink, we created a spherical control volume that is centered at the middle of the heat sink. The heat sink is symmetrical; thus, only half of the heat sink and the air region were considered as the computational domain. The assumptions for the numerical analysis are as follows: (1) The flow is three-dimensional, steady state, and laminar. (2) The density of air is calculated by the ideal gas law. (3) The surface of the heat sink is gray and diffuse. The governing equations for the numerical analysis are as follows: Continuity equation:
r ðqv Þ ¼ 0
ð1Þ
Momentum equation:
qðv rÞv ¼ rP þ lr2 m þ F ðfor z-direction F ¼ qgÞ
ð2Þ
Energy equation:
qC v rT ¼ r ðkrTÞ
ð3Þ
The boundary conditions are indicated in Table 1. Radiation heat transfer was calculated by using the discrete transfer radiation model (DTRM) [16–18], which is applicable for the symmetrical condition. 2.2. Numerical procedure
2. Mathematical modeling 2.1. Numerical model Fig. 1 shows the inclined cross-cut heat sink considered in this study. The heat sink consists of a cylindrical base and inclined
The SIMPLE algorithm was selected to combine the pressure and velocity of the flow field. The convective terms of the governing equations were discretized using a second-order upwind scheme to improve the accuracy of the numerical result. In the iterative calculation, we concluded that the dependent variables
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
3
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
independency, we tested between 650,000 and 2,300,000 grid points and selected 1,303,688 nodes as the reference mesh when the temperature variation was less than 0.5%.
3. Experiment and validation An experiment was performed to validate the numerical model. The geometric parameters of the tested heat sink were N = 12, / = 45°, L = 50 mm, H = 30 mm, lf = 10 mm, Di = 20 mm, Do = 60 mm, and t = 2 mm (Fig. 1). The heat sink was made of aluminum alloy 6061. A black anodizing surface treatment was applied to the heat sink, and its emissivity was 0.9. The emissivity of the heat sink was calculated using a thermal infrared camera. The test section of the experimental apparatus is shown in Fig. 2. To minimize the thermal contact resistance, thermal grease was used at the contact surface between the heat sink and the cartridge heater. To calculate the heat loss through the top and bottom directions of the heat sink, a 20-mm layer of polystyrene (k = 0.2 W/m°C) was used. The heat loss from the supporting blocks, which were installed on the upper and bottom sides of the heat sink, was calculated based on Fourier’s heat conduction law. To prevent heat loss from the side surfaces of the supporting blocks, insulators were equipped at the sides of the supporting blocks. The average temperature of the heat sink was measured using thermocouples at eight test points on the heat sink. The thermal resistance was used as the performance index of the heat sink, which is defined as follows:
(a) Isometric view
Symmetric plane
RTH ¼
T avg;heatsink T 1 Q_ supply Q_ loss
ð4Þ
In the experiment, the maximum uncertainty of the thermal resistance was estimated to be 6.7%. Fig. 3 shows the numerical and experimental results. The maximum error was 7.1%; thus, the numerical analysis accurately predicted the experimental results.
4. Results and discussion
(b) Computational domain Fig. 1. Schematic diagram of cross-cut cylindrical heat sink.
converged when the maximum values of their relative errors were less than 105. The radius of the computational region was varied between two and four times the radius of the heat sink ðH þ Do =2Þ while accounting for the heat sink temperature convergence and CPU time. Consequently, we determined the radius of the spherical control volume to be three times the radius of the heat sink with a temperature variation of less than 0.5%. To determine the grid
The flow characteristics and thermal resistance of straight and inclined cross-cut heat sinks were compared. Through this analysis, the effects of fin shape on cooling performance were investigated. Based on these results, a correlation that can predict the degree of improvement in the cooling performance of an inclined cross-cut heat sink relative to that of a straight cross-cut heat sink was suggested as a function of the heat sink design variables, the installation angle of the heat sink, and the Rayleigh number. Finally, a contour map was developed that can be used to select the optimum heat sink type in terms of the installation angle of the heat sink and the inclined angle of the fins.
Table 1 Boundary conditions for the computational domain. Wall
Momentum equation
Energy equation
Fluid domain Outer face
Pressure inlet/pressure outlet condition
T inlet ¼ T outlet;backflow ¼ T 1
Solid domain Heat sink base
ui = 0
Symmetric face
ui = 0
solid ksolid @T@n ¼ q_ heat sink base @T solid ¼ 0 @n section wall
Interface between fluid and solid domains Interface ui = 0
T fluid;w ¼ T solid;w ; R fluid solid kfluid @T@n þ q_ out ¼ ksolid @T@n þ q_ in q_ in ¼ sn>0 Iin s ndX; q_ out ¼ ð1 ew Þq_ in þ ew rT 4w w
w
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
4
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Fig. 2. Experimental setup.
effect still existed to some extent due to the horizontally positioned cross-cut fins. Therefore, the contribution of the back side of the cross-cut fins to the overall heat transfer was diminished. In the case of the inclined cross-cut heat sink with h = 90°, the blocking effect was reduced due to the fact that the inclined cross-cut fins enabled the air to smoothly flow over both sides of the fins, thereby contributing to the overall heat transfer. The ranges of the operating angle of the straight and inclined cross-cut fins with respect to the installation angle of the heat sink are illustrated in Fig. 5. The operating angle range of the reference model (/ = 45°) is presented by way of example. The operating angle range is the difference in the angle between the fin direction and the flow direction; it is also the angle that the rising flow experiences when the flow meets the fins. In the case of a straight crosscut fin, the heat sink installation angle can vary from h = 0° to 90°, and at the same time, the operating angle ranges from c = 0° to 90°. In the case of the inclined cross-cut fin, although the installation angle can change from h = 0° to 90°, it was determined that the operating angle actually experienced ranged from c = 45° to 45°, which improved the flow path throughout the installation angle range. 4.2. Cooling performance of the inclined cross-cut cylindrical heat sink
Fig. 3. Validation result (q_ ¼ 6000 W=m2 , T1 = 24 °C).
4.1. Flow characteristics of the inclined cross-cut cylindrical heat sink In the case of h = 0° and 90°, the path lines of the straight and inclined cross-cut cylindrical heat sinks are shown in Fig. 4. The geometric parameters and operating conditions of the reference model were the same as those in a previous study [15], i.e., N = 12, L = 50 mm, H = 30 mm, lf = 10 mm, Di = 20 mm, Do = 60 mm, t = 2 mm, e = 0.84, q_ ¼ 5000 W=m2 , and T1 = 26 °C. The only difference in the reference model was the inclined angle of the fin (/ = 45°). In the case of the straight cross-cut heat sink with h = 0°, the flow direction was coincident with the fin direction. Alternatively, in the case of the inclined cross-cut fin with h = 0°, the air flow through the lower side of the heat sink changed direction due to the inclined angle of the fin (/). As a result, the natural convection flow was affected by the inclined fin angle (/), and thus, had a longer flow path in comparison to the flow path of the straight cross-cut heat sink case. In the case of the straight cross-cut heat sink with h = 90°, the cooling performance was improved by allowing air to flow through the spaces between the cross-cut fins [15]. However, the blocking
Fig. 6(a) shows the variation of thermal resistance in the cylindrical heat sink with cross-cut fins inclined at an angle of /, when the heat sink is installed vertically (h = 0°). According to our findings, as the inclined angle of the fins increased, the thermal resistance was decreased relative to the thermal resistance of the straight cross-cut fin (/ = 0°). This was because the flow path length was stretched due to the fact that the inflow direction changed according to the fin direction. Minimum thermal resistance appeared at / = 25–30°. For inclined angles (/) greater than approximately 50°, however, the thermal resistance increased with increasing / in comparison to the thermal resistance of the straight cross-cut heat sink (/ = 0°). This is because the fins of the inclined cross-cut heat sink began to lean toward the horizontal line, and as a result, the blocking effect was enhanced, i.e., the cooling performance declined, resulting in an increase in the thermal resistance of heat sink. Fig. 6(b) shows the variation of thermal resistance according to the inclined angle of the fins (/) and the installation angle of the heat sink (h). Optimum cooling performance occurred at h = 20– 30° and / = 30°. For the inclined cross-cut fins with / = 30°, the thermal resistance was decreased by 10% in comparison to that of the straight cross-cut fin (/ = 0°). In the case of the inclined cross-cut cylindrical heat sink, the flow path was stretched throughout the entire range of installation angles, which increased the heat transfer rate between the air and the fins. 4.3. Heat transfer augmentation factor (n) To compare the cooling performance of the straight and inclined cross-cut fins, a heat transfer augmentation factor (n) is suggested. This factor is defined as the ratio of the thermal resistance of the inclined cross-cut heat sink to the thermal resistance of the straight cross-cut heat sink.
n¼
RTH;inclined cross-cut RTH;straight cross-cut
ð5Þ
The heat transfer augmentation factor (n) is the degree of improvement in the cooling performance when the straight cross-cut fin is replaced by the inclined cross-cut fin. If n > 1, then it is better to select the straight cross-cut heat sink; conversely, if n < 1, then it is better to select the inclined cross-cut heat sink.
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
5
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
0
(a)
( Fr ont view )
( b)
90
(Front view)
Straight cross-cut heat sink 0 ) (
Inclined cross-cut heat sink 45 ) (
Fig. 4. Path lines around a cylindrical heat sink for various installation angles (Q_ ¼ 5000 W=m2 , T1 = 26 °C).
Straight cross-cut fin
Inclined cross-cut fin
0
45
0 0
Operating angle range
90
Operating angle range lf lf
90
Buoyancy flow
Buoyancy flow
Fig. 5. Operating angle range in cross-cut heat sinks.
Fig. 7 shows the heat transfer augmentation factor according to the unit fin length (lf) at / = 30°, which was the optimum inclined angle of the fins in the reference model. In the case of lf = 10 mm, the thermal resistance was decreased by 10% with the use of the inclined cross-cut fins. In the case of lf = 2 mm, the thermal resistance was reduced by 5% with the use of the inclined cross-cut fins. This occurred because the effect of inclined angle (/) on the cooling performance was greater for longer unit fin lengths (lf). Overall, the most significant observed improvement in cooling performance was obtained by using the inclined cross-cut heat sink with a range of h = 50–60°. Over the entire h range, the heat transfer augmentation factor was less than 1; thus, the use of the inclined cross-cut heat sink is recommended to improve the cooling performance. 4.4. Correlation The results of this study lead us to suggest a correlation to predict the heat transfer augmentation factor as a function of the
cross-cut heat sink geometry parameters and installation angle. The design parameters of the cylindrical heat sink (N, lf, and /) and installation angle (h) were selected as the variables of the design of experiment (DOE). Using the full factorial design (FFD, three levels of N and lf and four levels of / and h), we selected a total of 144 design points. We selected a design range that can be manufactured and applied to actual commercial LED bulbs. The correlation form was based on the form in a previous study [15], which investigated the heat transfer augmentation factor in consideration of fin geometry. The heat transfer augmentation factor correlation obtained through a regression analysis of the design points is as follows:
ðc1 þc2 hþc3 h2 þc4 h3 Þ ðc5 þc6 hþc7 h2 þc8 h3 Þ n ¼ RaL N
ðc9 þc10 hþc11 h2 þc12 h3 Þ ðc13 þc14 hþc15 h2 þc16 h3 Þ lc / L
ð6Þ
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
6
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
Fig. 7. Effect of the fin unit length on the augmentation factor.
(a) Effect of the inclined fin angle
(b) Effect of the installation angle
Fig. 8. Comparison of the augmentation factor between the numerical analysis and the correlation (t = 2 mm, 0° 6 h 6 90°, 0° 6 / 6 45°, 12 6 N 6 36, 0.04 6 lf/L 6 0.33, 4.4 104 6 RaL 6 3.5 106).
Fig. 6. Parametric study.
The coefficient of determination (R2) of the correlation is 0.96. The applicable range of the correlation is t = 2 mm, 0° 6 h 6 90°, 0° 6 / 6 90°, 12 6 N 6 36, 0.04 6 lf/L 6 0.33, and 4.4 104 6 RaL 6 3.5 106. The distributed discrete data in Fig. 8 shows the results of numerical analysis and the predicted values according to the correlation. The data are close to the thick diagonal line, which
where, gb T 1 ÞL3 ðT RaL ¼ film avg;heatsink . mfilm afilm h = 1 + h/90° (h: Installation angle of heat sink [°]). = 1 + //45° (/: Inclined angle of fin [°]). /
c1 ¼ 2:80 103 ; 3
c2 ¼ 1:69 104 ;
3
c5 ¼ 1:70 10 ;
c6 ¼ 0;
c9 ¼ 0;
c10 ¼ 9:83 103 ; 4
c3 ¼ 8:50 105 ; c7 ¼ 1:02 10 ;
c4 ¼ 0 c8 ¼ 1:18 103
c11 ¼ 1:07 102 ; c12 ¼ 7:01 104
4
c13 ¼ 3:95 10 ; c14 ¼ 786 10 ; c15 ¼ 4:56 103 ; c16 ¼ 10:05 103
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056
S.-J. Park et al. / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx
7
improvement of cooling performance achieved by using an inclined cross-cut heat sink was the most significant at h = 50– 60°. Over the entire installation angle range, the heat transfer augmentation factor was less than 1. Thus, the use of an inclined crosscut heat sink was recommended for every installation angle. A correlation that predicts the degree of improvement in the cooling performance relative to a straight cross-cut heat sink was suggested as a function of the heat sink design variables and the installation angle of the heat sink. Finally, a contour map to select the optimum heat sink type with respect to the installation angle of the heat sink and the inclined angle of the fins was developed. Conflicts of interest We declare no conflict of interest in this paper. Acknowledgements This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (Nos. 20162010103830, 20164010200860). References Fig. 9. Contour map for heat sink selection.
demonstrates that the correlation predicted the results of numerical analysis well. 4.5. Contour map With the suggested correlation, we have developed a contour map to determine the optimum heat sink type. If the external design parameters of the heat sink are established, then the correlation n(N, lf, h, /) becomes n(h, /). The contour map compares the cooling performance of straight and inclined cross-cut heat sinks by using the heat transfer augmentation factor as a function of the installation angle (h) and the inclined angle (/). As an example, the heat transfer augmentation factor of the reference shape is indicated in Fig. 9. As shown in Fig. 9, the augmentation factor was less than 1 regardless of the installation angle; thus, the inclined cross-cut heat sink is recommended for every installation angle. Moreover, an inclined angle of 25–30° is recommended for most of the design range. Therefore, by using the contour map developed herein, the optimum fin shape for a given design condition can be determined. 5. Conclusion The present study investigated an inclined cross-cut cylindrical heat sink in an attempt to improve the cooling performance of cylindrical heat sinks, which is the cooling apparatus used for LED light bulbs. In the case of a straight cross-cut fin from h = 0° to 90°, the operating angle range is also between c = 0° and 90°. Using the inclined cross-cut fin, although the installation angle range from h = 0° to 90°, the actual operating angle range is from c = 0° to 45°. This led to an improved flow path in the overall installation angle range. For the inclined cross-cut heat sink, the natural convection flow with an incidence angle had a flow path that was stretched in length compared to the flow path of the straight cross-cut heat sink; accordingly, the flow efficiency was improved. At an inclined fin angle of 25–30°, the thermal resistance was the smallest. However, at inclined angles greater than 50°, only the blocking effect was increased, and the flow path length was not stretched; hence, the cooling performance declined. Overall, the
[1] E. Mills, A. Jacobson, From carbon to light: a new framework for estimating greenhouse gas emissions reductions from replacing fuel-based lighting with LED systems, Energy Effic. 4 (2011) 523–546. [2] A. De Almeida, B. Santos, B. Paolo, M. Quicheron, Solid state lighting review – potential and challenges in Europe, Renewable Sustainable Energy Rev. 34 (2014) 30–48. [3] I.L. Azevedo, M.G. Morgan, F. Morgan, The transition to solid-state lighting, Proc. IEEE 97 (2009) 481–510. [4] F. Salata, A. de Lieto Vollaro, A. Ferraro, An economic perspective on the reliability of lighting systems in building with highly efficient energy: a case study, Energy Convers. Manage. 84 (2014) 623–632. [5] J. Wang, X.J. Zhao, Y.X. Cai, C. Zhang, W.W. Bao, Experimental study on the thermal management of high-power LED headlight cooling device integrated with thermoelectric cooler package, Energy Convers. Manage. 101 (2015) 532– 540. [6] S.J. Park, D. Jang, S.J. Yook, K.S. Lee, Optimization of a chimney design for cooling efficiency of a radial heat sink in a LED downlight, Energy Convers. Manage. 114 (2016) 180–187. [7] V.A.F. Costa, A.M.G. Lopes, Improved radial heat sink for led lamp cooling, Appl. Therm. Eng. 70 (2014) 131–138. [8] D. Jang, S.H. Yu, K.S. Lee, Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications, Int. J. Heat Mass Transfer 55 (2012) 515– 521. [9] I. Tari, M. Mehrtash, Natural convection heat transfer from inclined plate-fin heat sinks, Int. J. Heat Mass Transfer 56 (2013) 574–593. [10] Q. Shen, D. Sun, Y. Xu, T. Jin, X. Zhao, Orientation effects on natural convection heat dissipation of rectangular fin heat sinks mounted on LEDs, Int. J. Heat Mass Transfer 75 (2014) 462–469. [11] R.-T. Huang, W.-J. Shew, C.-C. Wang, Orientation effect of natural convective performance of square pin fin heat sinks, Int. J. Heat Mass Transfer 51 (2008) 2368–2376. [12] B. Li, C. Byon, Orientation effects on thermal performance of radial heat sinks with a concentric ring subject to natural convection, Int. J. Heat Mass Transfer 90 (2015) 102–108. [13] B.H. An, H.J. Kim, D. Kim, Nusselt number correlation for natural convection from vertical cylinders with vertically oriented plate fins, Exp. Thermal Fluid Sci. 41 (2012) 59–66. [14] D. Jang, S.J. Park, S.J. Yook, K.S. Lee, The orientation effect for cylindrical heat sinks with application to LED light bulbs, Int. J. Heat Mass Transfer 71 (2014) 496–502. [15] D. Jang, D.R. Kim, K.S. Lee, Correlation of cross-cut cylindrical heat sink to improve the orientation effect of LED light bulbs, Int. J. Heat Mass Transfer 84 (2015) 821–826. [16] M.G. Carvalho, T. Faris, P. Fontes, Predicting radiative heat transfer in absorbing, emitting and scattering media using the discrete transfer method, in: W.A. Fiveland et al. (Eds.), Fundamentals of Radiation Heat Transfer, ASME HTD 160, 1991, pp. 17–26. [17] S.H. Yu, D. Jang, K.S. Lee, Effect of radiation in a radial heat sink under natural convection, Int. J. Heat Mass Transfer 55 (2012) 505–509. [18] D. Jang, S.J. Yook, K.S. Lee, Optimum design of a radial heat sink with a finheight profile for high-power LED lighting applications, Appl. Energy 116 (2014) 260–268.
Please cite this article in press as: S.-J. Park et al., Thermal performance and orientation effect of an inclined cross-cut cylindrical heat sink for LED light bulbs, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.08.056