- Email: [email protected]
Optimization of a staggered pin-fin for a radial heat sink under free convection
International Journal of Heat and Mass Transfer 87 (2015) 184–188
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Optimization of a staggered pin-fin for a radial heat sink under free convection Seung-Jae Park, Daeseok Jang, Se-Jin Yook, Kwan-Soo Lee ⇑ School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 133-791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 20 January 2015 Received in revised form 29 March 2015 Accepted 30 March 2015
Keywords: LED Cooling system Staggered pin-fin array Natural convection Radial heat sink
a b s t r a c t The design of a staggered pin-fin radial heat sink was optimized for light-emitting diode (LED) device cooling. A numerical model for various pin-fin array heat sinks was developed and verified experimentally. The design variables were determined from sensitivity analysis. Multidisciplinary optimization was conducted based on the heat sink thermal resistance and mass, using an evolutionary algorithm. From the analysis results, the staggered pin-fin radial heat sink was identified as the optimal configuration, demonstrating improved thermal performance by up to 10% while maintaining the same mass or reducing the mass by up to 12% for a given thermal resistance. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Light-emitting diodes (LEDs) are an eco-friendly item, offering a long lifetime and high energy conversion efficiency. Thus, much existing lighting has been replaced by LED devices. An abrupt increase in the temperature of the LED chip results in a sharply reduced lifetime and considerably lower light emission efficiency. Studies have shown that 60% of the input power to the LED is converted into thermal energy, as evidenced by the high heat flux [1]. Therefore, it is necessary to cool the LED system sufficiently for stable light emission. The most common passive cooling device for the electrics is a heat sink. Heat sinks are becoming increasingly larger and heavier to accommodate the increasing thermal performance demands of LED devices, at the expense of the lighting device’s safety and manufacturing cost. Thus, technology is needed to improve the performance of the heat sink while reducing its mass. Recently, numerous studies have investigated the cooling effects of radial heat sinks applied to LED down light and high bay devices [2–4]. Yu et al. [2,3] analyzed the thermal performance of various plate-fin radial heat sinks using a numerical method with natural convection considerations; the long fin and middle fin type heat sink was identified as the heat sink with the best thermal performance. Jang et al. [4] applied multidisciplinary design optimization to a pin-fin radial heat sink with thermal ⇑ Corresponding author. Tel.: +82 2 2220 0426; fax: +82 2 2295 9021. E-mail address: [email protected] (K.-S. Lee). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.03.089 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
resistance and mass as the key factors; however, their study targeted radial heat sinks having only an in-line array. Deshmukh et al. [5] and Bahadur et al. [6] examined in-line and staggered pin-fin arrays in a square heat sink set on a vertical wall. Chen et al. [7] and Yuan et al. [8] studied the thermal performance of staggered array heat sinks by forced convection. However, this study focusses on the thermal performance of the heat sink by natural convection. In the present study, a staggered pin-fin radial heat sink mounted on a horizontal wall was considered for LED device cooling. Sensitivity analysis was used to identify the geometric factors that had a significant influence on the heat sink mass and its thermal performance. The heat sink design was further modified via multidisciplinary design optimization.
2. Mathematical modeling 2.1. Numerical model Fig. 1(a) shows the staggered pin-fin radial heat sink, the focus of this study. The heat sink consisted of a circular base with pin-fin arrays positioned periodically along the perimeter of the circular base. Fig. 1(b) and (c) show the computational analysis domain, including the heat sink and surrounding air. To minimize the computing time, only one period domain was analyzed with periodic conditions [9–11]. The following assumptions were adopted to simulate natural convection and radiation heat transfer.
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Nomenclature A g H h k L M N q_ RTH r T t w y
surface area gravity height [mm] heat transfer coefficient [W/m2 °C ] thermal conductivity [W/m °C ] length [mm] mass of heat sink [kg] number of fin array heat flux [W/m2] thermal resistance [°C/W] radius [mm] temperature [°C] thickness of fin [mm] weight factor height from base [mm]
(1) The flow is laminar, steady, and three dimensional. (2) The air properties are constant, with the exception of the density. (3) Air is an ideal gas. (4) The surfaces of the heat sink are gray and diffuse. Radiation heat transfer was calculated using the discrete transfer radiation model (DTRM) [12], given periodic conditions. 2.2. Numerical method The radius and height of the analysis domain ranged from 1.2ro to 1.8ro and 2H to 8H, respectively. Values of 1.5ro and 5H were selected as the domain size in which the average temperature variation of the heat sink was small (1%). A quadrilateral mesh was used; the mesh distance became narrower close to the heat sink surfaces, in the proximity of the predicted existence of the boundary layer. The parameters of the reference heat sink were N = 20, LL = 40 mm, LM = 20 mm, LF = 4 mm, LS = 5 mm, ro = 90 mm,
(a)
Greek symbols e emissivity Subscripts acr acrylic ave average c characteristic facet facet of cell F fin i inner L long fin M middle fin o outer ref reference S space between fins 1 ambient
ri = 5 mm, H = 40 mm, t = 3 mm. The grid dependence was considered by changing the number of grids from 104,946 to 881,725 in the reference model. Grid points totaling 518,312 were set as the reference, given that the average temperature variation of the heat sink was <1%. Numerical analysis was performed using ANSYS FLUENT release 14.5, a commercial computational fluid dynamics (CFD) code based on the finite volume method; the mesh was generated using the ANSYS ICEM release 14.5. The semi-implicit method for pressure linked equations (SIMPLE) algorithm was used to calculate the flow field based on the pressure and velocity. The convective term and energy equation were discretized with the second-order upwind scheme. The convergence criteria for the dependent variables was set to 105. 3. Experiment and validation The heat sink was made from aluminum alloy 6061 (k = 171 W/ m °C) with a black anodizing surface treatment (e = 0.9) for the validation procedure. The parameters of the heat sink were N = 24,
(b)
(c)
Fig. 1. Schematic diagram of a heat sink and computational analysis domain: (a) isometric view (b) top view (c) side view.
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Fig. 2. Experimental setup.
L L = 40 mm, L M = 40 mm, L F = 4 mm, L S = 5 mm, r o = 90 mm, ri = 5 mm, H = 40 mm, t = 3 mm. Fig. 2 shows an experimental setup and location of thermocouples. Two thermocouples were used to measure the ambient temperature. Six thermocouples were installed on the heat sink base, six thermocouples on the upper surface of the acrylic plate, and six thermocouples at the bottom of the acrylic plate. Then, the temperature on each surface was averaged. The steady-state criterion required <0.1 °C variation in the heat sink temperature. The thermal resistance of the heat sink was selected as the performance factor for comparison of the numerical and experimental results. The thermal resistance of the heat sink can be obtained from the following:
RTH ¼
T ave heatsink T 1 q_ Aheatsink base
ð1Þ
where,
q_ ¼
The maximum uncertainty in the heat sink thermal resistance was 4.7% [13]. Seven heat flux conditions in the range of q_ = 400 W/m2 (20 W LED lightings) and q_ = 1000 W/m2 (50 W LED lightings) were selected as experiment points. The maximum difference between the numerical and experimental results was 5%. 4. Results and discussion The reference parameters of various array pin-fin radial heat sinks were examined. After the optimal array heat sink was identified, sensitivity analysis was conducted to identify the design variables associated with optimization. Multidisciplinary design optimization was carried out based on the thermal resistance and mass of the heat sink (as objective functions). 4.1. Thermal analysis of various pin-fin arrays
T ðQ_ heater kacr Aacr acr
Aheatsink
top T acr bottom
t acr
Þ
base
ð2Þ
Fig. 3 shows in-line type, radial-direction staggered type, and theta-direction staggered type pin-fin radial heat sinks with
(a) In-line array
(b) Radial-direction staggered array
(c) Theta-direction staggered array
Tave_heatsink = 49.0°C
Tave_heatsink = 48.7°C
Tave_heatsink = 46.4°C
Fig. 3. Configuration of the heat sink array with a constant fin height for all fins.
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S.-J. Park et al. / International Journal of Heat and Mass Transfer 87 (2015) 184–188
Fig. 4. Average heat transfer coefficient of each pin-fin row. Fig. 6. Pareto fronts of the in-line and the staggered array heat sinks (q_ = 1000 W/ m2).
reference parameters. The radial-direction staggered type is an array in which the middle pin fins move LF toward the base center point. The theta-direction staggered type is an array in which the pin fins of the even numbered rows of in-line array move h/4 counterclockwise along the circumference of the base. For all fins, H was set constant at 40 mm. To compare the thermal performance of various arrays, a heat flux of 1000 W/m2 was adopted for the base surface of the heat sinks. The results showed no improvement in the radial-direction staggered type; however, the heat sink average temperature decreased by 2.6 °C with the theta-direction staggered type array. Fig. 4 describes the average heat transfer coefficient of each pin-fin row and the base surface. The average heat transfer coefficient value corresponded to the average of the heat transfer coefficient of cells’ facets on the pin-fin surfaces.
R have ¼
hfacet dA A
ð3Þ
4.2. Optimization In this research, Morris’s One At a Time (OAT) design method [14], a global sensitivity analysis tool, was applied to identify the design variables that have a strong influence on the heat sink thermal resistance and mass. Numerical efficiency can be improved by decreasing the number of design variables with sensitivity analysis. The sensitivity of the number of fin arrays N, long fin length LL, middle fin length LM, pin-fin length LF, and the length of the space between pin-fins LS were investigated. Consequently, N = X1, LM = X2, and LS = X3, were selected as the design variables. Other heat sink parameters were set to LL = 40 mm, LF = 4 mm, ro = 90 mm, ri = 5 mm, H = 40 mm and t = 3 mm. The object function and constraints of the multidisciplinary design optimization were defined as follows:
Minimize f ðX 1 ; X 2 ; X 3 Þ ¼ x1 RRth ðXðX1 ;1 ;XX2 ;2 ;XX3 Þ3 Þ þ x2 MMðXðX1 ;1 ;XX2 ;2 ;XX3 Þ3 Þ th;ref
In the case of the theta-direction staggered type array, the average heat transfer coefficient of the second row of pin fins was 35% higher than that for the other array types. Fig. 5 shows the air temperature around pin-fins at y = 20 mm. Note that the second row of pin fins comes into contact with the heated air from the first row of pin fins in the in-line and radial-direction staggered arrays. However, if the second row of pin fins were to move h/4 toward the theta direction, then it is possible to transfer heat to the cool air, improving the thermal performance. As a result, the thetadirection staggered type was selected as the heat sink array for optimization analysis.
(a) In-line array
ref
subject to 16 6 X 1 6 32 3 6 X 2 6 45
;
3 6 X3 6 9 Twenty-five experimental points were obtained using the orthogonal array (OA) L25(53), and a response surface was generated with the Kriging model. The optimization progressed based on the response surface using an evolutionary algorithm (EA). The optimum points were gained using the heat flux from a 50 W LED lighting device (q_ = 1000 W/m2) and a heat sink with black anodizing surface treatment.
(b) Radial-direction staggered array
(c) Theta-direction staggered array
Fig. 5. Temperature contour graph of the air at y = 20 mm.
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Fig. 6 shows the Pareto front used to compare the performance of the in-line pin-fin radial heat sink proposed by Jang et al. [4] with the staggered pin-fin radial heat sink. The Pareto front corresponds to a plot of the optimal solutions identified during the multidisciplinary design optimization procedure, in which optimization of one parameter occurs at the expense of the other. For this study, the two parameters considered were the thermal resistance and mass of the heat sink. When the staggered array was adopted, the heat sink’s thermal resistance reduced by a maximum of 10% while maintaining a given mass, i.e. with a fixed number of pin fins; likewise the mass could be reduced by a maximum of 12% while maintaining the thermal resistance. 5. Conclusions In this study, a staggered pin-fin radial heat sink used as a cooling system for LED down light and as a high bay device was optimized. Numerical analysis was conducted, taking into account natural convection and radiation. The maximum difference between the numerical and experimental results was 5%. The possibilities of heat sink performance improvement with in-line, radial-direction staggered, and theta-direction staggered arrays were examined. The theta-direction staggered pin-fin radial heat sink was chosen as the target heat sink configuration for optimization. Three design variables were selected among the five heat sink parameters using sensitivity analysis. The heat sink was optimized using the OA and the EA for Pareto front construction. Compared with the in-line pin-fin array and staggered array, the staggered pin-fin radial heat sink resulted in up to 10% reduction in thermal resistance while maintaining the same mass; likewise, the mass of the heat sink could be reduced by a maximum of 12% while maintaining the thermal resistance. This approach is expected to provide LED lighting options that demonstrate enhanced performance and safety, as well as lower manufacturing cost. 6. Conflict of interest None declared.
Acknowledgement This work was supported by technology upgrade R&D program through the Commercialization Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science, ICT and Future Planning (MSIP) (No. 2013A000021). References [1] N. Narendran, Y. Gu, Life of LED-based white light sources, IEEE/OSA J. Disp. Technol. 1 (2005) 167–170. [2] S.H. Yu, K.S. Lee, S.J. Yook, Natural convection around a radial heat sink, Int. J. Heat Mass Transfer 53 (2010) 2935–2938. [3] S.H. Yu, K.S. Lee, S.J. Yook, Optimum design of a radial heat sink under natural convection, Int. J. Heat Mass Transfer 54 (2011) 2499–2505. [4] 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. [5] P.A. Deshmukh, R.M. Warkhedkar, Thermal performance of elliptical pin fin heat sink under combined natural and forced convection, Exp. Therm. Fluid Sci. 50 (2013) 61–68. [6] R. Bahadur, A. Bar-Cohen, Thermal design and optimization of natural convection polymer pin fin heat sinks, IEEE Trans. Compon. Packag. Technol. 28 (2005) 238–246. [7] C.-T. Chen, M.-H. Chen, W.-T. Horng, Reliability-based design optimization of pin-fin heat sinks using a cell evolution method, Int. J. Heat Mass Transfer 79 (2014) 450–467. [8] W. Yuan, J. Zhao, C.P. Tso, T. Wu, W. Liu, T. Ming, Numerical simulation of the thermal hydraulic performance of a plate pin fin heat sink, Appl. Therm. Eng. 48 (2012) 81–88. [9] 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. [10] K.S. Lee, W.S. Kim, J.M. Si, Optimal shape and arrangement of staggered pins in the channel of a plate heat exchanger, Int. J. Heat Mass Transfer 44 (2001) 3223–3231. [11] 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. [12] M.d.G. Carvalho, T. Farias, P. Fontes, Predicting radiative heat transfer in absorbing, emitting, and scattering media using the discrete transfer method, in: American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, 1991, pp. 17–26. [13] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17. [14] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saiana, S. Tarantola, Global Sensitivity Analysis. The Primer, Wiley, New York, 2008. 38-39.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Optimization of a staggered pin-fin for a radial heat sink under free convection Seung-Jae Park, Daeseok Jang, Se-Jin Yook, Kwan-Soo Lee ⇑ School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 133-791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 20 January 2015 Received in revised form 29 March 2015 Accepted 30 March 2015
Keywords: LED Cooling system Staggered pin-fin array Natural convection Radial heat sink
a b s t r a c t The design of a staggered pin-fin radial heat sink was optimized for light-emitting diode (LED) device cooling. A numerical model for various pin-fin array heat sinks was developed and verified experimentally. The design variables were determined from sensitivity analysis. Multidisciplinary optimization was conducted based on the heat sink thermal resistance and mass, using an evolutionary algorithm. From the analysis results, the staggered pin-fin radial heat sink was identified as the optimal configuration, demonstrating improved thermal performance by up to 10% while maintaining the same mass or reducing the mass by up to 12% for a given thermal resistance. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Light-emitting diodes (LEDs) are an eco-friendly item, offering a long lifetime and high energy conversion efficiency. Thus, much existing lighting has been replaced by LED devices. An abrupt increase in the temperature of the LED chip results in a sharply reduced lifetime and considerably lower light emission efficiency. Studies have shown that 60% of the input power to the LED is converted into thermal energy, as evidenced by the high heat flux [1]. Therefore, it is necessary to cool the LED system sufficiently for stable light emission. The most common passive cooling device for the electrics is a heat sink. Heat sinks are becoming increasingly larger and heavier to accommodate the increasing thermal performance demands of LED devices, at the expense of the lighting device’s safety and manufacturing cost. Thus, technology is needed to improve the performance of the heat sink while reducing its mass. Recently, numerous studies have investigated the cooling effects of radial heat sinks applied to LED down light and high bay devices [2–4]. Yu et al. [2,3] analyzed the thermal performance of various plate-fin radial heat sinks using a numerical method with natural convection considerations; the long fin and middle fin type heat sink was identified as the heat sink with the best thermal performance. Jang et al. [4] applied multidisciplinary design optimization to a pin-fin radial heat sink with thermal ⇑ Corresponding author. Tel.: +82 2 2220 0426; fax: +82 2 2295 9021. E-mail address: [email protected] (K.-S. Lee). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.03.089 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
resistance and mass as the key factors; however, their study targeted radial heat sinks having only an in-line array. Deshmukh et al. [5] and Bahadur et al. [6] examined in-line and staggered pin-fin arrays in a square heat sink set on a vertical wall. Chen et al. [7] and Yuan et al. [8] studied the thermal performance of staggered array heat sinks by forced convection. However, this study focusses on the thermal performance of the heat sink by natural convection. In the present study, a staggered pin-fin radial heat sink mounted on a horizontal wall was considered for LED device cooling. Sensitivity analysis was used to identify the geometric factors that had a significant influence on the heat sink mass and its thermal performance. The heat sink design was further modified via multidisciplinary design optimization.
2. Mathematical modeling 2.1. Numerical model Fig. 1(a) shows the staggered pin-fin radial heat sink, the focus of this study. The heat sink consisted of a circular base with pin-fin arrays positioned periodically along the perimeter of the circular base. Fig. 1(b) and (c) show the computational analysis domain, including the heat sink and surrounding air. To minimize the computing time, only one period domain was analyzed with periodic conditions [9–11]. The following assumptions were adopted to simulate natural convection and radiation heat transfer.
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Nomenclature A g H h k L M N q_ RTH r T t w y
surface area gravity height [mm] heat transfer coefficient [W/m2 °C ] thermal conductivity [W/m °C ] length [mm] mass of heat sink [kg] number of fin array heat flux [W/m2] thermal resistance [°C/W] radius [mm] temperature [°C] thickness of fin [mm] weight factor height from base [mm]
(1) The flow is laminar, steady, and three dimensional. (2) The air properties are constant, with the exception of the density. (3) Air is an ideal gas. (4) The surfaces of the heat sink are gray and diffuse. Radiation heat transfer was calculated using the discrete transfer radiation model (DTRM) [12], given periodic conditions. 2.2. Numerical method The radius and height of the analysis domain ranged from 1.2ro to 1.8ro and 2H to 8H, respectively. Values of 1.5ro and 5H were selected as the domain size in which the average temperature variation of the heat sink was small (1%). A quadrilateral mesh was used; the mesh distance became narrower close to the heat sink surfaces, in the proximity of the predicted existence of the boundary layer. The parameters of the reference heat sink were N = 20, LL = 40 mm, LM = 20 mm, LF = 4 mm, LS = 5 mm, ro = 90 mm,
(a)
Greek symbols e emissivity Subscripts acr acrylic ave average c characteristic facet facet of cell F fin i inner L long fin M middle fin o outer ref reference S space between fins 1 ambient
ri = 5 mm, H = 40 mm, t = 3 mm. The grid dependence was considered by changing the number of grids from 104,946 to 881,725 in the reference model. Grid points totaling 518,312 were set as the reference, given that the average temperature variation of the heat sink was <1%. Numerical analysis was performed using ANSYS FLUENT release 14.5, a commercial computational fluid dynamics (CFD) code based on the finite volume method; the mesh was generated using the ANSYS ICEM release 14.5. The semi-implicit method for pressure linked equations (SIMPLE) algorithm was used to calculate the flow field based on the pressure and velocity. The convective term and energy equation were discretized with the second-order upwind scheme. The convergence criteria for the dependent variables was set to 105. 3. Experiment and validation The heat sink was made from aluminum alloy 6061 (k = 171 W/ m °C) with a black anodizing surface treatment (e = 0.9) for the validation procedure. The parameters of the heat sink were N = 24,
(b)
(c)
Fig. 1. Schematic diagram of a heat sink and computational analysis domain: (a) isometric view (b) top view (c) side view.
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Fig. 2. Experimental setup.
L L = 40 mm, L M = 40 mm, L F = 4 mm, L S = 5 mm, r o = 90 mm, ri = 5 mm, H = 40 mm, t = 3 mm. Fig. 2 shows an experimental setup and location of thermocouples. Two thermocouples were used to measure the ambient temperature. Six thermocouples were installed on the heat sink base, six thermocouples on the upper surface of the acrylic plate, and six thermocouples at the bottom of the acrylic plate. Then, the temperature on each surface was averaged. The steady-state criterion required <0.1 °C variation in the heat sink temperature. The thermal resistance of the heat sink was selected as the performance factor for comparison of the numerical and experimental results. The thermal resistance of the heat sink can be obtained from the following:
RTH ¼
T ave heatsink T 1 q_ Aheatsink base
ð1Þ
where,
q_ ¼
The maximum uncertainty in the heat sink thermal resistance was 4.7% [13]. Seven heat flux conditions in the range of q_ = 400 W/m2 (20 W LED lightings) and q_ = 1000 W/m2 (50 W LED lightings) were selected as experiment points. The maximum difference between the numerical and experimental results was 5%. 4. Results and discussion The reference parameters of various array pin-fin radial heat sinks were examined. After the optimal array heat sink was identified, sensitivity analysis was conducted to identify the design variables associated with optimization. Multidisciplinary design optimization was carried out based on the thermal resistance and mass of the heat sink (as objective functions). 4.1. Thermal analysis of various pin-fin arrays
T ðQ_ heater kacr Aacr acr
Aheatsink
top T acr bottom
t acr
Þ
base
ð2Þ
Fig. 3 shows in-line type, radial-direction staggered type, and theta-direction staggered type pin-fin radial heat sinks with
(a) In-line array
(b) Radial-direction staggered array
(c) Theta-direction staggered array
Tave_heatsink = 49.0°C
Tave_heatsink = 48.7°C
Tave_heatsink = 46.4°C
Fig. 3. Configuration of the heat sink array with a constant fin height for all fins.
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Fig. 4. Average heat transfer coefficient of each pin-fin row. Fig. 6. Pareto fronts of the in-line and the staggered array heat sinks (q_ = 1000 W/ m2).
reference parameters. The radial-direction staggered type is an array in which the middle pin fins move LF toward the base center point. The theta-direction staggered type is an array in which the pin fins of the even numbered rows of in-line array move h/4 counterclockwise along the circumference of the base. For all fins, H was set constant at 40 mm. To compare the thermal performance of various arrays, a heat flux of 1000 W/m2 was adopted for the base surface of the heat sinks. The results showed no improvement in the radial-direction staggered type; however, the heat sink average temperature decreased by 2.6 °C with the theta-direction staggered type array. Fig. 4 describes the average heat transfer coefficient of each pin-fin row and the base surface. The average heat transfer coefficient value corresponded to the average of the heat transfer coefficient of cells’ facets on the pin-fin surfaces.
R have ¼
hfacet dA A
ð3Þ
4.2. Optimization In this research, Morris’s One At a Time (OAT) design method [14], a global sensitivity analysis tool, was applied to identify the design variables that have a strong influence on the heat sink thermal resistance and mass. Numerical efficiency can be improved by decreasing the number of design variables with sensitivity analysis. The sensitivity of the number of fin arrays N, long fin length LL, middle fin length LM, pin-fin length LF, and the length of the space between pin-fins LS were investigated. Consequently, N = X1, LM = X2, and LS = X3, were selected as the design variables. Other heat sink parameters were set to LL = 40 mm, LF = 4 mm, ro = 90 mm, ri = 5 mm, H = 40 mm and t = 3 mm. The object function and constraints of the multidisciplinary design optimization were defined as follows:
Minimize f ðX 1 ; X 2 ; X 3 Þ ¼ x1 RRth ðXðX1 ;1 ;XX2 ;2 ;XX3 Þ3 Þ þ x2 MMðXðX1 ;1 ;XX2 ;2 ;XX3 Þ3 Þ th;ref
In the case of the theta-direction staggered type array, the average heat transfer coefficient of the second row of pin fins was 35% higher than that for the other array types. Fig. 5 shows the air temperature around pin-fins at y = 20 mm. Note that the second row of pin fins comes into contact with the heated air from the first row of pin fins in the in-line and radial-direction staggered arrays. However, if the second row of pin fins were to move h/4 toward the theta direction, then it is possible to transfer heat to the cool air, improving the thermal performance. As a result, the thetadirection staggered type was selected as the heat sink array for optimization analysis.
(a) In-line array
ref
subject to 16 6 X 1 6 32 3 6 X 2 6 45
;
3 6 X3 6 9 Twenty-five experimental points were obtained using the orthogonal array (OA) L25(53), and a response surface was generated with the Kriging model. The optimization progressed based on the response surface using an evolutionary algorithm (EA). The optimum points were gained using the heat flux from a 50 W LED lighting device (q_ = 1000 W/m2) and a heat sink with black anodizing surface treatment.
(b) Radial-direction staggered array
(c) Theta-direction staggered array
Fig. 5. Temperature contour graph of the air at y = 20 mm.
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S.-J. Park et al. / International Journal of Heat and Mass Transfer 87 (2015) 184–188
Fig. 6 shows the Pareto front used to compare the performance of the in-line pin-fin radial heat sink proposed by Jang et al. [4] with the staggered pin-fin radial heat sink. The Pareto front corresponds to a plot of the optimal solutions identified during the multidisciplinary design optimization procedure, in which optimization of one parameter occurs at the expense of the other. For this study, the two parameters considered were the thermal resistance and mass of the heat sink. When the staggered array was adopted, the heat sink’s thermal resistance reduced by a maximum of 10% while maintaining a given mass, i.e. with a fixed number of pin fins; likewise the mass could be reduced by a maximum of 12% while maintaining the thermal resistance. 5. Conclusions In this study, a staggered pin-fin radial heat sink used as a cooling system for LED down light and as a high bay device was optimized. Numerical analysis was conducted, taking into account natural convection and radiation. The maximum difference between the numerical and experimental results was 5%. The possibilities of heat sink performance improvement with in-line, radial-direction staggered, and theta-direction staggered arrays were examined. The theta-direction staggered pin-fin radial heat sink was chosen as the target heat sink configuration for optimization. Three design variables were selected among the five heat sink parameters using sensitivity analysis. The heat sink was optimized using the OA and the EA for Pareto front construction. Compared with the in-line pin-fin array and staggered array, the staggered pin-fin radial heat sink resulted in up to 10% reduction in thermal resistance while maintaining the same mass; likewise, the mass of the heat sink could be reduced by a maximum of 12% while maintaining the thermal resistance. This approach is expected to provide LED lighting options that demonstrate enhanced performance and safety, as well as lower manufacturing cost. 6. Conflict of interest None declared.
Acknowledgement This work was supported by technology upgrade R&D program through the Commercialization Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science, ICT and Future Planning (MSIP) (No. 2013A000021). References [1] N. Narendran, Y. Gu, Life of LED-based white light sources, IEEE/OSA J. Disp. Technol. 1 (2005) 167–170. [2] S.H. Yu, K.S. Lee, S.J. Yook, Natural convection around a radial heat sink, Int. J. Heat Mass Transfer 53 (2010) 2935–2938. [3] S.H. Yu, K.S. Lee, S.J. Yook, Optimum design of a radial heat sink under natural convection, Int. J. Heat Mass Transfer 54 (2011) 2499–2505. [4] 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. [5] P.A. Deshmukh, R.M. Warkhedkar, Thermal performance of elliptical pin fin heat sink under combined natural and forced convection, Exp. Therm. Fluid Sci. 50 (2013) 61–68. [6] R. Bahadur, A. Bar-Cohen, Thermal design and optimization of natural convection polymer pin fin heat sinks, IEEE Trans. Compon. Packag. Technol. 28 (2005) 238–246. [7] C.-T. Chen, M.-H. Chen, W.-T. Horng, Reliability-based design optimization of pin-fin heat sinks using a cell evolution method, Int. J. Heat Mass Transfer 79 (2014) 450–467. [8] W. Yuan, J. Zhao, C.P. Tso, T. Wu, W. Liu, T. Ming, Numerical simulation of the thermal hydraulic performance of a plate pin fin heat sink, Appl. Therm. Eng. 48 (2012) 81–88. [9] 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. [10] K.S. Lee, W.S. Kim, J.M. Si, Optimal shape and arrangement of staggered pins in the channel of a plate heat exchanger, Int. J. Heat Mass Transfer 44 (2001) 3223–3231. [11] 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. [12] M.d.G. Carvalho, T. Farias, P. Fontes, Predicting radiative heat transfer in absorbing, emitting, and scattering media using the discrete transfer method, in: American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, 1991, pp. 17–26. [13] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17. [14] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saiana, S. Tarantola, Global Sensitivity Analysis. The Primer, Wiley, New York, 2008. 38-39.