Design and Optimization of Horizontally-located Plate Fin Heat Sink for High Power LED Street Lamps

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1 Design and Optimization of Horizontally-located Plate Fin Heat Sink for High Power LED Street Lamps Xiaobing Luo 1,2*, Wei Xiong 1, Ting Cheng 1 and Sheng Liu 2, 3 1 School of Energy and Power Engineering, Huazhong University of Science & Technology, Wuhan, Hubei, , China 2 Wuhan National Lab for Optoelectronics, Huazhong University of Science & Technology, Wuhan, Hubei, , China 3 School of Mechanical Engineering, Huazhong University of Science & Technology, Wuhan, Hubei, , China * Corresponding author, Tel: , Fax: , luoxb@mail.hust.edu.cn Abstract When junction temperatures of the light emitting diode (LED) chips packaged inside LED lamps exceed their maximal limits, the optical extraction and the reliability/durability of the LED lamps will be jeopardized, therefore, thermal management is very important for high power LED street lamps. In this research, a design and optimization method of horizontally-located plate fin heat sink was presented to improve the heat dissipation of high power LED street lamps. To prove the feasibility of the present design and optimization method, a 112-W LED street lamp was co-designed by concurrent engineering of optical, thermal, and stress requirements. The engineering prototypes were manufactured and experimentally investigated. The experimental results demonstrated that the maximal heat sink temperature remained to be stable at 45 C when the ambient temperature was 25 C, the maximal temperature difference between steady state temperature and environment temperature for the heat sink was less than 21 C. Comparing the results achieved by the design with the ones by the experiment, it is found that the design and optimization method is feasible and works well for realizing the horizontally-located heat sink of such kind of high power LED street lamp. Nomenclatures A bp exposed base area between two fins, [m 2 ] A c cross section area of the fin Ht, [m 2 ] A fin a single fin surface area, [m 2 ] Gr Grashof number gβθδ3/ν 2 H fin height, [m] L length of array, [m] g acceleration of gravity, m/s 2 h fin average fin heat transfer coefficient, [W/ m 2 K] h bp average heat transfer coefficient of exposed base area, [W/ m 2 K] k fin thermal conductivity of heat sink, [W/mK] k f thermal conductivity of fluid, [W/mK] l characteristic dimension,[m] m fin parameter (hp/ka) 1/2,[m -1 ] n number of plate-fins of the array Nu Nusselt number hδ/ kf P cross section circumference of the fin 2(H+t), [ m 2 ] Pr Prandtl number P fin fin perimeter 2(H+t), [m] expected heat dissipation, [W] Q T Q bp Q fin Q hs Ra s t t b heat dissipation of exposed base area, [W] heat dissipation of single fin, [W] actual heat dissipation of heat sink, [W] Raleigh number GrPr fin spacing, [m] fin thickness, [m] thickness of base plate, [m] Greek Symbols β thermal coefficient of expansion, [1/K] θ excess temperature to the ambient temperature, [K] ν mean kinematic viscosity of fluid, [m 2 /s] ρ fin material density, [kg/m 3 ] δ characteristic dimension, [m] Subscripts b p base plate fin fin f fluid. (air) hs heat sink Amb ambient Introduction In recent years, light emitting diode (LED) has begun to play more and more important role in many applications including back lighting for cell phones, LCD displays, interior and exterior automotive lighting such as headlights, large signs and displays, signals and illumination. [1] LED will soon be used in general illumination because of its distinctive advantages including high efficiency, good reliability, long life, variable colors and low power consumption. An expectation about high power LED is that it will be the dominant lighting technology by 2025[2]. In China, with the push of the government for more energy saving, the LED may be used earlier than this time. The estimation by Chinese authorities is that if LED dominates general lighting market in 2010, one third of the present lighting power consumption could be saved. One typical general lighting product of LED is LED street lamp, which is emerging in market, in particular in China. For modern LED street lamps, both optical extraction and thermal management are two critical factors for their high performance. In general, most of the electronic power of street lamp is converted into heat, which greatly reduces the chips luminosity. In addition, the high junction temperature of LED chips in the lamp will shift the peak wavelength, which will change the color of light. Narendran and Gu have experimentally demonstrated that the life of LEDs decreases with the increase of the junction temperature in an /09/$ IEEE Electronic Components and Technology Conference

2 exponential manner.[3] Therefore, a low operation temperature is essential for LED chips in the LED street lamp. Since the market demands that LED street lamp have high power and small size, there is a contradiction between the power density and the operation temperature, especially when applications require LED street lamp operate at high power to obtain the desired brightness. [4] In terms of thermal management of LED street lamps, fin heat sinks are widely used because of their good reliability and low cost. There are few reports on the fin heat sink design for LEDs, but lots of professonals have done plenty of research on the fin heat sink for other electronic cooling. Typically, Culham and Muzychka developed a procedure which presented optimization of fin heat sink design parameters based on a minimization of the entropy generation associated with heat transfer and fluid friction. [5] All relevant design parameters for plate fin heat sinks, including geometric parameters, heat dissipation, material properties and flow conditions could be simultaneously optimized to characterize a heat sink that minimizes entropy generation and in turn results in a minimum operation temperature. Culham and Khan developed an analytical model to calculate the best possible design parameters for plate fin heat sinks using an entropy generation minimization procedure with constrained variable optimization. [6] The method characterized the contribution to entropy production of all relevant thermal resistances in the path between source and sink as well as the contribution to viscous dissipation associated with fluid flow on the boundaries of the heat sink. Teertstra et al. proposed an analytical model to predict the average heat transfer rate for forced convection, air cooled plate fin heat sinks for use in the design and selection of heat sinks for electronics applications. [7] By using a composite solution based on the limiting cases of fully-developed and developing flow between isothermal parallel plates, the average Nusselt number could be calculated as a function of the heat sink geometry and fluid velocity. Lee obtained an analytical simulation model to predict and optimize the thermal performance of bidirectional fin heat sinks in a partially confined configuration. [8] Sample calculations were carried out, and parametric plots were provided, the results illustrated the effect of various design parameters on the performance of a heat sink. Azar et al. developed a narrow channel heat sink, which was a departure from the micro channel heat sink, and could be used for air cooling of high power components. [9] In the above references, most of them have focused on the vertically-located plate fin heat sink design, however, in LED street lamp, the heat sink base should be located in the horizontal direction. For horizontally-located heat sink, the design and optimization have more difficulty because the gravity direction is along the fin height. In this case, the heat transfer coefficient between the fins is difficult to determine. Such a situation brings much trouble for the LED engineers, especially when they design LED lamps. A simple engineering solution to horizontally-located heat sinks is strongly demanded for LED industry. In this paper, a new design method for horizontallylocated plate fin heat sinks was presented and the corresponding code was developed. Fin height, fin thickness and fin spacing of horizontal plate fin heat sinks were designed and optimized with the aim of maximal heat dissipation and least material. The method is based on the empirical equations and easy for engineers. Based on the method, heat sink for a 112 watts LED street lamp was designed and manufactured, the experimental studies on the 112 watts street lamp were conducted. The comparison between experiment and design demonstrates that the method works well for horizontally-located fin heat sinks. Design and Optimization of Horizontally-located Fin Heat Sink 1. Design Model For the heat sink of LED street lamp, it is usually designed as horizontally-located plate fin heat sink, as shown in Figure.1. Although the heat transfer coefficient is comparatively low in natural convection (usually less than 10W/Km2), the plate-fin natural convection heat sinks offer distinctive advantages in cost and reliability. (a) (c) Fig.1. Horizontally-located rectangular plate fin heat sink (a) horizontal configuration; (b) side elevation; and (c) Top view. In the design and optimization of the horizontally-located plate fin heat sinks, heat transfer coefficient is a key factor. However, the averaging heat transfer coefficient is associated with the fin dimensions, which are the optimization factors and they are strongly coupled. In addition, due to the overlapping of the boundary layers between the adjacent fins, it is difficult to solve boundary layer equations, correspondingly, it is very difficult to calculate the fin heat transfer coefficient during computation process. For the application of horizontally-located plate fin heat sink in LED, heat is generated by the LED chips and then conducted through aluminum alloy base board and finally dissipated to the surroundings by convection. To simplify the heat transfer and optimize the heat sink of high power LED street lamp, there are certain assumptions: 1)The material is (b) Electronic Components and Technology Conference

3 isotropic; and 2)The spreading and contact resistance is neglected in heat sink. 2. Design and Optimization Method Figure 1 shows the heat sink dimensions and their indications. The total heat Q hs that a heat sink can dissipate is expressed by the formula: Q hs = Q bp +n Q fin (1) where Q bp is the heat that is dissipated by the exposed base of the heat sink and is defined by formula (2), Q fin is the heat that is dissipated by fins of the heat sink and is defined by formula (3): Qbp= h bp (n-1) θ bp A bp (2) where h bp is the average heat transfer coefficient of the exposed base area, n is the number of plate-fins of the array, θ bp is the excess temperature from the heat sink base to the ambient temperature, A bp is the surface area of the exposed base and could be defined as: A bp =s L (3) where s is the fin spacing, L is the fin thickness. Q fin =h fin A fin θ bp (4) where h fin is the averaging heat transfer coefficient of the heat sink, A fin is the surface area of a single fin and could be defined as: A fin =2(H t+l H+L t/2) (5) where H is the fin height, and t is the fin thickness. For most of the applications, especially for the heat sink design for LED street lamp, the heat transfer and the approximate temperature difference between the heat sink and the environment are given, the heat dissipation are designed to meet the amount of heat dissipation and the heat sink mass. Since most plate fin heat sinks are produced with extrusion aluminum alloys [6], with considerations of manufacturability and strength, the ranges of fin parameters should be as follows; 1) fin thickness is between 1mm to 3mm; 2) fin spacing is between 1mm to 15mm; and 3) fin height is between 25mm to 50mm. In order to obtain the averaged heat transfer coefficient of the heat sink, the total heat dissipation area can be divided into two parts. One is from exposed base area and the other is from fin array. A. Heat Dissipation from Exposed Base Area 1)When the ratio of fin spacing to fin height is less than 0.28, the flow inside the fins is enclosed space natural convection. In this case, the characteristic dimension is the height of enclosed space. If the value in the square brackets of Eq. (8) is negative, Nusselt number of base plate Nu bp is replaced with 1. Eq. (6) to Eq. (7) are available when the Raleigh number of base plate Rabp <4 10 6, Grashof number of base plate can be defined as: Gr bp =g B θ bp H 3 2 /ν bp (6) where ν bp is the mean kinematic viscosity of air which is around the base plate. And then Ra bp = Gr bp Pr bp (7) where Pr bp is Prandtl number of air which is around the base plate. The Nusselt number of base plate Nu bp can be given by [10] Nu bp = [1-1708/Ra bp ]+[(Ra bp /5830) 1/3-1] (8) 2)When the ratio of fin spacing to fin height is more than 0.28, large space natural convection is assumed[.11] In this case, characteristic dimension is (s+l)/2. Then: Grbp=g β θ bp ((s+l)/2) 3 2 /ν bp (9) where g is the acceleration of gravity, β is the thermal coefficient of expansion. Then Ra bp is obtained by the Eq. (7) If Ra bp <2 10 4,then Nu bp =1 (10) If <Ra bp <8 10 6,then 1/4 Nu bp =0.54 Ra bp (11) If <Ra bp <10 11, then 1/3 Nu bp =0.15 Ra bp (12) And we can obtain different Nu bp values according to the different value of Ra bp. Then the averaged heat transfer coefficient of base plate h bp could be written as, h bp = Nu bp k bp / l bp (13) where l bp is the characteristic dimension of the base plate. B. Heat Dissipation from Fin Array 1)For enclosed space nature convection, the problem is to determine the characteristic dimension. Owing to the different temperature of the fin surface, it is necessary to replace excess temperature with the heat flux to calculate the Grashof number of the fin Gr fin, so the place with the lowest temperature should be the center of the space between the two fins. In other words, the characteristic dimension is half of the fin space s/2. Then Gr fin =g β (Q fin /(2 H L)) (s/2) 4 /( k f ν 2 f ) (14) where k f is the thermal conductivity of air around the fin, ν f is the mean kinematic viscosity of air around the fin. Therefore, the heat dissipation from the single fin is given by Q fin =k fin A c θ bp m tanh(m H) (15) where k fin is the thermal conductivity of fin, A c is the cross section area of the fin and can be defined as A c =H t, m is the fin parameter and can be written as m = ( h fin P/ k fin A c ) 1/2, hfin is the averaged heat transfer coefficient of the fin, P is the cross section circumference of the fin which can be written as P = 2(H+t), then Raleigh number of the fin Ra fin can be defined as, Ra fin = Gr fin Pr fin (16) where Pr fin is the Prandtl number of the air which is around the fin. If Ra fin <10 4, the heat transfer in the vertical enclosed space is pure conduction, then the Nusselt number of the fin Nu fin can be defined as: Nu fin =1 (17) If 10 4 <Ra fin <10 7, then Nu fin =0.42 Ra fin 1/4 Pr fin (H/(s/2)) -0.3 (18) Electronic Components and Technology Conference

4 If 10 7 <Ra fin <10 9, then Nu fin =0.46 Ra 1/3 fin [13] (19) 2)When the ratio of fin spacing to fin height is more than 0.28, it is large space natural convection. The characteristic dimension is the fin height H. Then Gr fin =g β (Q fin /(2 H L)) H 4 /( k f ν 2 f ) (20) and Ra fin is obtained by the Eq. (16) then [14] 1/5 Nu fin =0.6 Ra fin (21) We can obtain a different Nu fin value according to the different value of Ra fin. Then the averaged heat transfer coefficient of the fin h fin could be written as. h fin = Nu fin k fin / l fin (22) where l fin is the characteristic dimension of the fin. The fin surface is not isothermal, but when heat sink is in steady state, in other words, the temperature distribution of fin surface never changes, it means that heat through each fin surface is constant. Therefore, the heat dissipation from single fin is a function of averaged fin heat transfer coefficient, their relation is provided by, Q fin =f (h fin ) (23) where its inverse function is, h fin =f -1(Q fin ) (24) then g(h)=h-h fin (25) where h is obtained through Newton iteration, φ(x)=x- f(x)/ f (x) (26) Then iteration convergence is used to obtain the value of h fin. C. Optimization and Code Realization When other parameters have been determined, the geometry of the heat sink need to be optimized including fin height H, fin thickness t and fin spacing s. Because of the function about heat transfer coefficient contains tanh, the relation turns into transcendental equation. After the partial difference on H, t and s, it is rather difficult to seek the best solution using Lagrange multiplier due to complex expression. Therefore, it is necessary to dispose the points discontinuously, and establish a matrix to store the values of these points and heat transfer coefficient by iteration structure of program. We choose optimization fin geometry according to least-material and least-volume criteria based on the data given by the Matlab program. Flowchart for plate-fin optimization is shown in Figure 2. Design and Optimization of A Heat Sink for 112-W LED Street Lamp For the heat sink of the 112-W LED street lamp, parameters to be evaluated are given below. Temperature difference between the ambient and the surface of the base plate is 18. The base plate dimensions are as follows, the thickness is 3mm, the length and width is 530mm and 350mm respectively. The material density of the base plate is 2700 kg/m3,and its thermal conductivity is 160W/m-K. The air properties are taken from reference [15], the gravitation acceleration is 9.8m/s 2. Fig.2 Plate-Fin Optimization Flowchart. Fig.3. Schematic diagram of the 112 watts LED street lamp By using the aforementioned design and optimization, the final 112W LED street lamp heat sink was designed and shown in Figure 3. Here the fin height H is 17mm, fin thickness t is 2mm and fin spacing s is 5mm. For the 112 watts LED street lamp shown in Figure 3, one hundred and twelve high power LED modules are bonded onto the heat sink. They are distributed on the heat sink base in seven rows. All the LED modules are the same, their input powers are 1 watt and the total input power for this lamp is 112 watts. When the electronic power is supplied, LEDs generate light and heat. The heat is dissipated out into the environment through the aluminum base and fins on the base. Temperature Test of the 112-W LED Street Lamp 1. Experimental Instruments To prove the correctness of the heat sink design, the temperature distributions of the aluminum base and the fins of the 112 watts LED street lamp were measured by thermocouples in the experiments. Figure 4 shows the experimental setup. The orientation of the heat sink and the system were set up as the application conditions. The fin base was placed blow, the fin tips were on the top. The tests were Electronic Components and Technology Conference

5 conducted at a natural environment. For 112 watts LED street lamp tests, the ambient temperature was about 25 C. Several thermocouples were placed at different positions of the aluminum base and fins. The temperature data obtained by the thermocouples was transferred to the data acquisition system and displayed on the PC monitor. The model of the data acquisition system in the experiment was Keithley 2700 multimeter and control unit In the experiments, the temperature was the main parameter for system evaluation, and it was directly measured by thermocouples. Since there were no other indirectly measured parameters, the errors associated with this experiment mainly included the measurement error of the thermocouples and the reading error of the digital multimeter. Standard T-type thermocouples (Cu-CuNi) were used in the experiments. During the temperature range from -30 C to 150 C, their measurement error was about 0.2 C. The data acquisition system had a reading error of 1 C since the cold junctions of the thermocouples used the default setup supplied by the system, not the ice bath with constant 0 C. Therefore, the total error of the temperature measurement for the experiments was about 1.2 C. ambient temperature was 25 C, the maximal temperature difference between steady heat sink temperature and environment temperature was 20 C, the minimum temperature difference is 17 C. Comparing the results achieved by the design with the ones by the experiment, it is found that the design and optimization method is feasible and works well for realizing the heat sink of such kind of high power LED street lamp. Temperature/ CH1 CH2 CH3 CH4 CH Time/Min. 22 Fig.5 Variation of the heat sink temperature with the operation time for 112 watts street lamp.. Fig.4. Experimental setup. 2. Experimental Results and Analysis Figure 5 shows the variation of the heat sink temperature with the operation time for the 112 watts LED street lamp. In the experiments, as described above, the room temperature was about 25 C and there were twenty thermocouples to measure the temperatures at different positions, much data was obtained and it was difficult to display them in one figure synchronously. Thus the temperatures obtained by five thermocouples numbered as 1, 2, 3, 4 and 5 were used for description. In Figure 5, it can be seen that the fin temperature increased as a function of time, initially, the fin temperature was nearly the same as the room temperature. After the lamp was turned on, its temperature increased. Several hours later, it reached steady state situation and the maximal temperature remained to be stable to be nearly 45 C, the minimum temperature remained to be stable to be nearly 42 C. It is also noted from Figure 5 that the temperatures achieved by all thermocouples showed the similar trend. 3. Comparison between Experimental Results and Design Expectation The averaged temperature difference in the design was 18 C, the experimental results demonstrated that the maximal heat sink temperature remained to be stable at 45 C when the Summary It is difficult to find an engineering solution to design and optimize the horizontally-located plate fin heat sink. In this paper, a simple method was used to achieve the target. By using the present method, a horizontally-located heat sink was designed and optimized for a 112-W high power LED street lamp. The tested results demonstrate that the temperature difference agrees well with the designed value, it proves that the present method can be used for the engineering design of horizontally-located plate fin heat sink. This heat sink design method can be used for not only LEDs, but also the other electronic cooling systems. Acknowledgments This work was supported by the grants from the National Basic Research Development Program of China under Ministry of Science and Technology (973 Program) (No. 2009CB320203) and the key program from the National Natural Science Foundation of China (No ). References 1. M. Alan, Solid state lighting-a world of expanding opportunities at LED 2002, III-Vs Review, Vol 16 (1)( 2003), pp M. Alan, Lighting: The progress & promise of LEDs, III-Vs review, Vol 17 (4)( 2004), pp N. Narendran, Y. M. Gu, Life of LED-Based white light sources, IEEE Journal of Display Technology, Vol 1 (1)( 2005), pp Electronic Components and Technology Conference

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