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Optimum design of a radial heat sink with a fin-height profile for high-power LED lighting applications
Applied Energy 116 (2014) 260–268
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Optimum design of a radial heat sink with a fin-height profile for high-power LED lighting applications 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
h i g h l i g h t s A radial heat sink was designed for high-power LED lighting applications. Fin-height profiles reflecting the chimney-flow characteristics of a radial heat sink were proposed. Multi-disciplinary optimization was carried out to simultaneously minimize the thermal resistance and mass. The cooling performance of the optimized design showed improvement without additional mass increment.
a r t i c l e
i n f o
Article history: Received 26 April 2013 Received in revised form 11 November 2013 Accepted 23 November 2013 Available online 20 December 2013 Keywords: LED lighting Electronic cooling Natural convection Heat sink Optimization Fin-height profile
a b s t r a c t Light-emitting diode (LED) lighting offers greater energy efficiency than conventional lighting. However, if the heat from the LEDs is not properly dissipated, the lifespan and luminous efficiency are diminished. In the present study, a heat sink of LED lighting was optimized with respect to its fin-height profile to obtain reliable cooling performance for high-power LED lighting applications. Natural convection and radiation heat transfer were taken into consideration and an experiment was conducted to validate the numerical model. Fin-height profiles reflecting a three-dimensional chimney-flow pattern were proposed. The outermost fin height, the difference between fin heights, and the number of fin arrays were adopted as design variables via sensitivity analysis, and the heat sink configuration was optimized in three dimensions. Optimization was conducted to simultaneously minimize the thermal resistance and mass. The result was compared with the Pareto fronts of a plate-fin heat sink examined in a previous study. The cooling performance of the optimized design showed an improvement of more than 45% while preserving a mass similar to that of the plate-fin heat sink. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Light-emitting diode (LED) lighting offers the advantages of a longer lifespan and greater energy efficiency than conventional lighting. LED lighting uses 75% less energy than incandescent or fluorescent lighting. Due to its greater energy efficiency, the market share of LED lighting is growing rapidly, and the market domain now includes high-power LED products. However, if high power is applied to LEDs to produce more light output, the amount of heat generated by the LEDs is greatly increased, which reduces both the lifespan and the luminous efficiency. Therefore, a technology for properly dissipating the heat from inside the LED package to the surroundings is as important as the electronic and optical characteristics. The LED lighting system shown Fig. 1 is composed of an LED chip, epoxy, a slug, a printed circuit board, and a heat sink. This study is confined to the heat sink, which can improve
⇑ Corresponding author. Tel.: +82 2 2220 0426; fax: +82 2 2295 9021. E-mail address: [email protected] (K.-S. Lee). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.11.063
its cooling performance via shape alteration. Optimization of the radial heat sinks used in LED lighting applications is necessary to obtain reliable cooling performance in high-power LED products. Numerous researchers have analyzed natural convection heat sinks with diverse fin configurations [1–8]. Elshafei [7] examined the heat transfer characteristics of hollow/perforated round pin– fin heat sink, and compared the results with those obtained for solid round pin–fin heat sink. Sertkaya et al. [8] investigated the orientation effect of a pin–fin heat sink under natural convection, and reported that the cooling performance with an upward-facing orientation was outstanding. However, most of these researches considered rectangular heat sink, which is ineffective for cooling in round LED lighting applications. Accordingly, diverse types of radial heat sinks have recently been proposed and optimized [9–12]. Multidisciplinary optimization is the primary method for improving heat sink performance because both mass and cooling performance are considered in the performance evaluation. Jang et al. [12] compared various pin–fin radial heat sinks to achieve a lighter heat sink with a cooling performance similar to that of a plate-fin
D. Jang et al. / Applied Energy 116 (2014) 260–268
261
Nomenclature A F H I k L ~ L M _ m N n P q_ RTH r ~ s T t
v
heat transfer area (mm2) body force vector per unit volume height (mm) radiation intensity thermal conductivity (W/m K) length (mm) periodic length vector mass of heat sink (kg) mass flow rate (kg/s) number normal vector pressure (Pa) heat flux (W/m2) thermal resistance (°C/W) radius (mm) ray vector temperature (K) fin thickness (mm) velocity vector (m/s)
r q h
e x X
standard deviation of elementary effects distribution density (kg/m3) angle, as in Fig. 3(b) (°) emissivity weight factor hemispherical solid angle (°)
Subscripts A array acr acrylic avg average D difference between fin heights f fin i inner L long fin M middle fin O outermost fin height o outer s space between fins in the radial direction w wall 1 ambient
Greek symbols l dynamic viscosity (N s/m2) ⁄ l mean of elementary effects distribution
heat sink reported in previous studies [9–11]. Using this approach, they were able to reduce the mass by more than 30% while preserving a cooling performance similar to that of the optimum plate-fin heat sink [10]. However, these studies were based on the assumption of uniform fin height, and hence their results are unsuitable for radial heat sinks with chimney-flow characteristics because non-uniform heat transfer occurs along the radial direction in a chimney flow. Therefore, it is necessary to determine fin-height profiles that are appropriate for chimney-flow characteristics. Several recent studies have focused on the effects of various fin-height profiles. Fabbri [13] studied the influence of fin-height profiles with polynomial forms and obtained an optimum profile for every polynomial degree by using a genetic algorithm. Kanyakam and Bureeret [14] studied the forced convection of splayed pin–fin heat sinks by varying the fin height and azimuthal angle with the heat sink base as the center. They concluded that a splayed heat sink offers outstanding cooling performance compared to a straight pin–fin heat sink, and Pareto fronts relating the cooling performance and the fan pumping power were obtained via multi-objective optimization. Shah et al. [15] numerically analyzed the performance of a heat sink with an impingement cooling system. The effect of the fin-height profile on the cooling performance (especially near the center of the heat sink) was analyzed. They found that reduction of fin volume around
the central region reduced the pressure drop in that region, and improved the flow penetration to the outer region. As a result, a fin-height profile with reduced fin volume in the central region enhanced both the thermal and hydraulic performance. Shah et al. [16] extended their previous work and optimized the configuration of the heat sink by investigating the removal of fin volume at the end fins, varying the number of fins, and reducing the size of the fan. Yang and Peng [17] studied impinging jets on pin–fin heat sinks with non-uniform fin heights. They found that the heat sink temperature could be decreased by increasing the fin height around the central region of the heat sink. However, there is a limit to how much the fin height around the central region of a heat sink can be increased because flow penetration into that region is weakened by the resulting increased flow resistance. In addition, if the fins around the central region are too tall in comparison to the other fins, heat transfer in the outer region will be poor and the overall thermal performance will be degraded. Bello-Ochende et al. [18] developed an optimized pin–fin heat sink design for maximizing forced convection with limited mass and found that cooling performance was maximized when the fin diameter and height were non-uniform. However, these studies [13–18] were concerned with the forced convection of heat sinks with rectangular bases, and the optimum fin-height profile differed with respect to the cooling method or shape. Therefore, a research of radial heat
Ambient air Heat sink
Printed circuit board
PCB
Slug Epoxy LED chip Fig. 1. Diagram of a typical LED lighting application.
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sink under natural convection with a non-uniform fin-height profile is still needed. In previous studies of radial heat sinks [10– 12], the thermo-flow characteristics around the heat sink were analyzed and geometric optimization was carried out. The temperature contours of various fin arrays on a horizontal plane were also compared, and the fin lengths and number of fin arrays were optimized to retard the growth of a fully developed thermal boundary layer. However, optimization results based on two-dimensional thermo-flow characteristics on a horizontal plane are not appropriate for the three-dimensional flow of a radial heat sink. To reflect chimney-flow characteristics, an optimum design based on the overall three-dimensional flow is necessary. In the present research, a radial heat sink with pin fins is optimized with respect to the fin-height profile. Fin-height profiles are proposed that can improve cooling performance without increasing the mass beyond that of a comparable plate-fin heat sink. The cooling performances of three profiles (the LM type, a pin–fin array with the tallest fins in the inner region, and a pin–fin array with the tallest fins in the outer region) with equal masses are analyzed and a reference profile is determined. Finally, a heat sink is designed using multi-objective optimization considering both mass and thermal resistance to provide improved cooling performance with a mass equivalent to that in previous studies.
(a)
(a)
LD LO
Lf
(b)
Ls LM
t
ri
LL
θ
ro g gravity
Fig. 3. Computational domain. (a) Isometric view of the computational domain. (b) Top view of the computational domain.
2. Mathematical modeling
(b)
2.1. Numerical model
g gravity
(c)
g
The LM type of heat sink addressed in previous studies [9–11], a pin–fin array with the tallest fins in the inner region (Type 1), and a pin–fin array with the tallest fins in the outer region (Type 2) were compared (see Fig. 2). The fins were circularly arranged at consistent intervals. The heat sink base was oriented horizontally, whereas the fins were arranged vertically. The fin array was duplicated around the circumference of the base plate. Due to the computational cost involved, only a single fin array was used for the computational domain, as shown in Fig. 3. The numerical analysis was based on the following assumptions. (1) The flow is laminar, steady, and three dimensional. (2) The density of air is computed using the ideal gas law. (3) Except for the density of air, the fluid properties are constant. (4) The heat sink surface is gray and diffuse.
gravity 2.2. Governing equations and boundary conditions
Fig. 2. Test heat sinks. (a) LM plate-fin type. (b) Pin–fin array with the tallest fins on the inside (Type 1). (c) Pin–fin array with the tallest fins on the outside (Type 2).
Table 1 enumerates the governing equations and boundary conditions. Radiation heat transfer was computed via the discrete transfer radiation model [19,20], which can support periodic conditions.
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D. Jang et al. / Applied Energy 116 (2014) 260–268 Table 1 Governing equations and boundary conditions for the computational domain. Wall
Continuity equation
r ðqv Þ ¼ 0
Momentum equations
Solid domain Interface between fluid and solid domain
2
Energy equation
¼ rP þ lr v þ F (for z-direction F = qg)
DP qC p DT Dt ¼ r ðkrTÞ þ Dt
r i Þ ¼ ui ð~ ri þ ~ LÞ, ui ð~
Tð~ r i Þ ¼ Tð~ ri þ ~ LÞ
q
Periodic face Fluid domain
Dv Dt
~
rpðxi Þ ¼ g j~LLj þ rp ðxi Þ Outer face
Pressure inlet/Pressure outlet condition
Heat sink base
ui ¼ 0
Symmetric face
ui ¼ 0
Interface
ui = 0
T inlet ¼ T outlet; back flow ¼ T 1 s _ ks @T @n heat sink base ¼ q @T s ¼0 @n sectional wall
f kf @T @n
T f;wall ¼ T s; wall ;
s þ q_ out ¼ ks @T þ q_ in @n wall ! R _qin ¼ ~s~n>0 Iin~ ~ s ndX; wall
q_ out ¼ ð1 ew Þqin þ ew rT 4w
2.3. Numerical procedure The numerical analysis was carried out using the finite volume method with Fluent V6.3, a commercial computational fluid dynamics software package. The SIMPLE algorithm was adopted to couple the velocity and pressure fields. To enhance the accuracy of the result, a second-order upwind scheme was employed to the convection terms of the governing equations. The result was determined to have converged when the relative error of all dependent variables between two successive iterations was less than 105. Taking into account both the convergence of the heat sink temperature and the computational time, the height of the domain changed from two to ten times the height of the tallest fin, and the radius of the domain changed from 1.3ro to 1.6ro. When the domain height was increased beyond five times the height of the
tallest fin, and the radius beyond 1.5 ro, the temperature of the heat sink changed by less than 0.5%; these results were used to set the size of the computational domain. A dense grid was generated in the region where a boundary layer developed near the heat sink. Grid dependence testing took place by increasing the number of grid points from 60,000 to 700,000, with 519,375 grid points being selected as a reference from our sensitivity analysis. The change in heat sink temperature with additional grid points was less than 0.5%. ICEM CFD 14.5 was used to generate the mesh, and the grid system was shown in Fig. 4.
(a)
Heat sink
Insulator (polystyrene) T3 Aluminum plate
T2
Film heater
T1 Acrylic plate
(b) Heat sink
Thermocouple
Fig. 4. Computational grid system. (a) Top view. (b) Side view.
Insulator (polystyrene)
Fig. 5. Experimental setup. (a) Illustration for the experimental setup. (b) Photo for the experimental setup.
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3. Experiments and validation The LM type of heat sink [10], a pin–fin array with the tallest fins in the inner region (Type 1), and a pin–fin array with the tallest fins in the outer region (Type 2) were evaluated to validate the numerical model. The heat sinks were made of black anodized aluminum (Al6061, e = 0.8). The parameters for the LM type were NA = 20, LL = 50 mm, LM = 20 mm, ro = 75 mm, ri = 10 mm, t = 2 mm, and H = 21.3 mm. The parameters for Type 1 were NA = 20, LL = 45 mm, LM = 25 mm, Lf = 5 mm, LO = 24.3 mm, LD = 8 mm, Ls = 5 mm, ro = 75 mm, ri = 10 mm, and t = 2 mm. For Type 2, LO = 50.3 mm; the other parameters were the same as those of Type 1. As shown in Fig. 5, the experimental setup comprised a heat sink, a film heater (Kapton-coated stainless steel, 25 lm), an insulator, a data acquisition device (NI SCXI-1303, 1100, 1600), type-T thermocouples (gauge 36), a power supply, a personal computer, and a wattmeter. Thin aluminum plates, 1 mm thick, were placed beneath and on top the film heater to apply a uniform heat flux. Thermal grease was employed to decrease the thermal contact resistance between the heat sink and the film heater. An acrylic plate, 5 mm thick, was inserted beneath the heater and used to evaluate the heat loss from the bottom of the heater as follows:
Q_ heat sink ¼ Q_ total Q_ heat loss
ð1Þ
ðT 1 T 2 Þ Q_ heat loss ¼ kacr Aacr tacr
ð2Þ
To minimize the heat loss through the sides, the section of film heater was enclosed by an insulator. The heat sink temperature was measured with eight thermocouples, and the ambient air temperature was measured with two thermocouples. Constant current and voltage were applied to the film heater during the experiment. When the temperature change was less than 0.1 °C over 30 min, the heat sink temperature was assumed to have reached a steady state, and the thermal performance was calculated. Fig. 6 compares the experimental and numerical results. The thermal resistance of the heat sink was adopted as the performance index, and defined by
RTH
T avg;heat sink T 1 ¼ p r2o r2i q_ heat sink
ð3Þ
3 Experiment Numerical Model
RTH (°C/W)
LM type Type 1 Type 2
2
1
0
400
800
1200
.
q (W/m2) Fig. 6. Comparison of the computational and experimental results (ro = 0.075 m, e = 0.8).
An uncertainty analysis was carried out as part of the experiment. The maximum uncertainty was estimated to be 2.7%. The numerical results agreed well with the results of experiment with an error of less than 6.8%. Accordingly, we validated that the numerical model explained in Section 2 could correctly simulate natural convection and radiation heat transfer around a heat sink with a specific fin-height profile. 4. Results and discussion Pin–fin heat sinks with diverse fin-height profiles were compared to the plate-fin heat sink suggested by Yu et al. [10] in terms of cooling performance and mass. The elementary effects method was utilized for the sensitivity analysis from which the design variables were determined. Finally, multi-objective optimization was conducted considering both mass and cooling performance, and application of the optimized design to high-power LED products was examined. 4.1. Thermo-flow characteristics around a plate-fin radial heat sink Fig. 7(a) illustrates the temperature contours around a radial heat sink with the LM-type design (NA = 20, LL = 50 mm, LM = 30 mm, ro = 75 mm, ri = 10 mm, t = 2 mm, H = 21.3 mm, and e = 0.7, where NA is the number of fin arrays, LL is the long fin length, and LM is the middle fin length). The reference heat flux was 700 W/m2, which is equivalent to the power consumption of a typical LED down light (20 W). To investigate the heat transfer characteristics, the overall flow characteristics were examined from two perspectives. The right-hand side of Fig. 7(a) shows the temperature contours for the first perspective, lying on a horizontal plane 10 mm above the heat sink base. The spaces between the plate fins of the heat sink are comparatively wide in the outer region, and become narrower in the inner region. The more the domain of interest penetrates into the inner region, the narrower these spaces become. In the inner region, the thermal boundary layers between the fins overlapped and become fully developed, leading to a decrease of the heat transfer coefficient. The left-hand side of Fig. 7(a) shows the temperature contours for the second perspective, lying on a vertical plane (h = 9°). The incoming cool air is warmed by the heat sink and rises. The overall flow typically has a chimney-like pattern. Most of the heat transfer occurs in the outer region and little heat transfer occurs in the central region. Most of the mass flow does not reach the inner fins because the inflow rises in accordance with the chimney pattern. Therefore, the mass flow rate for cooling decreases in the inner region, resulting in non-uniform heat transfer. In previous studies that only considered the thermo-flow characteristics on a horizontal plane, the fin lengths and the number of fin arrays that influence the thermal boundary layer development on the horizontal plane were adopted as design variables for optimum design. However, design variables pertaining exclusively to two-dimensional thermo-flow characteristics are inappropriate for three-dimensional radial heat sink flow analysis because nonuniform heat transfer with respect to the radial direction must be reflected in the design procedure. Taking into account the chimney pattern of flow and the fully developed thermal boundary layer in the inner region, the uniform fin height assumed in previous studies is unsuitable for analyzing a non-uniform heat transfer distribution. 4.2. Non-uniform fin-height profiles To investigate the three-dimensional flow characteristics of a radial heat sink, the effects of diverse fin-height profiles on the
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(a)
53.64 (oC) 51.27 48.91 46.55 44.18 41.82 39.46 37.09 34.73 32.36 30.00
(b)
θ = 9°
H = 10 mm
θ = 9°
H = 10 mm
θ = 9°
H = 10 mm
53.64 (oC) 51.27 48.91 46.55 44.18 41.82 39.46 37.09 34.73 32.36 30.00
(c)
53.64 (oC) 51.27 48.91 46.55 44.18 41.82 39.46 37.09 34.73 32.36 30.00
Fig. 7. Temperature contours at h = 9° and H = 10 mm (ro = 0.075 m, q_ ¼ 700 W=m2 , T1 = 30 °C, e = 0.7). (a) LM plate-fin model. (b) Pin–fin array with the tallest fins on the inside (Type 1). (c) Pin–fin array with the tallest fins on the outside (Type 2).
heat sink mass and temperature were examined. The LM type of heat sink, a pin–fin array with the tallest fins in the inner region (Type 1), and a pin–fin array with the tallest fins in the outer region Table 2 Comparison of various fin height profiles (ro = 0 075 m, q_ ¼ 700 W=m2 , T1 = 30 °C, e = 0.7). Model
A (mm2)
LO (mm)
LD (mm)
_ air (105 kg/s) m
Tavg (°C)
LM plate-fin Type 1 Type 2
4499 5000 5000
21.3 22 46
0 15 15
3.04 4.39 6.4
53.12 48.86 44.80
(Type 2) were compared. In general, cooling performance improves with increasing heat sink mass. Accordingly, pin–fin heat sinks with a mass equal to that of the LM type (M = 0.288 kg) were used for the comparison. The parameters for the Type 1 pin–fin array were NA = 20, LL = 50 mm, LM = 30 mm, Lf = 10 mm, LO = 22 mm, LD = 15 mm, Ls = 10 mm, ro = 75 mm, ri = 10 mm, t = 2 mm, Tair = 30 °C, e = 0.7, and q_ ¼ 700 W=m2 , where LO is the outermost fin height and LD is the fin-height difference between the fins. For the Type 2 pin–fin array, LO = 46 mm, and the other parameters were the same as those of Type 1. Fig. 7 shows the temperature contours on the horizontal plane at H = 10 mm and the vertical plane at h = 9° for the LM type [10] and the two fin-height profiles
D. Jang et al. / Applied Energy 116 (2014) 260–268
(a) 1.0 RTH Mass
0.8
0.6
μ*
considered in this study. Table 2 shows the result of the numerical analysis. When the Type 1 profile was used in place of the LM type, the average heat sink temperature decreased by 4 °C. For the pin–fin array with the tallest fins in the inner region (Type 1), heated air from the outermost fins rose in the direction of the chimney pattern and heat transfer resumed at the second row of fins. The thermal boundary layer of the flow developed steadily as the air entered along the chimney flow path. Hence, a relatively high local heat transfer coefficient was obtained on the upper sections in the second row. In addition, a fresh inflow entered from the second row of fins, since they were taller than the outermost fins. In the radial direction, such flow characteristics were repeated, increasing the mass flow rate by 44% compared to the LM type. Thus, the cooling performance was better even though the mass of the Type 1 was the same as that of the LM type. When the Type 2 height profile was used in place of the LM type, the heat sink temperature decreased by 8.3 °C. Compared to the Type 1 height profile, the ratio of the outermost fin area to the total fin area increased by 90%. Under natural convection, a heat source causes the temperature of cooling air to rise, and thus the air density decreases. A flow then develops toward the heat source from the outer region. Therefore, the increased heat transfer area in the outermost region, which is the flow entrance of a radial heat sink, increased the driving force of the inflow. Consequently, the mass flow rate increased by 46% and the cooling performance was improved. Although the Type 1 profile offers the advantage of repeated heat transfer along the chimney flow path, the increased mass flow rate of the Type 2 profile had a greater influence on cooling performance. Therefore, the Type 2 model was the best design among the fin arrays examined. These results were compared with those of previous studies of fin-height profiles. For impingement heat sinks [15–17], the pressure drop in the central region due to flow resistance has a decisive effect on flow penetration to the outer region, and the optimum fin-height profile is obtained by considering this. However, natural convection flow arises from the density difference due to increasing temperature. Therefore, the cooling performance of the Type 2 profile in which the driving force was increased by the larger heat transfer area in the outer region was better than that of the Type 1 profile, which had a lesser flow resistance in the outer region where the flow enters.
0.4
0.2
0.0
NA
LL
LM
LO
LD
Geometric parameters
(b) 1.0 RTH Mass
0.8
0.6
σ
266
0.4
0.2
0.0
NA
LL
LM
LO
LD
Geometric parameters Fig. 8. Design sensitivity analysis of the geometric parameters. (a) Mean of the elementary effects distribution (l⁄). (b) Standard deviation of the elementary effects distribution (r).
4.3. Sensitivity analysis Since the optimization step entails multi-objective optimization that takes into account cooling performance and mass, it is essential to select the influential parameters for the output. The influences of the number of fin arrays (NA), the long fin length (LL), the middle fin length (LM), the outermost fin height (LO), and the difference between fin heights (LD) on the mass and thermal resistance were evaluated. The space between pin fins (Ls) and the single pin–fin length (Lf) were excluded from the sensitivity analysis because the influences of these parameters on the output were relatively unimportant [12]. In addition, the smaller the space between pin fins (Ls) and the single pin–fin length (Lf), the greater the leading-edge effects and the surface area per unit volume of the fin. Therefore, Lf = 2 mm and Ls = 3 mm were fixed values in the sensitivity analysis and the optimization procedure. The elementary effects method, which can be used to extract the important parameters from many design parameters, was employed for the sensitivity analysis. This method [21,22] considers two sensitivity measures (l⁄, r) to select the design variables from many interacting parameters. Normalized parameters and outputs were adopted to exclude uncertainties induced by differing magnitudes.
Fig. 8 shows the sensitivity analysis of the design parameters with respect to mass and thermal resistance. The number of fin arrays (NA), the outermost fin height (LO), and the difference between the fin heights (LD) were significant for thermal resistance and mass. For these three design parameters, both the mean l⁄, which evaluates the overall effect of the design parameter on the outputs, and the standard deviation r, which assesses the ensemble of the parameter’s effects due to interactions with other parameters, were significant. This means that the deviations of the elementary effects were affected by the values of other parameters and exhibited remarkable distinctions depending on the design points. Although the difference between the fin heights (LD) was the third-most important parameter when only l⁄ was taken into consideration, it was necessary to consider the parameters as design variables rather than fixed parameters in the optimization step. This is because the value of r for the difference between the fin heights (LD) was largest with respect to cooling performance, and thus was most affected by the values of the other parameters. In contrast, the long fin length (LL) and middle fin length (LM) had low r values and were nearly free of interactions. The three parameters (NA, LO, LD) that markedly influenced the outputs were
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4.0
LM type Type 2
RTH (°C/W)
300W/m2 700W/m2 1100W/m2
the weight factor for the normalized thermal resistance and x2 is the weight factor for the normalized mass. The objective function and constraints are described as follows: 2 ;X 3 Þ 2 ;X 3 Þ Minimize f ðX 1 ; X 2 ; X 3 Þ ¼ x1 RRTH ðXðX1 ;X þ x2 MMðXðX1 ;X 1 ;X 2 ;X 3 Þ 1 ;X 2 ;X 3 Þ TH;ref
ref
subject to 20 6 X 1 6 28 ðX 1 is a natural numberÞ 2.5
LM type
The optimum design was carried out in the following sequence. First, 25 design points were adopted for optimization using an orthogonal array L25(53) to construct a Kriging model [25]. The Kriging model was constructed after numerical analysis of the 25 design points. The optimum point for X1, X2, and X3 was obtained from the Kriging model by employing an evolutionary algorithm, the specific parameters of which were as follows:
Type 2
1.0
0.15
0.20
0.25
40 6 X 2 6 56 2 ðNL ¼ Number of unit pin-fins in the long finÞ X 3 6 NXL 1
0.30
Mass (kg) Fig. 9. Comparison of the Pareto fronts for the LM type and Type 2 heat sinks (ro = 0.075 m, T1 = 30 °C, e = 0).
adopted as the design variables and the optimum design was based on these results. 4.4. Optimization The number of fin arrays (X1 = NA), the outermost fin height (X2 = LO), and the difference between the fin heights (X3 = LD) were adopted as the design variables. The pin–fin array with the tallest fins in the outer region (Type 2) was selected as the reference model. On the basis of a parametric study, the parameters for the reference model were NA = 24, LO = 48 mm, LD = 3 mm, LL = 42 mm, LM = 27 mm, Lf = 2 mm, Ls = 3 mm, NL = 9, ro = 75 mm, ri = 10 mm, and t = 2 mm. Since the objective of this research was to design a radial heat sink for high-power LED products, it was necessary to investigate various heat fluxes. In addition, the optimum configuration of a heat sink varies with the radiation heat transfer [11]. Therefore, the optimum design was performed with heat fluxes of 300, 700, 1100, and 1500 W/m2, and emissivities of 0 and 0.9, using commercial software, the process integration and design optimization (PIDO) tool known as PIAnO (Process Integration, Automation, and Optimization) [23]. The objective function considers thermal resistance and mass simultaneously via a weighted sum method [24] in which x1 is
Population size: 50. Maximum number of generations: 1000. Violated constraint limit: 0.003. Number of consecutive generations without improvement: 50. Mutation probability: 0.01. Selection probability: 0.15.
Fig. 9 compares the Pareto fronts of the Type 2 design and the LM type for various heat fluxes. Multi-objective optimization was carried out with various weight factors considering only natural convection (e = 0). The thermal resistance was decreased by more than 50% with the Type 2 design, while preserving a mass similar to that of the LM type. This was because of the increased mass flow rate through the large heat transfer area in the outer region of the Type 2 model. Table 3 shows the optimum results for the LM type and the Type 2 design with the same mass as the optimum LM type, taking both natural convection and radiation heat transfer into consideration. For the Type 2 heat sink, the thermal resistance was improved by an average of 45%. At 1500 W/m2, which is more than twice the reference heat flux of 700 W/m2, the heat sink temperature for the Type 2 model was approximately 20 °C lower than that of LM type. Therefore, reliable cooling performance for high-power LED products can be achieved by using a non-uniform fin-height profile of a pin–fin heat sink and the same mass as the LM type. Almost 25% of the total heat transfer was due to radiation. The optimum configuration was obtained in the direction of maximizing radiation heat transfer, and thus the difference between the fin heights (LD) was greater than in the case where only natural
Table 3 Optimization results when the mass is equal to that of the LM type heat sink (ro = 0075 m, T1 = 30 °C). Model
q_ (W/m2)
e
NA
LO (mm)
LD (mm)
Mass (kg)
Theatsink (°C)
RTH (°C/W)
LM Type LM Type LM Type LM Type LM Type LM Type LM Type LM Type
300 300 300 300 700 700 700 700 1100 1100 1100 1100 1500 1500 1500 1500
0 0 0.9 0.9 0 0 0.9 0.9 0 0 0.9 0.9 0 0 0.9 0.9
– 22 – 20 – 27 – 22 – 27 – 23 – 28 – 25
– 56 – 54.825 – 52.495 – 55.072 – 52.874 – 53.631 – 53.457 – 53.896
– 1 – 3.986 – 1.721 – 1.873 – 1.241 – 1.733 – 1.358 – 1.884
0.291 0.291 0.240 0.240 0.308 0.308 0.269 0.269 0.317 0.317 0.281 0.281 0.328 0.327 0.290 0.291
45.1 37.6 39.6 36.4 57.6 44 50.6 41.9 68.3 49.7 59.7 46.8 77.9 54.1 67.5 51.7
2.899 1.455 1.843 1.224 2.268 1.153 1.695 0.977 2.007 1.034 1.556 0.881 1.839 0.926 1.440 0.833
2 2 2 2 2 2 2 2
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convection was taken into account. Due to the radiation heat transfer (e = 0.9), the thermal resistance diminished by an average of 15% compared with the case where only natural convection was taken into account (e = 0). However, there was a smaller improvement in the thermal resistance in the case where only natural convection was taken into consideration. This was because only natural convection was significantly improved, while the radiation heat transfer did not change significantly. 5. Conclusion In this paper, a pin–fin radial heat sink with a fin-height profile was optimized. Natural convection and radiation heat transfer were taken into account, and an experiment was conducted to validate the numerical model. Among the various fin-height profiles, the pin–fin array with the tallest fins in the outer region (Type 2) showed the best cooling performance. The sensitivity of various parameters was investigated to determine the design variables, which were the outermost fin height, the difference between fin heights, and the number of fin arrays. Multi-objective optimization was carried out considering only natural convection, and the cooling performance was improved by 50% with a design having the same mass as the LM type. In the case where both natural convection and radiation heat transfer were taken into account, the cooling performance was improved by 15% compared with the case in which only natural convection was taken into account. However, no significant enhancement of the radiation heat transfer was obtained by using the Type 2 model instead of a plate-fin design, and thus the improvement in cooling performance was diminished in contrast to the case where only natural convection was taken into account. In summary, the cooling performance of a pin–fin radial heat sink with a fin-height profile showed an improvement of more than 45% while preserving a mass comparable to that of a plate-fin heat sink. Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2012R1A1B3000492). References [1] Naik S, Probert SD, Wood CI. Natural-convection characteristics of a horizontally-based vertical rectangular fin-array in the presence of a shroud. Appl Energy 1987;28(4):295–319.
[2] Leung CW, Probert SD. Heat-exchanger design: optimal uniform thickness of vertical rectangular fins protruding perpendicularly outwards, at uniform separations, from a vertical rectangular ‘base’. Appl Energy 1987;26(2):111–8. [3] Leung CW, Probert SD. Heat-exchanger performance: effect of orientation. Appl Energy 1989;33(4):235–52. [4] Leung CW, Probert SD, Rapley CW. Natural convection and radiation from vertically-based arrays of vertical, rectangular fins: a numerical model. Appl Energy 1990;35(4):253–66. [5] Leung CW, Probert SD. Heat-exchanger performance: influence of gap width between consecutive vertical rectangular fin-arrays. Appl Energy 1997;56(1):1–8. [6] Harahap F, Setio D. Correlations for heat dissipation and natural convection heat-transfer from horizontally-based, vertically-finned arrays. Appl Energy 2001;69(1):29–38. [7] Elshafei EAM. Natural convection heat transfer from a heat sink with hollow/ perforated circular pin fins. Energy 2010;35:2870–7. [8] Sertkaya AA, Bilir S ß , Kargıcı S. Experimental investigation of the effects of orientation angle on heat transfer performance of pin-finned surfaces in natural convection. Energy 2011;36:1513–7. [9] Yu SH, Lee KS, Yook SJ. Natural convection around a radial heat sink. Int J Heat Mass Transfer 2010;53:2935–8. [10] Yu SH, Lee KS, Yook SJ. Optimum design of a radial heat sink under natural convection. Int J Heat Mass Transfer 2011;54:2499–505. [11] Yu SH, Jang D, Lee KS. Effect of radiation in a radial heat sink under natural convection. Int J Heat Mass Transfer 2012;55:505–9. [12] Jang D, Yu SH, Lee KS. Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications. Int J Heat Mass Transfer 2012;55:515–21. [13] Fabbri G. A genetic algorithm for fin profile optimization. Int J Heat Mass Transfer 1997;40:2165–72. [14] Kanyakam S, Bureerat S. Multi objective evolutionary optimization of splayed pin-fin heat sink. Eng Appl Comput Fluid Mech 2011;5:553–65. [15] Shah A, Sammakia BG, Srihari H, Ramakrishna K. A numerical study of the thermal performance of an impingement heat sink-fin shape optimization. IEEE Trans Compon Packag Technol 2004;27(4):710–7. [16] Shah A, Sammakia BG, Srihari H, Ramakrishna K. Optimization study for a parallel plate impingement heat sink. J Electron Packag 2006;128:311–8. [17] Yang Y, Peng H. Numerical study of pin-fin heat sink with un-uniform fin height design. Int J Heat Mass Transfer 2008;51:4788–96. [18] Bello-Ochende T, Meyer JP, Bejan A. Constructal multi-scale pin–fins. Int J Heat Mass Transfer 2010;53:2773–9. [19] Carvalho MG, Faris T, Fontes P. Predicting radiative heat transfer in absorbing, emitting, and scattering media using the discrete transfer method. Fund Radiat Heat Transfer ASME HTD 1991;160:17–26. [20] Bianco N, Langellotto L, Manca O, Nardini S. Radiative effects on natural convection in vertical convergent channels. Int J Heat Mass Transfer 2010;53:3513–24. [21] Morris MD. Factorial sampling plans for preliminary computational experiments. Technometrics 1991;33:161–74. [22] Campolongo F, Cariboni J, Saltelli A. An effective screening design for sensitivity analysis of large models. Environ Model Software 2007;22:1509–18. [23] Framax INC. PIAnO (Process Integration, Automation and Optimization) User’s manual, Version 3.3. 2011. [24] Arora JS. Introduction to optimum design. United States of America: Elsevier Academic Press; 2004. [25] Sacks J, Welch WJ, Mitchell TJ, Wynn HP. Design and analysis of computer experiments. Stat Sci 1989;4:409–35.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Optimum design of a radial heat sink with a fin-height profile for high-power LED lighting applications 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
h i g h l i g h t s A radial heat sink was designed for high-power LED lighting applications. Fin-height profiles reflecting the chimney-flow characteristics of a radial heat sink were proposed. Multi-disciplinary optimization was carried out to simultaneously minimize the thermal resistance and mass. The cooling performance of the optimized design showed improvement without additional mass increment.
a r t i c l e
i n f o
Article history: Received 26 April 2013 Received in revised form 11 November 2013 Accepted 23 November 2013 Available online 20 December 2013 Keywords: LED lighting Electronic cooling Natural convection Heat sink Optimization Fin-height profile
a b s t r a c t Light-emitting diode (LED) lighting offers greater energy efficiency than conventional lighting. However, if the heat from the LEDs is not properly dissipated, the lifespan and luminous efficiency are diminished. In the present study, a heat sink of LED lighting was optimized with respect to its fin-height profile to obtain reliable cooling performance for high-power LED lighting applications. Natural convection and radiation heat transfer were taken into consideration and an experiment was conducted to validate the numerical model. Fin-height profiles reflecting a three-dimensional chimney-flow pattern were proposed. The outermost fin height, the difference between fin heights, and the number of fin arrays were adopted as design variables via sensitivity analysis, and the heat sink configuration was optimized in three dimensions. Optimization was conducted to simultaneously minimize the thermal resistance and mass. The result was compared with the Pareto fronts of a plate-fin heat sink examined in a previous study. The cooling performance of the optimized design showed an improvement of more than 45% while preserving a mass similar to that of the plate-fin heat sink. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Light-emitting diode (LED) lighting offers the advantages of a longer lifespan and greater energy efficiency than conventional lighting. LED lighting uses 75% less energy than incandescent or fluorescent lighting. Due to its greater energy efficiency, the market share of LED lighting is growing rapidly, and the market domain now includes high-power LED products. However, if high power is applied to LEDs to produce more light output, the amount of heat generated by the LEDs is greatly increased, which reduces both the lifespan and the luminous efficiency. Therefore, a technology for properly dissipating the heat from inside the LED package to the surroundings is as important as the electronic and optical characteristics. The LED lighting system shown Fig. 1 is composed of an LED chip, epoxy, a slug, a printed circuit board, and a heat sink. This study is confined to the heat sink, which can improve
⇑ Corresponding author. Tel.: +82 2 2220 0426; fax: +82 2 2295 9021. E-mail address: [email protected] (K.-S. Lee). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.11.063
its cooling performance via shape alteration. Optimization of the radial heat sinks used in LED lighting applications is necessary to obtain reliable cooling performance in high-power LED products. Numerous researchers have analyzed natural convection heat sinks with diverse fin configurations [1–8]. Elshafei [7] examined the heat transfer characteristics of hollow/perforated round pin– fin heat sink, and compared the results with those obtained for solid round pin–fin heat sink. Sertkaya et al. [8] investigated the orientation effect of a pin–fin heat sink under natural convection, and reported that the cooling performance with an upward-facing orientation was outstanding. However, most of these researches considered rectangular heat sink, which is ineffective for cooling in round LED lighting applications. Accordingly, diverse types of radial heat sinks have recently been proposed and optimized [9–12]. Multidisciplinary optimization is the primary method for improving heat sink performance because both mass and cooling performance are considered in the performance evaluation. Jang et al. [12] compared various pin–fin radial heat sinks to achieve a lighter heat sink with a cooling performance similar to that of a plate-fin
D. Jang et al. / Applied Energy 116 (2014) 260–268
261
Nomenclature A F H I k L ~ L M _ m N n P q_ RTH r ~ s T t
v
heat transfer area (mm2) body force vector per unit volume height (mm) radiation intensity thermal conductivity (W/m K) length (mm) periodic length vector mass of heat sink (kg) mass flow rate (kg/s) number normal vector pressure (Pa) heat flux (W/m2) thermal resistance (°C/W) radius (mm) ray vector temperature (K) fin thickness (mm) velocity vector (m/s)
r q h
e x X
standard deviation of elementary effects distribution density (kg/m3) angle, as in Fig. 3(b) (°) emissivity weight factor hemispherical solid angle (°)
Subscripts A array acr acrylic avg average D difference between fin heights f fin i inner L long fin M middle fin O outermost fin height o outer s space between fins in the radial direction w wall 1 ambient
Greek symbols l dynamic viscosity (N s/m2) ⁄ l mean of elementary effects distribution
heat sink reported in previous studies [9–11]. Using this approach, they were able to reduce the mass by more than 30% while preserving a cooling performance similar to that of the optimum plate-fin heat sink [10]. However, these studies were based on the assumption of uniform fin height, and hence their results are unsuitable for radial heat sinks with chimney-flow characteristics because non-uniform heat transfer occurs along the radial direction in a chimney flow. Therefore, it is necessary to determine fin-height profiles that are appropriate for chimney-flow characteristics. Several recent studies have focused on the effects of various fin-height profiles. Fabbri [13] studied the influence of fin-height profiles with polynomial forms and obtained an optimum profile for every polynomial degree by using a genetic algorithm. Kanyakam and Bureeret [14] studied the forced convection of splayed pin–fin heat sinks by varying the fin height and azimuthal angle with the heat sink base as the center. They concluded that a splayed heat sink offers outstanding cooling performance compared to a straight pin–fin heat sink, and Pareto fronts relating the cooling performance and the fan pumping power were obtained via multi-objective optimization. Shah et al. [15] numerically analyzed the performance of a heat sink with an impingement cooling system. The effect of the fin-height profile on the cooling performance (especially near the center of the heat sink) was analyzed. They found that reduction of fin volume around
the central region reduced the pressure drop in that region, and improved the flow penetration to the outer region. As a result, a fin-height profile with reduced fin volume in the central region enhanced both the thermal and hydraulic performance. Shah et al. [16] extended their previous work and optimized the configuration of the heat sink by investigating the removal of fin volume at the end fins, varying the number of fins, and reducing the size of the fan. Yang and Peng [17] studied impinging jets on pin–fin heat sinks with non-uniform fin heights. They found that the heat sink temperature could be decreased by increasing the fin height around the central region of the heat sink. However, there is a limit to how much the fin height around the central region of a heat sink can be increased because flow penetration into that region is weakened by the resulting increased flow resistance. In addition, if the fins around the central region are too tall in comparison to the other fins, heat transfer in the outer region will be poor and the overall thermal performance will be degraded. Bello-Ochende et al. [18] developed an optimized pin–fin heat sink design for maximizing forced convection with limited mass and found that cooling performance was maximized when the fin diameter and height were non-uniform. However, these studies [13–18] were concerned with the forced convection of heat sinks with rectangular bases, and the optimum fin-height profile differed with respect to the cooling method or shape. Therefore, a research of radial heat
Ambient air Heat sink
Printed circuit board
PCB
Slug Epoxy LED chip Fig. 1. Diagram of a typical LED lighting application.
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sink under natural convection with a non-uniform fin-height profile is still needed. In previous studies of radial heat sinks [10– 12], the thermo-flow characteristics around the heat sink were analyzed and geometric optimization was carried out. The temperature contours of various fin arrays on a horizontal plane were also compared, and the fin lengths and number of fin arrays were optimized to retard the growth of a fully developed thermal boundary layer. However, optimization results based on two-dimensional thermo-flow characteristics on a horizontal plane are not appropriate for the three-dimensional flow of a radial heat sink. To reflect chimney-flow characteristics, an optimum design based on the overall three-dimensional flow is necessary. In the present research, a radial heat sink with pin fins is optimized with respect to the fin-height profile. Fin-height profiles are proposed that can improve cooling performance without increasing the mass beyond that of a comparable plate-fin heat sink. The cooling performances of three profiles (the LM type, a pin–fin array with the tallest fins in the inner region, and a pin–fin array with the tallest fins in the outer region) with equal masses are analyzed and a reference profile is determined. Finally, a heat sink is designed using multi-objective optimization considering both mass and thermal resistance to provide improved cooling performance with a mass equivalent to that in previous studies.
(a)
(a)
LD LO
Lf
(b)
Ls LM
t
ri
LL
θ
ro g gravity
Fig. 3. Computational domain. (a) Isometric view of the computational domain. (b) Top view of the computational domain.
2. Mathematical modeling
(b)
2.1. Numerical model
g gravity
(c)
g
The LM type of heat sink addressed in previous studies [9–11], a pin–fin array with the tallest fins in the inner region (Type 1), and a pin–fin array with the tallest fins in the outer region (Type 2) were compared (see Fig. 2). The fins were circularly arranged at consistent intervals. The heat sink base was oriented horizontally, whereas the fins were arranged vertically. The fin array was duplicated around the circumference of the base plate. Due to the computational cost involved, only a single fin array was used for the computational domain, as shown in Fig. 3. The numerical analysis was based on the following assumptions. (1) The flow is laminar, steady, and three dimensional. (2) The density of air is computed using the ideal gas law. (3) Except for the density of air, the fluid properties are constant. (4) The heat sink surface is gray and diffuse.
gravity 2.2. Governing equations and boundary conditions
Fig. 2. Test heat sinks. (a) LM plate-fin type. (b) Pin–fin array with the tallest fins on the inside (Type 1). (c) Pin–fin array with the tallest fins on the outside (Type 2).
Table 1 enumerates the governing equations and boundary conditions. Radiation heat transfer was computed via the discrete transfer radiation model [19,20], which can support periodic conditions.
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D. Jang et al. / Applied Energy 116 (2014) 260–268 Table 1 Governing equations and boundary conditions for the computational domain. Wall
Continuity equation
r ðqv Þ ¼ 0
Momentum equations
Solid domain Interface between fluid and solid domain
2
Energy equation
¼ rP þ lr v þ F (for z-direction F = qg)
DP qC p DT Dt ¼ r ðkrTÞ þ Dt
r i Þ ¼ ui ð~ ri þ ~ LÞ, ui ð~
Tð~ r i Þ ¼ Tð~ ri þ ~ LÞ
q
Periodic face Fluid domain
Dv Dt
~
rpðxi Þ ¼ g j~LLj þ rp ðxi Þ Outer face
Pressure inlet/Pressure outlet condition
Heat sink base
ui ¼ 0
Symmetric face
ui ¼ 0
Interface
ui = 0
T inlet ¼ T outlet; back flow ¼ T 1 s _ ks @T @n heat sink base ¼ q @T s ¼0 @n sectional wall
f kf @T @n
T f;wall ¼ T s; wall ;
s þ q_ out ¼ ks @T þ q_ in @n wall ! R _qin ¼ ~s~n>0 Iin~ ~ s ndX; wall
q_ out ¼ ð1 ew Þqin þ ew rT 4w
2.3. Numerical procedure The numerical analysis was carried out using the finite volume method with Fluent V6.3, a commercial computational fluid dynamics software package. The SIMPLE algorithm was adopted to couple the velocity and pressure fields. To enhance the accuracy of the result, a second-order upwind scheme was employed to the convection terms of the governing equations. The result was determined to have converged when the relative error of all dependent variables between two successive iterations was less than 105. Taking into account both the convergence of the heat sink temperature and the computational time, the height of the domain changed from two to ten times the height of the tallest fin, and the radius of the domain changed from 1.3ro to 1.6ro. When the domain height was increased beyond five times the height of the
tallest fin, and the radius beyond 1.5 ro, the temperature of the heat sink changed by less than 0.5%; these results were used to set the size of the computational domain. A dense grid was generated in the region where a boundary layer developed near the heat sink. Grid dependence testing took place by increasing the number of grid points from 60,000 to 700,000, with 519,375 grid points being selected as a reference from our sensitivity analysis. The change in heat sink temperature with additional grid points was less than 0.5%. ICEM CFD 14.5 was used to generate the mesh, and the grid system was shown in Fig. 4.
(a)
Heat sink
Insulator (polystyrene) T3 Aluminum plate
T2
Film heater
T1 Acrylic plate
(b) Heat sink
Thermocouple
Fig. 4. Computational grid system. (a) Top view. (b) Side view.
Insulator (polystyrene)
Fig. 5. Experimental setup. (a) Illustration for the experimental setup. (b) Photo for the experimental setup.
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3. Experiments and validation The LM type of heat sink [10], a pin–fin array with the tallest fins in the inner region (Type 1), and a pin–fin array with the tallest fins in the outer region (Type 2) were evaluated to validate the numerical model. The heat sinks were made of black anodized aluminum (Al6061, e = 0.8). The parameters for the LM type were NA = 20, LL = 50 mm, LM = 20 mm, ro = 75 mm, ri = 10 mm, t = 2 mm, and H = 21.3 mm. The parameters for Type 1 were NA = 20, LL = 45 mm, LM = 25 mm, Lf = 5 mm, LO = 24.3 mm, LD = 8 mm, Ls = 5 mm, ro = 75 mm, ri = 10 mm, and t = 2 mm. For Type 2, LO = 50.3 mm; the other parameters were the same as those of Type 1. As shown in Fig. 5, the experimental setup comprised a heat sink, a film heater (Kapton-coated stainless steel, 25 lm), an insulator, a data acquisition device (NI SCXI-1303, 1100, 1600), type-T thermocouples (gauge 36), a power supply, a personal computer, and a wattmeter. Thin aluminum plates, 1 mm thick, were placed beneath and on top the film heater to apply a uniform heat flux. Thermal grease was employed to decrease the thermal contact resistance between the heat sink and the film heater. An acrylic plate, 5 mm thick, was inserted beneath the heater and used to evaluate the heat loss from the bottom of the heater as follows:
Q_ heat sink ¼ Q_ total Q_ heat loss
ð1Þ
ðT 1 T 2 Þ Q_ heat loss ¼ kacr Aacr tacr
ð2Þ
To minimize the heat loss through the sides, the section of film heater was enclosed by an insulator. The heat sink temperature was measured with eight thermocouples, and the ambient air temperature was measured with two thermocouples. Constant current and voltage were applied to the film heater during the experiment. When the temperature change was less than 0.1 °C over 30 min, the heat sink temperature was assumed to have reached a steady state, and the thermal performance was calculated. Fig. 6 compares the experimental and numerical results. The thermal resistance of the heat sink was adopted as the performance index, and defined by
RTH
T avg;heat sink T 1 ¼ p r2o r2i q_ heat sink
ð3Þ
3 Experiment Numerical Model
RTH (°C/W)
LM type Type 1 Type 2
2
1
0
400
800
1200
.
q (W/m2) Fig. 6. Comparison of the computational and experimental results (ro = 0.075 m, e = 0.8).
An uncertainty analysis was carried out as part of the experiment. The maximum uncertainty was estimated to be 2.7%. The numerical results agreed well with the results of experiment with an error of less than 6.8%. Accordingly, we validated that the numerical model explained in Section 2 could correctly simulate natural convection and radiation heat transfer around a heat sink with a specific fin-height profile. 4. Results and discussion Pin–fin heat sinks with diverse fin-height profiles were compared to the plate-fin heat sink suggested by Yu et al. [10] in terms of cooling performance and mass. The elementary effects method was utilized for the sensitivity analysis from which the design variables were determined. Finally, multi-objective optimization was conducted considering both mass and cooling performance, and application of the optimized design to high-power LED products was examined. 4.1. Thermo-flow characteristics around a plate-fin radial heat sink Fig. 7(a) illustrates the temperature contours around a radial heat sink with the LM-type design (NA = 20, LL = 50 mm, LM = 30 mm, ro = 75 mm, ri = 10 mm, t = 2 mm, H = 21.3 mm, and e = 0.7, where NA is the number of fin arrays, LL is the long fin length, and LM is the middle fin length). The reference heat flux was 700 W/m2, which is equivalent to the power consumption of a typical LED down light (20 W). To investigate the heat transfer characteristics, the overall flow characteristics were examined from two perspectives. The right-hand side of Fig. 7(a) shows the temperature contours for the first perspective, lying on a horizontal plane 10 mm above the heat sink base. The spaces between the plate fins of the heat sink are comparatively wide in the outer region, and become narrower in the inner region. The more the domain of interest penetrates into the inner region, the narrower these spaces become. In the inner region, the thermal boundary layers between the fins overlapped and become fully developed, leading to a decrease of the heat transfer coefficient. The left-hand side of Fig. 7(a) shows the temperature contours for the second perspective, lying on a vertical plane (h = 9°). The incoming cool air is warmed by the heat sink and rises. The overall flow typically has a chimney-like pattern. Most of the heat transfer occurs in the outer region and little heat transfer occurs in the central region. Most of the mass flow does not reach the inner fins because the inflow rises in accordance with the chimney pattern. Therefore, the mass flow rate for cooling decreases in the inner region, resulting in non-uniform heat transfer. In previous studies that only considered the thermo-flow characteristics on a horizontal plane, the fin lengths and the number of fin arrays that influence the thermal boundary layer development on the horizontal plane were adopted as design variables for optimum design. However, design variables pertaining exclusively to two-dimensional thermo-flow characteristics are inappropriate for three-dimensional radial heat sink flow analysis because nonuniform heat transfer with respect to the radial direction must be reflected in the design procedure. Taking into account the chimney pattern of flow and the fully developed thermal boundary layer in the inner region, the uniform fin height assumed in previous studies is unsuitable for analyzing a non-uniform heat transfer distribution. 4.2. Non-uniform fin-height profiles To investigate the three-dimensional flow characteristics of a radial heat sink, the effects of diverse fin-height profiles on the
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(a)
53.64 (oC) 51.27 48.91 46.55 44.18 41.82 39.46 37.09 34.73 32.36 30.00
(b)
θ = 9°
H = 10 mm
θ = 9°
H = 10 mm
θ = 9°
H = 10 mm
53.64 (oC) 51.27 48.91 46.55 44.18 41.82 39.46 37.09 34.73 32.36 30.00
(c)
53.64 (oC) 51.27 48.91 46.55 44.18 41.82 39.46 37.09 34.73 32.36 30.00
Fig. 7. Temperature contours at h = 9° and H = 10 mm (ro = 0.075 m, q_ ¼ 700 W=m2 , T1 = 30 °C, e = 0.7). (a) LM plate-fin model. (b) Pin–fin array with the tallest fins on the inside (Type 1). (c) Pin–fin array with the tallest fins on the outside (Type 2).
heat sink mass and temperature were examined. The LM type of heat sink, a pin–fin array with the tallest fins in the inner region (Type 1), and a pin–fin array with the tallest fins in the outer region Table 2 Comparison of various fin height profiles (ro = 0 075 m, q_ ¼ 700 W=m2 , T1 = 30 °C, e = 0.7). Model
A (mm2)
LO (mm)
LD (mm)
_ air (105 kg/s) m
Tavg (°C)
LM plate-fin Type 1 Type 2
4499 5000 5000
21.3 22 46
0 15 15
3.04 4.39 6.4
53.12 48.86 44.80
(Type 2) were compared. In general, cooling performance improves with increasing heat sink mass. Accordingly, pin–fin heat sinks with a mass equal to that of the LM type (M = 0.288 kg) were used for the comparison. The parameters for the Type 1 pin–fin array were NA = 20, LL = 50 mm, LM = 30 mm, Lf = 10 mm, LO = 22 mm, LD = 15 mm, Ls = 10 mm, ro = 75 mm, ri = 10 mm, t = 2 mm, Tair = 30 °C, e = 0.7, and q_ ¼ 700 W=m2 , where LO is the outermost fin height and LD is the fin-height difference between the fins. For the Type 2 pin–fin array, LO = 46 mm, and the other parameters were the same as those of Type 1. Fig. 7 shows the temperature contours on the horizontal plane at H = 10 mm and the vertical plane at h = 9° for the LM type [10] and the two fin-height profiles
D. Jang et al. / Applied Energy 116 (2014) 260–268
(a) 1.0 RTH Mass
0.8
0.6
μ*
considered in this study. Table 2 shows the result of the numerical analysis. When the Type 1 profile was used in place of the LM type, the average heat sink temperature decreased by 4 °C. For the pin–fin array with the tallest fins in the inner region (Type 1), heated air from the outermost fins rose in the direction of the chimney pattern and heat transfer resumed at the second row of fins. The thermal boundary layer of the flow developed steadily as the air entered along the chimney flow path. Hence, a relatively high local heat transfer coefficient was obtained on the upper sections in the second row. In addition, a fresh inflow entered from the second row of fins, since they were taller than the outermost fins. In the radial direction, such flow characteristics were repeated, increasing the mass flow rate by 44% compared to the LM type. Thus, the cooling performance was better even though the mass of the Type 1 was the same as that of the LM type. When the Type 2 height profile was used in place of the LM type, the heat sink temperature decreased by 8.3 °C. Compared to the Type 1 height profile, the ratio of the outermost fin area to the total fin area increased by 90%. Under natural convection, a heat source causes the temperature of cooling air to rise, and thus the air density decreases. A flow then develops toward the heat source from the outer region. Therefore, the increased heat transfer area in the outermost region, which is the flow entrance of a radial heat sink, increased the driving force of the inflow. Consequently, the mass flow rate increased by 46% and the cooling performance was improved. Although the Type 1 profile offers the advantage of repeated heat transfer along the chimney flow path, the increased mass flow rate of the Type 2 profile had a greater influence on cooling performance. Therefore, the Type 2 model was the best design among the fin arrays examined. These results were compared with those of previous studies of fin-height profiles. For impingement heat sinks [15–17], the pressure drop in the central region due to flow resistance has a decisive effect on flow penetration to the outer region, and the optimum fin-height profile is obtained by considering this. However, natural convection flow arises from the density difference due to increasing temperature. Therefore, the cooling performance of the Type 2 profile in which the driving force was increased by the larger heat transfer area in the outer region was better than that of the Type 1 profile, which had a lesser flow resistance in the outer region where the flow enters.
0.4
0.2
0.0
NA
LL
LM
LO
LD
Geometric parameters
(b) 1.0 RTH Mass
0.8
0.6
σ
266
0.4
0.2
0.0
NA
LL
LM
LO
LD
Geometric parameters Fig. 8. Design sensitivity analysis of the geometric parameters. (a) Mean of the elementary effects distribution (l⁄). (b) Standard deviation of the elementary effects distribution (r).
4.3. Sensitivity analysis Since the optimization step entails multi-objective optimization that takes into account cooling performance and mass, it is essential to select the influential parameters for the output. The influences of the number of fin arrays (NA), the long fin length (LL), the middle fin length (LM), the outermost fin height (LO), and the difference between fin heights (LD) on the mass and thermal resistance were evaluated. The space between pin fins (Ls) and the single pin–fin length (Lf) were excluded from the sensitivity analysis because the influences of these parameters on the output were relatively unimportant [12]. In addition, the smaller the space between pin fins (Ls) and the single pin–fin length (Lf), the greater the leading-edge effects and the surface area per unit volume of the fin. Therefore, Lf = 2 mm and Ls = 3 mm were fixed values in the sensitivity analysis and the optimization procedure. The elementary effects method, which can be used to extract the important parameters from many design parameters, was employed for the sensitivity analysis. This method [21,22] considers two sensitivity measures (l⁄, r) to select the design variables from many interacting parameters. Normalized parameters and outputs were adopted to exclude uncertainties induced by differing magnitudes.
Fig. 8 shows the sensitivity analysis of the design parameters with respect to mass and thermal resistance. The number of fin arrays (NA), the outermost fin height (LO), and the difference between the fin heights (LD) were significant for thermal resistance and mass. For these three design parameters, both the mean l⁄, which evaluates the overall effect of the design parameter on the outputs, and the standard deviation r, which assesses the ensemble of the parameter’s effects due to interactions with other parameters, were significant. This means that the deviations of the elementary effects were affected by the values of other parameters and exhibited remarkable distinctions depending on the design points. Although the difference between the fin heights (LD) was the third-most important parameter when only l⁄ was taken into consideration, it was necessary to consider the parameters as design variables rather than fixed parameters in the optimization step. This is because the value of r for the difference between the fin heights (LD) was largest with respect to cooling performance, and thus was most affected by the values of the other parameters. In contrast, the long fin length (LL) and middle fin length (LM) had low r values and were nearly free of interactions. The three parameters (NA, LO, LD) that markedly influenced the outputs were
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4.0
LM type Type 2
RTH (°C/W)
300W/m2 700W/m2 1100W/m2
the weight factor for the normalized thermal resistance and x2 is the weight factor for the normalized mass. The objective function and constraints are described as follows: 2 ;X 3 Þ 2 ;X 3 Þ Minimize f ðX 1 ; X 2 ; X 3 Þ ¼ x1 RRTH ðXðX1 ;X þ x2 MMðXðX1 ;X 1 ;X 2 ;X 3 Þ 1 ;X 2 ;X 3 Þ TH;ref
ref
subject to 20 6 X 1 6 28 ðX 1 is a natural numberÞ 2.5
LM type
The optimum design was carried out in the following sequence. First, 25 design points were adopted for optimization using an orthogonal array L25(53) to construct a Kriging model [25]. The Kriging model was constructed after numerical analysis of the 25 design points. The optimum point for X1, X2, and X3 was obtained from the Kriging model by employing an evolutionary algorithm, the specific parameters of which were as follows:
Type 2
1.0
0.15
0.20
0.25
40 6 X 2 6 56 2 ðNL ¼ Number of unit pin-fins in the long finÞ X 3 6 NXL 1
0.30
Mass (kg) Fig. 9. Comparison of the Pareto fronts for the LM type and Type 2 heat sinks (ro = 0.075 m, T1 = 30 °C, e = 0).
adopted as the design variables and the optimum design was based on these results. 4.4. Optimization The number of fin arrays (X1 = NA), the outermost fin height (X2 = LO), and the difference between the fin heights (X3 = LD) were adopted as the design variables. The pin–fin array with the tallest fins in the outer region (Type 2) was selected as the reference model. On the basis of a parametric study, the parameters for the reference model were NA = 24, LO = 48 mm, LD = 3 mm, LL = 42 mm, LM = 27 mm, Lf = 2 mm, Ls = 3 mm, NL = 9, ro = 75 mm, ri = 10 mm, and t = 2 mm. Since the objective of this research was to design a radial heat sink for high-power LED products, it was necessary to investigate various heat fluxes. In addition, the optimum configuration of a heat sink varies with the radiation heat transfer [11]. Therefore, the optimum design was performed with heat fluxes of 300, 700, 1100, and 1500 W/m2, and emissivities of 0 and 0.9, using commercial software, the process integration and design optimization (PIDO) tool known as PIAnO (Process Integration, Automation, and Optimization) [23]. The objective function considers thermal resistance and mass simultaneously via a weighted sum method [24] in which x1 is
Population size: 50. Maximum number of generations: 1000. Violated constraint limit: 0.003. Number of consecutive generations without improvement: 50. Mutation probability: 0.01. Selection probability: 0.15.
Fig. 9 compares the Pareto fronts of the Type 2 design and the LM type for various heat fluxes. Multi-objective optimization was carried out with various weight factors considering only natural convection (e = 0). The thermal resistance was decreased by more than 50% with the Type 2 design, while preserving a mass similar to that of the LM type. This was because of the increased mass flow rate through the large heat transfer area in the outer region of the Type 2 model. Table 3 shows the optimum results for the LM type and the Type 2 design with the same mass as the optimum LM type, taking both natural convection and radiation heat transfer into consideration. For the Type 2 heat sink, the thermal resistance was improved by an average of 45%. At 1500 W/m2, which is more than twice the reference heat flux of 700 W/m2, the heat sink temperature for the Type 2 model was approximately 20 °C lower than that of LM type. Therefore, reliable cooling performance for high-power LED products can be achieved by using a non-uniform fin-height profile of a pin–fin heat sink and the same mass as the LM type. Almost 25% of the total heat transfer was due to radiation. The optimum configuration was obtained in the direction of maximizing radiation heat transfer, and thus the difference between the fin heights (LD) was greater than in the case where only natural
Table 3 Optimization results when the mass is equal to that of the LM type heat sink (ro = 0075 m, T1 = 30 °C). Model
q_ (W/m2)
e
NA
LO (mm)
LD (mm)
Mass (kg)
Theatsink (°C)
RTH (°C/W)
LM Type LM Type LM Type LM Type LM Type LM Type LM Type LM Type
300 300 300 300 700 700 700 700 1100 1100 1100 1100 1500 1500 1500 1500
0 0 0.9 0.9 0 0 0.9 0.9 0 0 0.9 0.9 0 0 0.9 0.9
– 22 – 20 – 27 – 22 – 27 – 23 – 28 – 25
– 56 – 54.825 – 52.495 – 55.072 – 52.874 – 53.631 – 53.457 – 53.896
– 1 – 3.986 – 1.721 – 1.873 – 1.241 – 1.733 – 1.358 – 1.884
0.291 0.291 0.240 0.240 0.308 0.308 0.269 0.269 0.317 0.317 0.281 0.281 0.328 0.327 0.290 0.291
45.1 37.6 39.6 36.4 57.6 44 50.6 41.9 68.3 49.7 59.7 46.8 77.9 54.1 67.5 51.7
2.899 1.455 1.843 1.224 2.268 1.153 1.695 0.977 2.007 1.034 1.556 0.881 1.839 0.926 1.440 0.833
2 2 2 2 2 2 2 2
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convection was taken into account. Due to the radiation heat transfer (e = 0.9), the thermal resistance diminished by an average of 15% compared with the case where only natural convection was taken into account (e = 0). However, there was a smaller improvement in the thermal resistance in the case where only natural convection was taken into consideration. This was because only natural convection was significantly improved, while the radiation heat transfer did not change significantly. 5. Conclusion In this paper, a pin–fin radial heat sink with a fin-height profile was optimized. Natural convection and radiation heat transfer were taken into account, and an experiment was conducted to validate the numerical model. Among the various fin-height profiles, the pin–fin array with the tallest fins in the outer region (Type 2) showed the best cooling performance. The sensitivity of various parameters was investigated to determine the design variables, which were the outermost fin height, the difference between fin heights, and the number of fin arrays. Multi-objective optimization was carried out considering only natural convection, and the cooling performance was improved by 50% with a design having the same mass as the LM type. In the case where both natural convection and radiation heat transfer were taken into account, the cooling performance was improved by 15% compared with the case in which only natural convection was taken into account. However, no significant enhancement of the radiation heat transfer was obtained by using the Type 2 model instead of a plate-fin design, and thus the improvement in cooling performance was diminished in contrast to the case where only natural convection was taken into account. In summary, the cooling performance of a pin–fin radial heat sink with a fin-height profile showed an improvement of more than 45% while preserving a mass comparable to that of a plate-fin heat sink. Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2012R1A1B3000492). References [1] Naik S, Probert SD, Wood CI. Natural-convection characteristics of a horizontally-based vertical rectangular fin-array in the presence of a shroud. Appl Energy 1987;28(4):295–319.
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