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Cooling performance and space efficiency improvement based on heat sink arrangement for power conversion electronics
Applied Thermal Engineering 164 (2020) 114458
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Cooling performance and space efficiency improvement based on heat sink arrangement for power conversion electronics Youngchan Yoona,b, Dong Rip Kima, Kwan-Soo Leea, a b
T
⁎
School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Electric Energy Engineering Team, Hyundai Mobis, 240 Mabuk-ro, Gigeung-gu, Yongin-si, Gyeonggi-do 16891, Republic of Korea
H I GH L IG H T S
overlapped heat sink was investigated for space efficiency and cooling performance improvement. • The confirmed that there was an optimum overlap ratio for maximizing the cooling performance. • ItFanwascharacteristic curves were generalized for the various operating environment. • When the overlapped heat sink is applied, the cooling performance was improved by up to about 35%. •
A R T I C LE I N FO
A B S T R A C T
Keywords: Plate fin heat sink Power conversion electronics cooling Forced convection Space efficiency
A heat sink system was miniaturized, and its cooling performance was improved by overlapping the heat sinks. To simulate an axial fan condition (typically used in air-cooled forced convection), a fan characteristic curve was applied to consider the relationship between the airflow rate and pressure drop. On investigating the cooling performance of the overlapped heat sinks, it was confirmed that the heat transfer coefficient was improved owing to the increase in the velocity inside the channel, even though the flow rate was decreased. In addition, the fan curves were generalized to be applied in various fan environments, and correlations were proposed to predict the pressure drop and cooling performance of the overlapped heat sinks. The correlations reflect the heat sink geometry and fan characteristics of the system. The cooling performance was improved by a maximum of 35%, and the volume occupied by the system decreased when the fins overlapped. This suggests the proposed method can maximize the space efficiency and improve the cooling performance in a given environment without changing the geometry of the heat sink.
1. Introduction In electronic power equipment, such as industrial inverters, heat is primarily generated in semiconductor devices, such as metal-oxide semiconductor field-effect transistors (MOSFETs) or insulated-gate bipolar transistors (IGBTs). These semiconductor devices are highly vulnerable to degradation at high temperatures. Therefore, MOSFETs or IGBTs are installed in cooling devices, such as heat sinks, to keep them below the maximum allowed temperature through forced cooling or natural convection [1]. To improve the cooling performance of heat sinks for heating elements, numerous studies have been conducted concerning the shape of the heat sink fin and channel [2–5]. Joo et al. [6] proposed a topology optimization technique to reduce the thermal resistance by 13%. Furthermore, Park et al. [7] and Bello-Ochende et al. [8] improved the heat
⁎
transfer coefficient by approximately 10% by changing the fin arrangement. In addition, Sakanova et al. [9] was able to reduce the heat resistance by approximately 20% and reduce the weight by applying a perforated fin drilled in a pin-fin heat sink. Research has also been conducted on improving the thermal efficiency by altering the airflow pattern around the heat sink. Li et al. [10] and Park et al. [11] installed a chimney to increase the airflow rate into the heat sink, and Jang et al. [12] improved the cooling performance at various angles by forming slots in an LED bulb. However, the abovementioned studies focus on conditions in which the entire bottom of the heat sink is heated. Given that most energy converters are equipped with high heat sources, it is necessary to study conditions under which heat is applied locally to the heat sink. To solve the issue of local heat application, research has been conducted with a primary focus on cases where the heat source is
Corresponding author. E-mail address: [email protected] (K.-S. Lee).
https://doi.org/10.1016/j.applthermaleng.2019.114458 Received 3 April 2019; Received in revised form 24 September 2019; Accepted 27 September 2019 Available online 27 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature A Dh d H h k L P p Q̇ Rth s T t u V V̇
Greek symbols ω ρ μ
area [m2] hydraulic diameter [m] distance [m] height [m] heat transfer coefficient [W/m2 K] kinetic energy of turbulence [m2/s2]/thermal conductivity [W/m K] length [m] normalized pressure pressure [Pa] heat transfer rate [W] thermal resistance [K/W] space [m] temperature [K] thickness [m] velocity [m/s] normalized volume flow rate volume flow rate [m3/s]
specific dissipation rate [s−1] density [kg/m3] dynamic viscosity [N s/m2]
Subscripts a avg b bot ch eff f h in p t top
air average base bottom channel effective fin heat sink in polyethylene turbulent top
resistance compared to a typical system under the same pumping power conditions. Osanloo et al. [22] found that a channel with a 4° tilt angle yields an optimal thermal performance and pressure drop characteristics. In addition, Hung et al. [23] reduced the thermal resistance by approximately 60% by optimizing the sizes of the upper and lower channels in a crossflow double-layer heat sink, and Zhai et al. [24] formed different cavity zones in two heat sink layers to improve the thermal performance. Furthermore, Shen et al. [25] investigated the cooling performance and pumping power by varying the length and height ratios of the upper to lower channels. The best performance was observed when the ratios of the length and height were 0.4 and 0.6, respectively. Kulkarni et al. [26] optimized three factors in the heat sink channel, proposing Pareto-optimal solutions for the cooling performance and pumping power. However, the abovementioned studies have the limitation that to enhance the cooling performance the shape of the heat sink should be changed, which raises additional issues in
smaller than the heat sink. For example, Maranzana et al. [13] and Ong et al. [14] conducted studies on spreading the heat transfer under local heat flux conditions, and Jo et al. [15] used a heat pipe to improve the heat spreading performance. Anbumeenakshi et al. [16] presented results demonstrating the highest temperature for a heat source located at the inlet of the heat sink, while Kim et al. [17] lowered the temperature of the localized heating region by 30% through the application of a hybrid heat sink shape. Furthermore, Yoon et al. [18,19] optimized the locations of single and multiple heat sources under partial heat conditions, and reduced the thermal resistance by 30% without changing the shape of the heat sink. However, the abovementioned studies only used single heat sinks, and did not address the complexity of multiple heat sinks. The majority of studies on multiple heat sinks have been performed on double-layered microchannel heat sinks. Sarlak et al. [20] and Wang et al. [21] proposed a shape capable of minimizing the thermal
(a) Industrial inverter
(b) Schematic of heat sink arrangement
Fig. 1. Power stack arrangement in an industrial inverter. 2
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terms of the cost and manufacturing processes in most industrial applications. Electronic devices such as the industrial inverter shown in Fig. 1(a) combine several power stacks to make up a single set. Here, each power stack is installed in a cabinet, and the heat sink is positioned without overlap, as shown in Fig. 1(b). As a result, the length in the z-direction increases considerably. Therefore, it is necessary to miniaturize the system by using the existing plate fin heat sink in an overlapping arrangement approach, unlike in a multichannel heat sink, which has a structure of stacked heat sinks. In this study, the space efficiency and cooling performance were maximized through the overlapped heat sink that could be applied immediately, without changing the shape of the heat sink. The pressure drop and thermal behavior of the system were investigated through the characteristic curves of the axial fan, which was mainly utilized under a forced convection condition. In addition, correlations were proposed for the pressure drop and cooling performance for a wide range of applications.
Table 1 Comparison of thermal resistance according to turbulence model.
ρ
Experiment k-ε standard k-ε RNG k-ε realizable k-ω standard k-ω SST
0.0423 0.0281 0.0279 0.0311 0.0403 0.0429
– 33% 34% 26% 5% 2%
∂p ∂ ⎡ ∂ ∂u + (ui uj ) = − (μ + μt ) i ⎤ ∂x i ∂x j ⎢ ∂x i ∂x j ⎥ ⎣ ⎦
(2)
∂ ∂ ⎛ ∂T (ui T ) = + ui (τij )eff ⎞⎟ ⎜k eff ∂x i ∂x j ⎝ ∂x j ⎠
(3)
Here, the thermal resistances were investigated to select the most appropriate turbulence model for this study. The numerical analysis was performed with a Reynolds number of 6000, which is the median of the range covered in this study. As a result, the error was the smallest when the k-ω Shear Stress Transport (SST) model was used, as shown in Table 1. Therefore, this was selected as the reference model.
A numerical analysis was performed on a plate fin heat sink, which is the most commonly used heat sink in industry. As shown in Fig. 2(a), when two heat sinks overlap, the entire bottom surface is heated by the heat flux. Fig. 2(b) shows the numerical domain and periodic conditions for heat sinks of various sizes. For the numerical analysis, the following assumptions were adopted.
(2) Boundary conditions A surface heat flux condition was adopted to mimic the heating element installed in the heat sink. The boundary conditions used in the numerical analysis are summarized in Table 2. A fan characteristic curve was applied to simulate forced convection by an axial fan. Furthermore, the pressure difference between the inlet and outlet of the overlapped heat sink was repeatedly calculated to automatically determine the flow rate according to the fan characteristic curve.
fluid flow is incompressible and in a steady state. properties of air are independent of the temperature. radiation effects are negligible. natural convection effect is negligible.
It should be noted that the effects of natural convection are neglected, because Richardson number (Ri = Gr/Re Dh 2 ) is less than 0.1. In addition, the radiation effects are not considered, because the change in thermal resistance with or without radiation heat transfer is about 1%. The governing equations and boundary conditions are as follows [27].
2.2. Computational methods The same heat sink was used for both the experiment and numerical analysis. The heat sink has a length, base thickness, fin thickness, and fin height of 0.15 m, 0.008 m, 0.003 m, and 0.042 m, respectively. A hexahedron grid was created, and a high-density mesh was used around the solids. The number of elements varied from 170,000 to 2,500,000, and the grid dependence was investigated. The air domain was varied from 1L to 3L toward the flow direction. Furthermore, the air domain in the flow direction, in which the average temperature change in the heating surface is within ± 0.1 °C, was defined as 1.5L. It was determined that 611,000 meshes should be used, with a minimum length of 0.5 mm and a growth rate of 1.2. ANSYS Fluent release 17.0 was used to perform the numerical analysis. The velocity and pressure fields were combined by the SIMPLE method, and the convective terms of the
(1) Governing equations Continuity:
∂ui =0 ∂x i
Error
ρcp
2.1. Mathematical model
The The The The
Thermal resistance (°C/W)
Energy:
2. Numerical modeling
– – – –
Model
(1)
Momentum:
(a) Schematic of overlapped heat sink
(b) Periodic region
Fig. 2. Overlapped heat sink and periodic region. 3
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Table 2 Boundary conditions for numerical analysis.
Table 3 Measurement range and accuracy.
Momentum equation
Energy equation
Periodic face
Periodic condition
∂T ∂η periodic
Inlet Outlet
Pressure inlet Fan characteristic curve –
Tin = Tout , backflow = T∞
No-slip condition
Ta, wall = Th, wall
Heat sink base Interface between solid and fluid
− kh
ka
Thermocouple (type T)
=0
∂Th ∂η base
Wattmeter (CLAMP ON POWER HiTESTER 3169, HIOKI)
Measurement range
Accuracy
Min.: −250 °C Max.: 350 °C Min.: 75 W Max.: 900 kW
± 0.5 °C ± 0.5% rdg.
= q̇
∂Ta ∂η interface
= kh
∂Th ∂η interface
governing equations were calculated using the second-order upwind scheme. In the iterative calculation, the convergence criterion was set as the condition that the relative errors of all governing equations, including turbulent terms, were below 10−5. 3. Experiments and validation As shown in Fig. 3, a constant-temperature chamber and a duct capable of maintaining a constant flow rate were utilized. The test section consists of an extruded plate fin heat sink (thermal conductivity = 200 W/m K) and a heater. The two heat sinks overlapped with each other. Here, because the ducts also varied depending on the overlap ratio, the experiment and verification were conducted for representative cases in which 50% of the fin height was overlapped. It should be noted that the 50% overlap ratio was selected as an intermediate value between 0% and 100%. The heat loss was minimized by installing a 10 mm thick polyethylene layer (thermal conductivity = 0.03 W/m K) under the heater. The heat transfer rate to the heat sink (Qḣ ) was obtained through the following equation, using the temperatures at the bottom and top surfaces of the polyethylene:
̇ Qḣ = Qheater − {kp Ap (Tp, top − Tp, bot )/ tp}
Fig. 4. Numerical and experimental results (kh = 200 W/m K, Qḣ = 300 W , and 50% overlap ratio).
A steady state was assumed when the measured temperature of the heat sink varied by less than 0.1 °C. The temperature was measured using a 0.5 mm thick type-T thermocouple, and data were saved using a device calibrated according to the influence of the electromagnetic field (NI SCXI-1000, 1125). A wattmeter was used to measure the power of the heater.
(4)
Fig. 3. Experimental apparatus. 4
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(a) Reference
(b) Overlapped heat sink
(c) Fan curve Fig. 5. Fan curve characteristics of reference and overlapped heat sinks.
cooling performance can be improved by overlapping the heat sinks in numerous plate fin heat sink configurations and operating environments.
Numerical results were validated through the thermal resistance as a function of the Reynolds number. Here, the thermal resistance was calculated by measuring the average temperature of the upper surface of the base at six points, and the Dh value used in the Reynolds number equation represented the hydraulic diameter of the heat sink channel.
Rth = (Tb, avg
− Ta, in )/ Qḣ
4.1. Analysis of overlapped heat sink effect
(5)
Re Dh = ρa uch, avg Dh / μa
(6)
Dh = 4A/ wetted perimeter
(7)
If multiple heat sinks are installed, then these are usually arranged without overlaps, as shown in Fig. 5(a). Here, the thermal features in the overlapped heat sink shown in Fig. 5(b) were investigated. For forced convection, the condition of the fan (UF300BNA, Fulltech, at a constant speed of 3600 rpm.) with the characteristic curve shown in Fig. 5(c) was applied, and a heat flux of 13,333 W/m2 was applied to the base. It should be noted that the fan power can be slightly different, although its speed remains constant, because of different fan specifications from each manufacturer. Therefore, in this study, we ignored the effects generated by the difference of fan specifications from each manufacturer. As shown in Fig. 5(c), the pressure drop increases owing to the flow resistance increase in the overlapped heat sink. Therefore, the flow rate tends to decrease according to the fan characteristic curve. Normally, if the flow rate decreases the cooling performance also decreases. However, for a 20% overlap ratio the numerical analysis confirms that the flow velocity is higher compared to that of the reference shape, because the cross-sectional area of the heat sink channel decreases, as shown in Fig. 6.
In the experiment, the uncertainty of the thermal resistance was calculated as approximately 6% [28], and the accuracy of the equipment used for validation is presented in Table 3. Fig. 4 depicts the results of the experiment and numerical analysis. The maximum error was approximately 7%, showing that the numerical analysis agreed well with the experimental results. Therefore, the numerical model was validated by comparison with the experimental results. 4. Results and discussion The thermal resistance was investigated by analyzing the thermal behavior of the overlapped heat sink. Here, the temperature used for calculating the thermal resistance was based on the maximum temperature, to protect the heating element. The cooling performance and pressure drop characteristics of the overlapped heat sink were investigated in a universal operating environment, by generalizing the characteristic curves of the axial fans, which are commonly used under forced convection conditions. The results of this study suggest that the
Overlap ratio = (2 − dh/ Hf ) × 100
(8)
Therefore, to investigate the cooling performance corresponding to 5
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(a) Reference
(b) 20% overlap ratio Fig. 6. Internal velocity field of reference and overlapped heat sink channels.
Fig. 8. Thermal resistance as a function of the overlap ratio.
Fig. 7. Nuy according to the y-direction.
effect, the thermal resistance was reduced by 10%, and the system size was also reduced by approximately 20%, as the heat sink fins overlapped.
the increase in the flow velocity, the local Nuy in the y-direction is defined as follows:
Nuy = h y Dh / ka
(9) 4.2. Cooling performance as a function of the overlap ratio
As a result, it is found that the local Nuy along the y-direction is larger than that of the reference shape, as shown in Fig. 7. Under this
In this section, the change in the cooling performance was 6
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▲ (beyond the recommended range) leads to system instability. Therefore, if the increase in the pressure drop owing to the overlap ratio can be predicted, then the cooling performance in the recommended region can be maximized. 4.3. Fan curve normalization The relationship between the pressure drop and flow rate is dependent on the fan system. Therefore, to predict the pressure drop according to the overlap ratio proposed in this study, the pressure drop and flow rate of each characteristic curve were generalized, as shown in Fig. 11(a). Then, the fan characteristic curves of 120 industrial fans were sampled, as shown in Fig. 11(b).
P = (ΔP − ΔPmin )/(ΔPmax − ΔPmin )
(10)
̇ )/(Vmax ̇ − Vmin ̇ ) V = (V̇ − Vmin
(11)
As a result, the recommended region within the generalized fan characteristic curve can be approximated by a linear polynomial (R2 ≥ 0.97), and the slope |dP/dV| converges from approximately 0.8–2.0, as shown in Fig. 11(c).
Fig. 9. Thermal resistance according to the fin thickness ratio and overlap ratio.
investigated for various overlap ratios. A value of 0 represents the reference state for the overlap ratio, while 100 represents the fully overlapping state. As shown in Fig. 8, as the overlap ratio increases the thermal resistance tends to decrease, until it begins to increase again after reaching a certain value. Here, a represents the region where the increase in the heat transfer coefficient is dominant over the decrease in the flow rate as the pressure drop increases. Thus, the cooling performance is improved in this region. However, b is the region where the cooling performance deteriorates owing to the dominant influence of the severe flow rate reduction. Fig. 9 shows the enhancement in the cooling performance in terms of the fin thickness ratio (tf/sf) and overlap ratio. As the fin thickness ratio increases, the cooling performance deteriorates, while the cooling performance improves as the fin thickness ratio decreases. This is attributed to the fact that as the fin thickness ratio increases, the channel flow path is narrowed, which increases the pressure drop and sharply decreases the flow rate. Therefore, there is an optimum overlap ratio, which is dependent on the fan characteristic curve and heat sink configuration. However, the fan curve has a recommended operating region, as shown in Fig. 10 [29]. Here, the characteristic curve reference state position for the nonoverlapped heat sink is marked by ●. By moving from the reference point to ★, the cooling performance in the recommended region can be improved. However, as the overlap ratio increases, moving to the point
(Min. value) 0.8
⩽ |dP / dV | ⩽ 2. 0(Max. value)
(12)
Therefore, the pressure drop characteristics were investigated according to the overlap ratio applicable to the fan characteristic curve in the above range. 4.4. Correlations The pressure drop characteristics and cooling performance according to the overlap ratio depend on the system specifications (heat sink shape and fan characteristic curve). As it is practically impossible to reflect all the system specifications used in industry, the general system specifications and overlap ratios used in the industrial field are provided in Table 4. The design parameters were used to extract the analysis points after dividing them by their levels. The orthogonal array table (L80(41151)) based on the experimental design method was used for numerical analysis. As a result, the cooling performance of the overlapped heat sink was better than that obtained with the reference shape for tf /sf ≤ 0.5. However, the thermal resistance of the overlapped heat sink tended to increase tf /sf ≥ 0.6. This occurs because when the fin thickness ratio is more than 0.6, the cross-sectional area of the channel as a function of the overlap ratio becomes excessively narrow, rapidly reducing the flow
Fig. 10. Fan characteristic curve at various overlapping conditions. 7
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rate. Therefore, the following correlations on the increase in pressure drop and decrease in thermal resistance are proposed for tf /sf ≤ 0.5. C
t f 3 Hf C4 ΔP dP = C1 + C2 ⎛⎜ ⎞⎟ ⎛ ⎞ ⎛⎜C5 ΔPref dV ⎝ sf ⎠ ⎝ L ⎠ ⎝ ⎜
⎟
C6
C8
⎞⎟ exp ⎛ ⎛C ⎛⎜2 − dh ⎟⎞ ⎞ ⎞ ⎜⎜ 7 Hf ⎠ ⎟ ⎟ ⎠ ⎠ ⎠ ⎝⎝ ⎝
(13)
Rth Rth, ref Hf C11 dP = C9 + C10 ⎛ ⎞ ⎛⎜C5 dV ⎝L⎠ ⎝ ⎜
⎟
C17
tf + C16 ⎜⎛ ⎟⎞ ⎝ sf ⎠
(a) Normalized fan curve
C12
C14
⎞⎟ ⎛C ⎜⎛ t f ⎟⎞ ⎜ 13 ⎠ ⎜⎝ ⎝ sf ⎠
C15
⎛⎛ d ⎞ ⎞ exp ⎜ ⎜ ⎛⎜2 − h ⎞⎟ × 100⎟ ⎟ H f ⎠ ⎠ ⎠ ⎝⎝⎝
C
18 ⎛ ⎛ d ⎞ ⎞⎞ exp ⎜−⎜ ⎜⎛2 − h ⎟⎞ × 100⎟ ⎟ ⎟ ⎟ Hf ⎠ ⎠ ⎠⎠ ⎝ ⎝⎝
(14)
The constant values used in the correlation are the following:
C1 = 1.9987 × 10−1, C2 = 7.0510 × 10−3, C3 = 1.6543 × 10−1, C4 = 2.2591 × 10−2, C5 = 1.8861 × 102, C6 = 2.6060 × 10−1, C7 = 1.7681, C8 = 1.3872, C9 = 2.9857, C10 = −1.3158 × 10−2, C11 = −6.9761 × 10−3, C12 = 2.2458 × 10−2, C13 = 2.7006 × 10−1, C14 = −3.7267 × 10−2, C15 = 2.1410 × 10−2, C16 = 4.2598 × 10−1, C17 = 9.4072 × 10−2, C18 = 9.9739 × 10−1 Fig. 12 compares the values calculated through the correlations with the numerical results for the thermal resistance ratios and pressure drop. The correlated and numerical data exhibited an agreement within approximately 20%. The cooling performance was improved by a maximum of 35% when the correlation was applied, and the system volume can be reduced by using the appropriate overlap ratio. These results can be applied to various industrial applications by employing the overlapped arrangements of heat sinks without changing their shapes or the type of fans.
(b) Plot of 120 fan curves
5. Conclusions The pressure drop characteristics and cooling performances of overlapped heat sinks were investigated. A forced convection condition provided by an axial fan was considered. The thermal resistance, which was calculated using the maximum temperature of the heat source, was used to quantify the cooling performance. (1) Investigation of the cooling performance of an overlapped heat sink For the cooling performance of the overlapped heat sink, the pressure drop and flow rate changes occurring along the fan characteristic curve must also be considered. The cooling performance of a heat sink with 20% of the fin height overlapped under the forced convection condition was investigated using the fan characteristic curve. As a result, the heat transfer coefficient increased, and the thermal resistance decreased by approximately 10%, owing to an increase in the flow velocity within the heat sink channel, despite the flow rate decreasing. Furthermore, the volume occupied by the system was reduced by 20%.
(c) Normalized fan curves of (dP/dV)high and (dP/dV)low Fig. 11. Normalized fan curves. Table 4 Design parameters and ranges. Parameters
tf/sf Hf/L |dP / dV | (2 − dh/ Hf ) × 100
Ranges
Level
Min.
Max.
0.1 0.1 0.8 0.0
0.5 0.5 2.0 100
(2) Cooling performance according to the overlap ratio A numerical analysis was performed, ranging from the reference non-overlapped heat sink to the completely overlapped heat sink. The thermal resistance tended to decrease until reaching a specific overlap ratio, after which it began to increase again. Therefore, it is possible to maximize the cooling performance in a given environment if the increase in the pressure drop owing to the overlap ratio can be predicted according to the fan characteristic curve.
4 5 4 5
8
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(b) Pressure drop ratio
(a) Thermal resistance ratio
Fig. 12. Comparison of numerical and correlated data.
(3) Normalization of the fan curves used in the industrial field [6]
We investigated and generalized the fan characteristic curves of 120 industrial axial fans. The slope of the recommended region of the generalized characteristic curve converged to approximately 0.8–2.0.
[7]
(4) Correlation to predict changes in the pressure drop and thermal resistance using the overlap ratio
[8]
Correlations were proposed to predict the pressure drop and cooling performance of the heat sink according to the overlap ratio and multiple parameters (height–length ratio, fin thickness–fin spacing ratio, and slope of the recommended region of the fan characteristic curve). Numerical analysis points were selected based on the experimental design method according to the design range of each variable. The cooling performance was improved by a maximum of 35%, and the size of the system was reduced. These results are expected to improve the space efficiency and cooling performance of electronic equipment in industry, owing to their simple application without changing the shapes of the heat sinks.
[9]
[10]
[11]
[12]
[13]
[14]
Declaration of Competing Interest
[15]
The authors declare that there is no conflict of interest. Acknowledgements
[16]
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20184010201710, No. 20181720201020).
[17]
[18]
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Cooling performance and space efficiency improvement based on heat sink arrangement for power conversion electronics Youngchan Yoona,b, Dong Rip Kima, Kwan-Soo Leea, a b
T
⁎
School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Electric Energy Engineering Team, Hyundai Mobis, 240 Mabuk-ro, Gigeung-gu, Yongin-si, Gyeonggi-do 16891, Republic of Korea
H I GH L IG H T S
overlapped heat sink was investigated for space efficiency and cooling performance improvement. • The confirmed that there was an optimum overlap ratio for maximizing the cooling performance. • ItFanwascharacteristic curves were generalized for the various operating environment. • When the overlapped heat sink is applied, the cooling performance was improved by up to about 35%. •
A R T I C LE I N FO
A B S T R A C T
Keywords: Plate fin heat sink Power conversion electronics cooling Forced convection Space efficiency
A heat sink system was miniaturized, and its cooling performance was improved by overlapping the heat sinks. To simulate an axial fan condition (typically used in air-cooled forced convection), a fan characteristic curve was applied to consider the relationship between the airflow rate and pressure drop. On investigating the cooling performance of the overlapped heat sinks, it was confirmed that the heat transfer coefficient was improved owing to the increase in the velocity inside the channel, even though the flow rate was decreased. In addition, the fan curves were generalized to be applied in various fan environments, and correlations were proposed to predict the pressure drop and cooling performance of the overlapped heat sinks. The correlations reflect the heat sink geometry and fan characteristics of the system. The cooling performance was improved by a maximum of 35%, and the volume occupied by the system decreased when the fins overlapped. This suggests the proposed method can maximize the space efficiency and improve the cooling performance in a given environment without changing the geometry of the heat sink.
1. Introduction In electronic power equipment, such as industrial inverters, heat is primarily generated in semiconductor devices, such as metal-oxide semiconductor field-effect transistors (MOSFETs) or insulated-gate bipolar transistors (IGBTs). These semiconductor devices are highly vulnerable to degradation at high temperatures. Therefore, MOSFETs or IGBTs are installed in cooling devices, such as heat sinks, to keep them below the maximum allowed temperature through forced cooling or natural convection [1]. To improve the cooling performance of heat sinks for heating elements, numerous studies have been conducted concerning the shape of the heat sink fin and channel [2–5]. Joo et al. [6] proposed a topology optimization technique to reduce the thermal resistance by 13%. Furthermore, Park et al. [7] and Bello-Ochende et al. [8] improved the heat
⁎
transfer coefficient by approximately 10% by changing the fin arrangement. In addition, Sakanova et al. [9] was able to reduce the heat resistance by approximately 20% and reduce the weight by applying a perforated fin drilled in a pin-fin heat sink. Research has also been conducted on improving the thermal efficiency by altering the airflow pattern around the heat sink. Li et al. [10] and Park et al. [11] installed a chimney to increase the airflow rate into the heat sink, and Jang et al. [12] improved the cooling performance at various angles by forming slots in an LED bulb. However, the abovementioned studies focus on conditions in which the entire bottom of the heat sink is heated. Given that most energy converters are equipped with high heat sources, it is necessary to study conditions under which heat is applied locally to the heat sink. To solve the issue of local heat application, research has been conducted with a primary focus on cases where the heat source is
Corresponding author. E-mail address: [email protected] (K.-S. Lee).
https://doi.org/10.1016/j.applthermaleng.2019.114458 Received 3 April 2019; Received in revised form 24 September 2019; Accepted 27 September 2019 Available online 27 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature A Dh d H h k L P p Q̇ Rth s T t u V V̇
Greek symbols ω ρ μ
area [m2] hydraulic diameter [m] distance [m] height [m] heat transfer coefficient [W/m2 K] kinetic energy of turbulence [m2/s2]/thermal conductivity [W/m K] length [m] normalized pressure pressure [Pa] heat transfer rate [W] thermal resistance [K/W] space [m] temperature [K] thickness [m] velocity [m/s] normalized volume flow rate volume flow rate [m3/s]
specific dissipation rate [s−1] density [kg/m3] dynamic viscosity [N s/m2]
Subscripts a avg b bot ch eff f h in p t top
air average base bottom channel effective fin heat sink in polyethylene turbulent top
resistance compared to a typical system under the same pumping power conditions. Osanloo et al. [22] found that a channel with a 4° tilt angle yields an optimal thermal performance and pressure drop characteristics. In addition, Hung et al. [23] reduced the thermal resistance by approximately 60% by optimizing the sizes of the upper and lower channels in a crossflow double-layer heat sink, and Zhai et al. [24] formed different cavity zones in two heat sink layers to improve the thermal performance. Furthermore, Shen et al. [25] investigated the cooling performance and pumping power by varying the length and height ratios of the upper to lower channels. The best performance was observed when the ratios of the length and height were 0.4 and 0.6, respectively. Kulkarni et al. [26] optimized three factors in the heat sink channel, proposing Pareto-optimal solutions for the cooling performance and pumping power. However, the abovementioned studies have the limitation that to enhance the cooling performance the shape of the heat sink should be changed, which raises additional issues in
smaller than the heat sink. For example, Maranzana et al. [13] and Ong et al. [14] conducted studies on spreading the heat transfer under local heat flux conditions, and Jo et al. [15] used a heat pipe to improve the heat spreading performance. Anbumeenakshi et al. [16] presented results demonstrating the highest temperature for a heat source located at the inlet of the heat sink, while Kim et al. [17] lowered the temperature of the localized heating region by 30% through the application of a hybrid heat sink shape. Furthermore, Yoon et al. [18,19] optimized the locations of single and multiple heat sources under partial heat conditions, and reduced the thermal resistance by 30% without changing the shape of the heat sink. However, the abovementioned studies only used single heat sinks, and did not address the complexity of multiple heat sinks. The majority of studies on multiple heat sinks have been performed on double-layered microchannel heat sinks. Sarlak et al. [20] and Wang et al. [21] proposed a shape capable of minimizing the thermal
(a) Industrial inverter
(b) Schematic of heat sink arrangement
Fig. 1. Power stack arrangement in an industrial inverter. 2
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terms of the cost and manufacturing processes in most industrial applications. Electronic devices such as the industrial inverter shown in Fig. 1(a) combine several power stacks to make up a single set. Here, each power stack is installed in a cabinet, and the heat sink is positioned without overlap, as shown in Fig. 1(b). As a result, the length in the z-direction increases considerably. Therefore, it is necessary to miniaturize the system by using the existing plate fin heat sink in an overlapping arrangement approach, unlike in a multichannel heat sink, which has a structure of stacked heat sinks. In this study, the space efficiency and cooling performance were maximized through the overlapped heat sink that could be applied immediately, without changing the shape of the heat sink. The pressure drop and thermal behavior of the system were investigated through the characteristic curves of the axial fan, which was mainly utilized under a forced convection condition. In addition, correlations were proposed for the pressure drop and cooling performance for a wide range of applications.
Table 1 Comparison of thermal resistance according to turbulence model.
ρ
Experiment k-ε standard k-ε RNG k-ε realizable k-ω standard k-ω SST
0.0423 0.0281 0.0279 0.0311 0.0403 0.0429
– 33% 34% 26% 5% 2%
∂p ∂ ⎡ ∂ ∂u + (ui uj ) = − (μ + μt ) i ⎤ ∂x i ∂x j ⎢ ∂x i ∂x j ⎥ ⎣ ⎦
(2)
∂ ∂ ⎛ ∂T (ui T ) = + ui (τij )eff ⎞⎟ ⎜k eff ∂x i ∂x j ⎝ ∂x j ⎠
(3)
Here, the thermal resistances were investigated to select the most appropriate turbulence model for this study. The numerical analysis was performed with a Reynolds number of 6000, which is the median of the range covered in this study. As a result, the error was the smallest when the k-ω Shear Stress Transport (SST) model was used, as shown in Table 1. Therefore, this was selected as the reference model.
A numerical analysis was performed on a plate fin heat sink, which is the most commonly used heat sink in industry. As shown in Fig. 2(a), when two heat sinks overlap, the entire bottom surface is heated by the heat flux. Fig. 2(b) shows the numerical domain and periodic conditions for heat sinks of various sizes. For the numerical analysis, the following assumptions were adopted.
(2) Boundary conditions A surface heat flux condition was adopted to mimic the heating element installed in the heat sink. The boundary conditions used in the numerical analysis are summarized in Table 2. A fan characteristic curve was applied to simulate forced convection by an axial fan. Furthermore, the pressure difference between the inlet and outlet of the overlapped heat sink was repeatedly calculated to automatically determine the flow rate according to the fan characteristic curve.
fluid flow is incompressible and in a steady state. properties of air are independent of the temperature. radiation effects are negligible. natural convection effect is negligible.
It should be noted that the effects of natural convection are neglected, because Richardson number (Ri = Gr/Re Dh 2 ) is less than 0.1. In addition, the radiation effects are not considered, because the change in thermal resistance with or without radiation heat transfer is about 1%. The governing equations and boundary conditions are as follows [27].
2.2. Computational methods The same heat sink was used for both the experiment and numerical analysis. The heat sink has a length, base thickness, fin thickness, and fin height of 0.15 m, 0.008 m, 0.003 m, and 0.042 m, respectively. A hexahedron grid was created, and a high-density mesh was used around the solids. The number of elements varied from 170,000 to 2,500,000, and the grid dependence was investigated. The air domain was varied from 1L to 3L toward the flow direction. Furthermore, the air domain in the flow direction, in which the average temperature change in the heating surface is within ± 0.1 °C, was defined as 1.5L. It was determined that 611,000 meshes should be used, with a minimum length of 0.5 mm and a growth rate of 1.2. ANSYS Fluent release 17.0 was used to perform the numerical analysis. The velocity and pressure fields were combined by the SIMPLE method, and the convective terms of the
(1) Governing equations Continuity:
∂ui =0 ∂x i
Error
ρcp
2.1. Mathematical model
The The The The
Thermal resistance (°C/W)
Energy:
2. Numerical modeling
– – – –
Model
(1)
Momentum:
(a) Schematic of overlapped heat sink
(b) Periodic region
Fig. 2. Overlapped heat sink and periodic region. 3
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Table 2 Boundary conditions for numerical analysis.
Table 3 Measurement range and accuracy.
Momentum equation
Energy equation
Periodic face
Periodic condition
∂T ∂η periodic
Inlet Outlet
Pressure inlet Fan characteristic curve –
Tin = Tout , backflow = T∞
No-slip condition
Ta, wall = Th, wall
Heat sink base Interface between solid and fluid
− kh
ka
Thermocouple (type T)
=0
∂Th ∂η base
Wattmeter (CLAMP ON POWER HiTESTER 3169, HIOKI)
Measurement range
Accuracy
Min.: −250 °C Max.: 350 °C Min.: 75 W Max.: 900 kW
± 0.5 °C ± 0.5% rdg.
= q̇
∂Ta ∂η interface
= kh
∂Th ∂η interface
governing equations were calculated using the second-order upwind scheme. In the iterative calculation, the convergence criterion was set as the condition that the relative errors of all governing equations, including turbulent terms, were below 10−5. 3. Experiments and validation As shown in Fig. 3, a constant-temperature chamber and a duct capable of maintaining a constant flow rate were utilized. The test section consists of an extruded plate fin heat sink (thermal conductivity = 200 W/m K) and a heater. The two heat sinks overlapped with each other. Here, because the ducts also varied depending on the overlap ratio, the experiment and verification were conducted for representative cases in which 50% of the fin height was overlapped. It should be noted that the 50% overlap ratio was selected as an intermediate value between 0% and 100%. The heat loss was minimized by installing a 10 mm thick polyethylene layer (thermal conductivity = 0.03 W/m K) under the heater. The heat transfer rate to the heat sink (Qḣ ) was obtained through the following equation, using the temperatures at the bottom and top surfaces of the polyethylene:
̇ Qḣ = Qheater − {kp Ap (Tp, top − Tp, bot )/ tp}
Fig. 4. Numerical and experimental results (kh = 200 W/m K, Qḣ = 300 W , and 50% overlap ratio).
A steady state was assumed when the measured temperature of the heat sink varied by less than 0.1 °C. The temperature was measured using a 0.5 mm thick type-T thermocouple, and data were saved using a device calibrated according to the influence of the electromagnetic field (NI SCXI-1000, 1125). A wattmeter was used to measure the power of the heater.
(4)
Fig. 3. Experimental apparatus. 4
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(a) Reference
(b) Overlapped heat sink
(c) Fan curve Fig. 5. Fan curve characteristics of reference and overlapped heat sinks.
cooling performance can be improved by overlapping the heat sinks in numerous plate fin heat sink configurations and operating environments.
Numerical results were validated through the thermal resistance as a function of the Reynolds number. Here, the thermal resistance was calculated by measuring the average temperature of the upper surface of the base at six points, and the Dh value used in the Reynolds number equation represented the hydraulic diameter of the heat sink channel.
Rth = (Tb, avg
− Ta, in )/ Qḣ
4.1. Analysis of overlapped heat sink effect
(5)
Re Dh = ρa uch, avg Dh / μa
(6)
Dh = 4A/ wetted perimeter
(7)
If multiple heat sinks are installed, then these are usually arranged without overlaps, as shown in Fig. 5(a). Here, the thermal features in the overlapped heat sink shown in Fig. 5(b) were investigated. For forced convection, the condition of the fan (UF300BNA, Fulltech, at a constant speed of 3600 rpm.) with the characteristic curve shown in Fig. 5(c) was applied, and a heat flux of 13,333 W/m2 was applied to the base. It should be noted that the fan power can be slightly different, although its speed remains constant, because of different fan specifications from each manufacturer. Therefore, in this study, we ignored the effects generated by the difference of fan specifications from each manufacturer. As shown in Fig. 5(c), the pressure drop increases owing to the flow resistance increase in the overlapped heat sink. Therefore, the flow rate tends to decrease according to the fan characteristic curve. Normally, if the flow rate decreases the cooling performance also decreases. However, for a 20% overlap ratio the numerical analysis confirms that the flow velocity is higher compared to that of the reference shape, because the cross-sectional area of the heat sink channel decreases, as shown in Fig. 6.
In the experiment, the uncertainty of the thermal resistance was calculated as approximately 6% [28], and the accuracy of the equipment used for validation is presented in Table 3. Fig. 4 depicts the results of the experiment and numerical analysis. The maximum error was approximately 7%, showing that the numerical analysis agreed well with the experimental results. Therefore, the numerical model was validated by comparison with the experimental results. 4. Results and discussion The thermal resistance was investigated by analyzing the thermal behavior of the overlapped heat sink. Here, the temperature used for calculating the thermal resistance was based on the maximum temperature, to protect the heating element. The cooling performance and pressure drop characteristics of the overlapped heat sink were investigated in a universal operating environment, by generalizing the characteristic curves of the axial fans, which are commonly used under forced convection conditions. The results of this study suggest that the
Overlap ratio = (2 − dh/ Hf ) × 100
(8)
Therefore, to investigate the cooling performance corresponding to 5
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(a) Reference
(b) 20% overlap ratio Fig. 6. Internal velocity field of reference and overlapped heat sink channels.
Fig. 8. Thermal resistance as a function of the overlap ratio.
Fig. 7. Nuy according to the y-direction.
effect, the thermal resistance was reduced by 10%, and the system size was also reduced by approximately 20%, as the heat sink fins overlapped.
the increase in the flow velocity, the local Nuy in the y-direction is defined as follows:
Nuy = h y Dh / ka
(9) 4.2. Cooling performance as a function of the overlap ratio
As a result, it is found that the local Nuy along the y-direction is larger than that of the reference shape, as shown in Fig. 7. Under this
In this section, the change in the cooling performance was 6
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▲ (beyond the recommended range) leads to system instability. Therefore, if the increase in the pressure drop owing to the overlap ratio can be predicted, then the cooling performance in the recommended region can be maximized. 4.3. Fan curve normalization The relationship between the pressure drop and flow rate is dependent on the fan system. Therefore, to predict the pressure drop according to the overlap ratio proposed in this study, the pressure drop and flow rate of each characteristic curve were generalized, as shown in Fig. 11(a). Then, the fan characteristic curves of 120 industrial fans were sampled, as shown in Fig. 11(b).
P = (ΔP − ΔPmin )/(ΔPmax − ΔPmin )
(10)
̇ )/(Vmax ̇ − Vmin ̇ ) V = (V̇ − Vmin
(11)
As a result, the recommended region within the generalized fan characteristic curve can be approximated by a linear polynomial (R2 ≥ 0.97), and the slope |dP/dV| converges from approximately 0.8–2.0, as shown in Fig. 11(c).
Fig. 9. Thermal resistance according to the fin thickness ratio and overlap ratio.
investigated for various overlap ratios. A value of 0 represents the reference state for the overlap ratio, while 100 represents the fully overlapping state. As shown in Fig. 8, as the overlap ratio increases the thermal resistance tends to decrease, until it begins to increase again after reaching a certain value. Here, a represents the region where the increase in the heat transfer coefficient is dominant over the decrease in the flow rate as the pressure drop increases. Thus, the cooling performance is improved in this region. However, b is the region where the cooling performance deteriorates owing to the dominant influence of the severe flow rate reduction. Fig. 9 shows the enhancement in the cooling performance in terms of the fin thickness ratio (tf/sf) and overlap ratio. As the fin thickness ratio increases, the cooling performance deteriorates, while the cooling performance improves as the fin thickness ratio decreases. This is attributed to the fact that as the fin thickness ratio increases, the channel flow path is narrowed, which increases the pressure drop and sharply decreases the flow rate. Therefore, there is an optimum overlap ratio, which is dependent on the fan characteristic curve and heat sink configuration. However, the fan curve has a recommended operating region, as shown in Fig. 10 [29]. Here, the characteristic curve reference state position for the nonoverlapped heat sink is marked by ●. By moving from the reference point to ★, the cooling performance in the recommended region can be improved. However, as the overlap ratio increases, moving to the point
(Min. value) 0.8
⩽ |dP / dV | ⩽ 2. 0(Max. value)
(12)
Therefore, the pressure drop characteristics were investigated according to the overlap ratio applicable to the fan characteristic curve in the above range. 4.4. Correlations The pressure drop characteristics and cooling performance according to the overlap ratio depend on the system specifications (heat sink shape and fan characteristic curve). As it is practically impossible to reflect all the system specifications used in industry, the general system specifications and overlap ratios used in the industrial field are provided in Table 4. The design parameters were used to extract the analysis points after dividing them by their levels. The orthogonal array table (L80(41151)) based on the experimental design method was used for numerical analysis. As a result, the cooling performance of the overlapped heat sink was better than that obtained with the reference shape for tf /sf ≤ 0.5. However, the thermal resistance of the overlapped heat sink tended to increase tf /sf ≥ 0.6. This occurs because when the fin thickness ratio is more than 0.6, the cross-sectional area of the channel as a function of the overlap ratio becomes excessively narrow, rapidly reducing the flow
Fig. 10. Fan characteristic curve at various overlapping conditions. 7
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rate. Therefore, the following correlations on the increase in pressure drop and decrease in thermal resistance are proposed for tf /sf ≤ 0.5. C
t f 3 Hf C4 ΔP dP = C1 + C2 ⎛⎜ ⎞⎟ ⎛ ⎞ ⎛⎜C5 ΔPref dV ⎝ sf ⎠ ⎝ L ⎠ ⎝ ⎜
⎟
C6
C8
⎞⎟ exp ⎛ ⎛C ⎛⎜2 − dh ⎟⎞ ⎞ ⎞ ⎜⎜ 7 Hf ⎠ ⎟ ⎟ ⎠ ⎠ ⎠ ⎝⎝ ⎝
(13)
Rth Rth, ref Hf C11 dP = C9 + C10 ⎛ ⎞ ⎛⎜C5 dV ⎝L⎠ ⎝ ⎜
⎟
C17
tf + C16 ⎜⎛ ⎟⎞ ⎝ sf ⎠
(a) Normalized fan curve
C12
C14
⎞⎟ ⎛C ⎜⎛ t f ⎟⎞ ⎜ 13 ⎠ ⎜⎝ ⎝ sf ⎠
C15
⎛⎛ d ⎞ ⎞ exp ⎜ ⎜ ⎛⎜2 − h ⎞⎟ × 100⎟ ⎟ H f ⎠ ⎠ ⎠ ⎝⎝⎝
C
18 ⎛ ⎛ d ⎞ ⎞⎞ exp ⎜−⎜ ⎜⎛2 − h ⎟⎞ × 100⎟ ⎟ ⎟ ⎟ Hf ⎠ ⎠ ⎠⎠ ⎝ ⎝⎝
(14)
The constant values used in the correlation are the following:
C1 = 1.9987 × 10−1, C2 = 7.0510 × 10−3, C3 = 1.6543 × 10−1, C4 = 2.2591 × 10−2, C5 = 1.8861 × 102, C6 = 2.6060 × 10−1, C7 = 1.7681, C8 = 1.3872, C9 = 2.9857, C10 = −1.3158 × 10−2, C11 = −6.9761 × 10−3, C12 = 2.2458 × 10−2, C13 = 2.7006 × 10−1, C14 = −3.7267 × 10−2, C15 = 2.1410 × 10−2, C16 = 4.2598 × 10−1, C17 = 9.4072 × 10−2, C18 = 9.9739 × 10−1 Fig. 12 compares the values calculated through the correlations with the numerical results for the thermal resistance ratios and pressure drop. The correlated and numerical data exhibited an agreement within approximately 20%. The cooling performance was improved by a maximum of 35% when the correlation was applied, and the system volume can be reduced by using the appropriate overlap ratio. These results can be applied to various industrial applications by employing the overlapped arrangements of heat sinks without changing their shapes or the type of fans.
(b) Plot of 120 fan curves
5. Conclusions The pressure drop characteristics and cooling performances of overlapped heat sinks were investigated. A forced convection condition provided by an axial fan was considered. The thermal resistance, which was calculated using the maximum temperature of the heat source, was used to quantify the cooling performance. (1) Investigation of the cooling performance of an overlapped heat sink For the cooling performance of the overlapped heat sink, the pressure drop and flow rate changes occurring along the fan characteristic curve must also be considered. The cooling performance of a heat sink with 20% of the fin height overlapped under the forced convection condition was investigated using the fan characteristic curve. As a result, the heat transfer coefficient increased, and the thermal resistance decreased by approximately 10%, owing to an increase in the flow velocity within the heat sink channel, despite the flow rate decreasing. Furthermore, the volume occupied by the system was reduced by 20%.
(c) Normalized fan curves of (dP/dV)high and (dP/dV)low Fig. 11. Normalized fan curves. Table 4 Design parameters and ranges. Parameters
tf/sf Hf/L |dP / dV | (2 − dh/ Hf ) × 100
Ranges
Level
Min.
Max.
0.1 0.1 0.8 0.0
0.5 0.5 2.0 100
(2) Cooling performance according to the overlap ratio A numerical analysis was performed, ranging from the reference non-overlapped heat sink to the completely overlapped heat sink. The thermal resistance tended to decrease until reaching a specific overlap ratio, after which it began to increase again. Therefore, it is possible to maximize the cooling performance in a given environment if the increase in the pressure drop owing to the overlap ratio can be predicted according to the fan characteristic curve.
4 5 4 5
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(b) Pressure drop ratio
(a) Thermal resistance ratio
Fig. 12. Comparison of numerical and correlated data.
(3) Normalization of the fan curves used in the industrial field [6]
We investigated and generalized the fan characteristic curves of 120 industrial axial fans. The slope of the recommended region of the generalized characteristic curve converged to approximately 0.8–2.0.
[7]
(4) Correlation to predict changes in the pressure drop and thermal resistance using the overlap ratio
[8]
Correlations were proposed to predict the pressure drop and cooling performance of the heat sink according to the overlap ratio and multiple parameters (height–length ratio, fin thickness–fin spacing ratio, and slope of the recommended region of the fan characteristic curve). Numerical analysis points were selected based on the experimental design method according to the design range of each variable. The cooling performance was improved by a maximum of 35%, and the size of the system was reduced. These results are expected to improve the space efficiency and cooling performance of electronic equipment in industry, owing to their simple application without changing the shapes of the heat sinks.
[9]
[10]
[11]
[12]
[13]
[14]
Declaration of Competing Interest
[15]
The authors declare that there is no conflict of interest. Acknowledgements
[16]
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20184010201710, No. 20181720201020).
[17]
[18]
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