- Email: [email protected]
Thermal performance improvement based on the partial heating position of a heat sink
International Journal of Heat and Mass Transfer 124 (2018) 752–760
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal performance improvement based on the partial heating position of a heat sink Youngchan Yoon a, Seung-Jae Park a,b, Dong Rip Kim a, Kwan-Soo Lee a,⇑ a b
School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Korea Institute for Defense Analyses, 37, Hoegi-ro, Dongdaemun-gu, Seoul 02455, Republic of Korea
a r t i c l e
i n f o
Article history: Received 10 January 2018 Received in revised form 22 March 2018 Accepted 23 March 2018
Keywords: Electronic cooling Heat sink Forced convection Partial heating
a b s t r a c t The thermal performance of a heat sink is analyzed according to the position of the partially heated surface. Numerical models for simulating forced convection were used to analyze the heat transfer between the heat sink and ambient air. The optimal partial heating position was discussed in terms of the effects of total heat transfer rate, air velocity, the ratio of total heat sink length to partially heated surface width, the thermal conductivity of the heat sink, and the thickness of the heat sink base. Finally, a correlation was suggested to determine the partial heating position that maximizes thermal performance by using the experimental design method. It was thus possible to reduce the thermal resistance of the heat sink by up to approximately 30% by finding the optimal partial heating position. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction As the performance of electronic devices improves, the amount of heat generation increases, which negatively impacts their performances. For the effective cooling of electronic devices, Joo et al. [1] optimized the fin geometry and compared the thermal performance, and Li et al. [2] promoted natural convective air flow by using a perforated heat sink. Many researchers have also improved thermal performance by changing the geometry of the heat sink [3–7] and by using surrounding structures [8–11]. The heating conditions of the studies described above are the case where heat is applied to the bottom parts of the heat sink. However, in the case of power electronic devices, the size of the heat sink is typically larger than the size of the heating element due to high heat generation. An insulated gate bipolar mode transistor (IGBT) is a typical example, as shown in Fig. 1. In the case of this partial heating condition, the above-mentioned geometric shape change or the use of surrounding structures cannot be directly applied because the temperature distribution and heat transfer characteristics of the heat sink are different. The effective cooling method of partial heating conditions has been studied by several researchers, mainly using microchannel heat sinks. In microchannel heat sinks, since the heat exchanging area is relatively small, nanofluids are mainly used as a working fluid to ensure heat transfer performance [12]. Toh et al. [13] ⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee). https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.080 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
studied the position of the maximum temperature in the microchannel heat sink under partial heating conditions. Sudhakar et al. [14] studied the transient temperature response of the microchannel heat sink under partial heating conditions, and Yoon et al. [15] found that the thermal performance was better in pin-fin than in strip-fin of the microchannel heat sink for the partial heating case. However, none of them investigated how the thermal performance can vary with the partial heating position in spite of their importance in improving the cooling performance. According to Cho et al. [16], a microchannel heat sink with a trapezoidal header has the highest temperature when the heater is located upstream. However, this is due to the flow distribution difference according to the header shape. Therefore, it cannot be generalized that the thermal performance is always poor when the heater is located at the upstream of the heat sink. In the studies by Anbumeenakshi et al. [17] and Lelea et al. [18], the thermal resistance had the smallest value when the heater was located at the upstream of the microchannel heat sink. However, the base thickness used in these studies was on the microscale, and the effects of axial heat conduction of the heat sink base are different in macroscale heat sinks. Therefore, in a macroscale heat sink, the thermal resistance is not always low when the heater is located at the upstream. In addition, all of the studies mentioned above utilized water or various nanofluids as the working fluid. Therefore, it is necessary to study the cooling system of a macroscale heat sink that uses air as a working fluid in the partial heating condition.
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
753
Nomenclature A Dh H h k L N p
q_ Q_ Rth s T t u
surface area [mm2] hydraulic diameter [mm] height [mm] convective heat transfer coefficient [W/m2 K] kinetic energy of turbulence [m2/s2]/thermal conductivity [W/m K] length [mm] number of fin arrays pressure [Pa] heat flux [W/m2] heat transfer rate [W] thermal resistance [°C/W] space [mm] temperature [°C] thickness [mm] velocity [m/s]
Greek symbols g normal direction vector q density [kg/m3]
dynamic viscosity [N s/m2] specific dissipation rate [s1]
l x
Subscripts a air avg average b base bot bottom ch channel eff effective f fin h heat sink in in p polyethylene t turbulent top top u upstream 1 ambient
Finally, a correlation was suggested to predict the optimal partial heating position to minimize the thermal resistance of the heat sink under various operating conditions by using the design of experiments method.
2. Mathematical modeling 2.1. Numerical model
Fig. 1. IGBT cooling system in an industrial inverter.
Emekwuru et al. [19] performed a numerical analysis by dividing the position of the partially heated surface into three positions (upstream, center, and downstream) for an air-cooled heat sink. The study found that the thermal resistance of the heat sink was the lowest when the partially heated surface was located at the center. However, since the partial heating position was limited to only three positions, the central position cannot be the optimum position. In addition, the average temperature of the entire heat sink was used as a measure of thermal performance. However, this limits the accurate evaluation of the optimal cooling of a macroscale heat sink for the partial heating condition because the heat sink typically has a large temperature distribution. In this study, the thermal performance of an air-cooled macroscale heat sink was numerically investigated in terms of the position of partial heating in the heat sink after verifying the numerical model with experiments. Here, the temperature used to calculate the thermal resistance of the heat sink is not the average temperature of the heat sink but the average temperature of the partially heated surface, which is suitable for power electronic device cooling in industrial fields. The effects of various factors, such as the total heat transfer rate, the velocity of the air, the ratio of total heat sink length to partially heated surface width, the thermal conductivity of the heat sink, and the thickness of the heat sink base, on the optimal partial heating position were investigated.
Fig. 2 illustrates the heat sink and the heater used in this study. The heat sink consisted of a fin and a base, with the top, left, and right sides making a physically closed system. The following assumptions were applied for the numerical analysis. (1) (2) (3) (4)
The flow is three-dimensional and steady state. The air properties do not change with temperature. Radiative heat transfer of the heat sink can be neglected. Heat transfer occurs only in the air and the heat sinks, and there is no heat transfer on the top and the sides surrounding the heat sink.
The governing equations used in the numerical analysis were as follows, and the shear stress transport (SST) k x model was used for turbulent flow. Validation of the numerical analysis and selection of the turbulence model are described in Section 2.3.
Fig. 2. Schematic of the heat sink.
754
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
Continuity:
2.2. Numerical method
@ðqui Þ ¼0 @xi
ð1Þ
Momentum:
@ @p @ @ui ðqui uj Þ ¼ þ ðl þ lt Þ @xi @xi @xj @xj Turbulent kinetic energy:
@ @ ðqkui Þ ¼ @xj @xj
lþ
lt @k þ Gk Y k rk @xj
Specific dissipation rate:
@ @ ðqxuj Þ ¼ @xj @xj
lþ
ð2Þ
ð3Þ
lt @ x þ Gx Y x þ Dx rx @xj
ð4Þ
Energy:
@ @ @T ðui qcp TÞ ¼ keff þ ui ðsij Þeff @xi @xj @xj
ð5Þ
where rk and rx are the turbulent Prandtl numbers for k and x. Gk and Gx are the production of turbulence kinetic energy and generation of x, respectively. Y k and Y x are the dissipation terms of k and x, and Dx is the cross diffusion term [20].
Gk ¼ qu0i u0j
@uj aa 0 0 @uj ; Gx ¼ qui uj @xi mt @xi
Y k ¼ qb kx; Y x ¼ qbf b x Dx ¼ 2ð1 F 1 Þq
lt ¼
1
xrx;2
2
@k @ x @xj @xj
qk 1 h i x max 1 ; SF 2 a
ðsij Þeff ¼ leff
Fig. 3 shows the model used for the numerical analysis. The geometric parameters were N = 14, tf = 3 mm, tb = 8 mm, L = 150 mm, Hh = 50 mm, and w = 60 mm. A partial heat flux condition was applied to the bottom surface of the base to simulate the heater. Considering the required computational time and number of grids, only half of the heat sink was used as the computational domain based on the symmetry condition. ANSYS MESH was used to generate hexahedral meshes. The grid dependence changed the number of meshes from 200,075 to 2,622,815, and the air domain changed from 0.5 L to 1.5 L for the heat sink air inlet and outlet, respectively. At this time, the reference mesh number was set to 1,416,000, where the relative error of the heat sink average temperature change was within 1%, and the air domain in the inlet/ outlet direction was set to 1 L. Numerical analysis was performed using ANSYS Fluent release 17.0, a commercial computational fluid dynamics (CFD) analysis program, using a finite volume method. The SIMPLE algorithm was chosen to solve the flow field by combining velocity and pressure during the numerical analysis. The convective terms and energy equations of each governing equation were discretized using a second-order upwind scheme to improve accuracy. The dependent variables in the iterative calculation were determined to have converged when the maximum relative error
ð6Þ ð7Þ ð8Þ
Table 1 Boundary conditions of numerical method. Boundary conditions
Momentum
Thermal
Air domain
Velocity inlet/pressure outlet condition ui = 0
Tin = 25 °C
Heat sink domain
ð9Þ
Insulated wall domain Symmetric face
a1 x
ui = 0 (no-slip condition) @u ¼0 @ g symmetric face
@uj @ui 2 @uk leff þ dij 3 @xi @xj @xk
ð10Þ
Interface between air and heat sink domain
Fig. 3. Domain for the numerical analysis.
ui = 0 (no-slip condition)
h _ kh @T @ g b;heating region ¼ q @T ¼ 0 (adiabatic) @g
wall
@T @ gsymmetric face
¼0
Ta,wall = Th,wall a h ka @T ¼ kh @T @g @g wall
wall
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
of the dependent variable was less than 105 for all governing equations. The boundary conditions used in the numerical analysis are shown in Table 1. 2.3. Experiment and validation As shown in Fig. 4, a chamber was used for forced convection, and air with a constant temperature and velocity was flown into the test section. The test section consisted of a heat sink, a heater, and a duct surrounding the heat sink, as shown in Fig. 5. The heat sink was an extruded heat sink made of aluminum alloy 6063 (kh = 200 W/m K). The geometry of the heat sink was the same as that used for the numerical analysis, and the duct around the heat sink was insulated using polyethylene insulation (kp = 0.03 W/m K). In order to maximize the amount of heat transferred from the heater to the heat sink, insulation (kp = 0.03 W/m K, tp = 20 mm) was installed around the heater, and the amount of heat transferred to the heat sink (Q_ h ) was calculated using the following equation by measuring the top and bottom temperature of the insulation.
T p;top T p;bot Q_ h ¼ Q_ in kp Ap tp
ð11Þ
The temperature was measured using a thermocouple (type-T, gauge 36) and a data acquisition device (NI 9213, cDAQ-9178). The steady state temperature was considered to be when the temperature change of the heat sink was less than 0.1 °C. The heater power was controlled by a Slidac transformer, and the power consumption was measured using a wattmeter (CLAMP ON POWER HiTESTER, HIOKI). Here, the accuracy of the thermocouple and wattmeter is ±0.5 °C and ±0.5% rdg., respectively. The numerical and experimental results were compared using the thermal resistance of the heat sink according to the Reynolds number variation when the heater is located at the center of the heat sink base. In addition, Q_ h = 100 W was applied to simulate medium size power electronics.
Rth;b ¼
T b;av g T 1 Q_ h
ð12Þ
ReDh ¼
qa uch;av g Dh la
755
ð13Þ
When a thermocouple is installed between the heater and the contact surface of the heat sink, an air gap can be formed due to the thickness of the thermocouple, which leads to the issue that the heat from the heater cannot be effectively transferred to the heat sink. Therefore, as shown in Fig. 5, the average temperature measured at the upper surface of the base where the heater was installed (Tb,avg) was used to calculate the thermal resistance. qa is the density of the air, la is the viscosity coefficient of the air, uch;av g is the average velocity of air in the heat sink channel, and Dh is the hydraulic diameter of the heat sink channel and is equivalent to
2ðsf Hf Þ sf þHf
in Fig. 3. The maximum uncertainty of the thermal
resistance in this experiment is approximately 5.1% [21]. As shown in Table 2, among the turbulence models used for the numerical analysis, the smallest error was found for the k-x SST model. This agrees well with the fact that the k-x SST model is commonly used for forced convection conditions in heat sinks [22,23]. Therefore, this was used as the reference model. Fig. 6 shows the verification results of the numerical model with experiments. The maximum error was within approximately 5%, showing that the numerical analysis was in good agreement with the experimental results. 3. Results and discussion The thermal performance of the heat sink under partial heating was investigated by combining the results of conduction in the heat sink and convective heat transfer to the air. The conductive and convective heat transfers are maximized when the partial heating is applied to different locations within the limited dimensions of rectangular heat sinks Therefore, there will be an optimal position for maximizing the thermal performance with respect to both the conductive and convective heat transfer. The optimal partial heating positions were suggested for a variety of operating conditions. To find this optimal position, the thermal performance of the heat sink was investigated based on the partial heating position. The average temperature of the partially heated surface, not the
Fig. 4. Constant temperature and velocity chamber.
756
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
Fig. 5. Test section.
Table 2 Numerical results according to turbulent models (Q_ h = 100 W, w/L = 0.4, ReDh = 9289). Model
Rth,b (°C/W)
Error (%)
Experiment k-e-standard k-e RNG k-x standard k-x SST
0.116 0.076 0.074 0.124 0.121
– 30 32 7 5
heat sink average temperature, was used as the index of thermal performance. This is because the temperature of the surface where the electronic device is actually installed directly affects the lifetime of the electronic device. Numerical analysis was performed by increasing the distance x from the upstream edge of the heat sink to the center of the partially heated surface by 1% of the total length (L) of the heat sink, as shown in Fig. 7. In order to determine the optimal partial heating position under various operating conditions, the thermal performance of the heat sink was investigated in terms of the total heat transfer rate (Q_ h ), the ReDh , the ratio of the partially heated surface width to the total heat sink length (w/L), the thermal conductivity of the heat sink (kh), and the ratio of the base thickness to the heat sink height (tb/Hh). Using these results and the design of experiments method, a correlation equation was suggested that can predict the optimal
Fig. 6. Validation of the numerical results (T1 = 25 °C, Q_ = 100 W).
Fig. 7. Schematic of the partially heated surface.
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
757
partial heating position to minimize thermal resistance under various operating conditions. 3.1. Thermal performance with variation in the partial heating position The partial heating problem is based on the local heat flux unlike the entire heating problem, so conductive heat transfer in the x direction is important, as shown in Fig. 8. Lee et al. [24] and Yovanovich et al. [25] calculated the heat spreading resistance in a plate when a partially heated surface was located at the center. Muzychka et al. [26] found that the spreading resistance increases as the partially heated surface is farther away from the center under the condition that the edges of the heat sink were insulated. Therefore, considering only conductive heat transfer, it is preferable that the partially heated surface is located at the center of the heat sink. However, the thermal design of the heat sink should consider both conductive and convective heat transfer with an air flow direction. If forced convection in the x direction is considered, the optimum partial heating position is influenced by convective heat transfer. Therefore, numerical analysis is performed to see the convective heat transfer effect, and the average NuDh is calculated as shown in Fig. 9. The average NuDh was obtained by using the following equation. Here, kh = 200 W/m °C, w/L = 0.4, Q_ h = 100
Fig. 9. Average NuDh as a function of x/L.
W, tb/Hh = 0.16, and the values of ReDh are 3096 and 9289 with uin = 2 m/s and 6 m/s.
NuDh ¼
hav g Dh ka
RL hav g ¼
0
hx dx L
ð14Þ
ð15Þ
In general, hx is the largest at the edge of the heat sink due to the leading edge effect, and it is expected that the average NuDh also increases when the partially heated surface is located upstream. However, when considering the entire heat sink, the average NuDh tends to decrease as the partial heating position goes upstream. This is attributed to the fact that the air passes through a high-temperature heating zone located upstream, rapidly raising the temperature and consequently reducing the capacity for heat exchange with the rear part of the heat sink. On the other hand, when the partially heated surface is located downstream, the direction of conduction through the base and the cold air flow direction are reversed. As a result, the heat exchange efficiency increases and the average NuDh increases. Fig. 10 shows the thermal resistance as a function of x/L, using the average temperature of the partially heated surface. Here, the optimal position Xopt, the position with the smallest thermal resistance, is located about 0.52–0.54 relative to the entire length from the upstream side. This is because considering the convection heat
Fig. 10. Thermal resistance as a function of x/L.
transfer, the average NuDh increases and the best thermal performance is shown when the partially heated surface is located behind the center. Also, Xopt increases as the Reynolds number increases.
X opt ¼
xopt L
ð16Þ
In addition, when the partial heating position is located at the optimal position, the thermal resistance decreases by about 7% at ReDh ¼ 3096 and by about 13% at ReDh ¼ 9289 compared to the case when it is located upstream (x/L = 0). 3.2. A parametric study of the optimal partial heating position In this study, Xopt can be expressed as a function of five parameters as follows.
X opt ¼ f ðQ_ h ; ReDh ; w=L; kh ; tb =Hh Þ
Fig. 8. Heat transfer schematic in partial heating conditions.
ð17Þ
Here, these parameters were selected for the following reasons: depending on the heat transfer rate, Q_ h may affect the temperatures of the heat sink and the air, thus causing the optimal position to vary. In the case of ReDh , the convective heat transfer coefficient varies with the rate of air flow through the channel of the heat sink. This affects the optimal position of the partially heated surface. The
758
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
spreading resistance of the heat sink is predominantly determined by w/L, kh and tb/Hh. Hence, these parameters were included because of their potential to affect the optimal partial heating position. The range of each factor is as follows.
50 W 6 Q_ h 6 200 W 3096 6 ReDh 6 9289 0:2 6 w=L 6 0:8
ð18Þ
20 W=m C 6 kh 6 220 W=m C 0:04 6 t b =Hh 6 0:22 First, to investigate the change in Xopt as a function of Q_ h , ReDh = 6192, w/L = 0.4, kh = 100 W/m °C, and tb/Hh = 0.1 were fixed, while the design parameter Q_ h was varied between 50 W and 200 W. As
a result, the change in Q_ h did not affect Xopt. The effects of ReDh , w/L, kh, and tb/Hh on Xopt at a fixed Q_ h = 100 W are shown in Fig. 11.
First, as w/L increased, Xopt decreased. As w/L increased, it became similar to the case of a uniform heat flux being applied to the entire base and the partial heating effect was reduced. Also, as kh decreased, Xopt increased because the conductive thermal resistance of the heat sink increased, which increased the relative influence of convection. Finally, Xopt decreased as the base thickness (tb) increased because as tb increased, the conductive thermal resistance in the x direction decreased. 3.3. Correlation The equation for determining Xopt was proposed using the parameters (ReDh , w/L, kh/kref, tb/Hh) mentioned above. Here, the thermal conductivity kh of the heat sink is non-dimensionalized using the thermal conductivity of Al 6061 (kref = 167 W/m °C), which is generally used as the material for extrusion-type heat sinks. Numerical analysis was performed on the Full Factorial Design model (480 points) using the design of experiments method based on the design range of each factor as shown in Table 3. Then, an equation of correlation (R2 ¼ 0:96) was generated, as shown below. As shown in Fig. 12, the predicted values were within 10% of the numerical analysis results, demonstrating that the correlation equation predicted the results of the numerical analysis well.
X opt ¼ C 1 þ C 2 ðReDh ÞC 3
wC 4 k C 5 t C6 h b L kref Hh
ð19Þ
where
C 1 ¼ 4:859 101 ; C 2 ¼ 2:020 104 ; C 3 ¼ 4:564 101 ; C 4 ¼ 4:399 101 ; C 5 ¼ 2:207 101 C 6 ¼ 3:471 101 ; kref ¼ 167 W=m C: The reduction in thermal resistance when the partial heating was located at the optimal point based on the correlation was investigated. For each parameter, the thermal resistance improvement was investigated when the partial heating was located at the upstream edge and at the optimal position. The improvements of the thermal resistance with kh, ReDh , and tb changes were 18%, 17% and 16%, respectively. In particular, the improvement in thermal resistance was most sensitive to the width of the partially heated surface relative to the heat sink length, and the degree of thermal resistance reduction as a function of the width ratio is shown in Fig. 13. The thermal performance was improved by approximately 30% at the maximum. This result indicates that the heat performance can be improved simply by placing the heating element at the optimal position without changing the shape of the heat sink.
Fig. 11. Results of the parametric study for Xopt.
Table 3 Design parameters and ranges. Design parameter
ReDh w/L kh/kref tb/Hh
Range
Level
Min.
Max.
3096 0.20 0.12 0.04
9289 0.80 1.32 0.22
5 4 6 4
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
759
3.4. Comparison between optimal positions under non-uniform/ uniform heat flux conditions The difference in the optimal partial heating positions was investigated under non-uniform and uniform heat flux conditions. For this, numerical analysis was performed at the heat flux condition where the heat flux decreases linearly from the center to both ends as shown in Fig. 14. The total heat transfer rate Q_ h was equal to 100 W under both non-uniform and uniform heat flux conditions, and the numerical analysis was performed with kh=200 W/m °C, w/L = 0.4, ReDh = 9289, and tb/Hh = 0.16. The optimal position, Xopt, with respect to minimizing the thermal resistance, was 0.54 in both cases. Therefore, the correlation proposed in Section 3.3 was valid under strip-shaped partial heating conditions, regardless of the non-uniformity of the heat flux.
4. Conclusions Fig. 12. Comparison of the numerical results with the predicted results for Xopt.
Fig. 13. Thermal resistance ratio between the optimal position and upstream edge, as functions of w/L and ReDh (Q_ h ¼ 100 W; kh = 100 W/m °C, tb/Hs = 0.1).
The thermal performance of a heat sink according to the partial heating position was investigated, and the parameters affecting the optimal position were analyzed. Based on this analysis, a correlation was proposed through the design of experiments method to determine the optimal partial heating position. Specifically, numerical analysis was performed for a heat sink with partial heat and forced convection, and an experiment was conducted to verify the results. Thermal resistance was used as an indicator for thermal performance. By calculating the thermal resistance in terms of the partial heating position, the thermal performance of the heat sink was the lowest when the partial heating was located behind the center of the heat sink. The effects of various parameters, including the total heat transfer rate, the partially heated surface width, the heat sink thermal conductivity, and the thickness of the heat sink base, on the optimum heating position were also analyzed. The optimum position was farther from the upstream of the heat sink for larger ReDh and smaller partial heating surface width, lower thermal conductivity, and smaller base thickness. On the other hand, the total heat transfer rate had no effect on the optimum position. Therefore, an equation for predicting the optimal partial heating position was presented using four parameters, excluding the total heat transfer rate. The predicted results showed good agreement with the numerical results within an error of 10%. Based on the optimal partial heating position, the thermal
Fig. 14. Non-uniform/uniform heat flux contour under heat sink base.
760
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
performance improved by up to 30% compared to when the partial heating was located at the upstream edge. Finally, the effects of nonuniform/uniform heat flux conditions on the optimal positions were compared. As a result, there was no difference in the optimal positions for both cases. Therefore, the optimal position could be determined by applying the correlation regardless of the nonuniformity. It is expected that the thermal performance can be improved by changing the installation position of the heating element on the heat sink for effective cooling of power electronic devices. Conflict of interest No conflict of interest. Acknowledgements This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20162010103830, No. 20164010200860). References [1] Y. Joo, S.J. Kim, Comparison of thermal performance between plate-fin and pinfin heat sinks in natural convection, Int. J. Heat Mass Transf. 83 (2015) 345– 356. [2] B. Li, S. Jeon, C. Byon, Investigation of natural convection heat transfer around a radial heat sink with a perforated ring, Int. J. Heat Mass Transf. 97 (2016) 705– 711. [3] D. Jang, S.J. Yook, K.S. Lee, Optimum design of a radial heat sink with a finheight profile for high-power LED lighting applications, Appl. Energy 116 (2014) 260–268. [4] C.H. Huang, Y.H. Chen, H.Y. Li, An impingement heat sink module design problem in determining optimal non-uniform fin widths, Int. J. Heat Mass Transf. 67 (2013) 992–1006. [5] W. Wan, D. Deng, Q. Huang, T. Zeng, Y. Huang, Experimental study and optimization of pin fin shapes in flow boiling of micro pin fin heat sinks, Appl. Therm. Eng. 114 (2017) 436–449. [6] X. Yu, J. Feng, Q. Feng, Q. Wang, Development of a plate-pin fin heat sink and its performance comparisons with a plate fin heat sink, Appl. Therm. Eng. 25 (2) (2005) 173–182. [7] K.S. Lee, W.S. Kim, J.M. Si, Optimal shape and arrangement of staggered pins in the channel of a plate heat exchanger, Int. J. Heat Mass Transf. 44 (17) (2001) 3223–3231.
[8] H.Y. Li, W.R. Liao, T.Y. Li, Y.Z. Chang, Application of vortex generators to heat transfer enhancement of a pin-fin heat sink, Int. J. Heat Mass Transf. 112 (2017) 940–949. [9] S.J. Park, D. Jang, K.S. Lee, Thermal performance improvement of a radial heat sink with a hollow cylinder for LED downlight applications, Int. J. Heat Mass Transf. 89 (2015) 1184–1189. [10] P. Suzana, B.C. Avram, ‘‘Heat Shield”—an enhancement device for an unshrouded, forced convection heat sink, J. Electron. Packag. 128 (2) (2006) 172–176. [11] H. Jonsson, B. Moshfegh, Modeling of the thermal and hydraulic performance of plate fin, strip fin, and pin fin heat sinks-influence of flow bypass, IEEE Trans. Compon. Packag. Technol. 24 (2) (2001) 142–149. [12] H. Li, Y. He, Y. Hu, B. Jiang, Y. Huang, Thermophysical and natural convection characteristics of ethylene glycol and water mixture based ZnO nanofluids, Int. J. Heat Mass Transf. 91 (2015) 385–389. [13] K.C. Toh, X.Y. Chen, J.C. Chai, Numerical computation of fluid flow and heat transfer in microchannels, Int. J. Heat Mass Transf. 45 (26) (2002) 5133–5141. [14] S. Sudhakar, J.A. Weibel, Transient analysis of nonuniform heat input propagation through a heat sink base, J. Electron. Packag. 139 (2) (2017), 020901-020901-020907. [15] S.H. Yoon, N. Saneie, Y.J. Kim, Two-phase flow maldistribution in minichannel heat-sinks under non-uniform heating, Int. J. Heat Mass Transf. 78 (2014) 527– 537. [16] E.S. Cho, J.W. Choi, J.S. Yoon, M.S. Kim, Experimental study on microchannel heat sinks considering mass flow distribution with non-uniform heat flux conditions, Int. J. Heat Mass Transf. 53 (9) (2010) 2159–2168. [17] C. Anbumeenakshi, M.R. Thansekhar, On the effectiveness of a nanofluid cooled microchannel heat sink under non-uniform heating condition, Appl. Therm. Eng. 113 (2017) 1437–1443. [18] D. Lelea, The heat transfer and fluid flow of a partially heated microchannel heat sink, Int. Commun. Heat Mass Transf. 36 (8) (2009) 794–798. [19] N.G. Emekwuru, F.R. Hall, P.J. Spence, Partially heated heat sinks in a zerobypass, Int. Commun. Heat Mass Transf. 39 (3) (2012) 343–349. [20] Ansys, Ansys Fluent 17.0 Theory Guide, 2016. [21] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm Fluid Sci. 1 (1988) 3–17. [22] F. Zhou, I. Catton, Numerical evaluation of flow and heat transfer in plate-pin fin heat sinks with various pin cross-sections, Numer. Heat Transf., Part A: Appl. 60 (2) (2011) 107–128. [23] C.S. Sharma, M.K. Tiwari, B. Michel, D. Poulikakos, Thermofluidics and energetics of a manifold microchannel heat sink for electronics with recovered hot water as working fluid, Int. J. Heat Mass Transf. 58 (1) (2013) 135–151. [24] S. Lee, V.A. Seaho Song, K.P. Moran, Constriction/spreading resistance model for electronics packaging, ASME/JSME Therm. Eng. Conf. 4 (1995) 109–206. [25] M.M. Yovanovich, Y.S. Muzychka, J.R. Culham, Spreading resistance of isoflux rectangles and strips on compound flux channels, J. Thermophys. Heat Transf. 13 (4) (1999) 495–500. [26] Y.S. Muzychka, J.R. Culham, M.M. Yovanovich, Thermal spreading resistance of eccentric heat sources on rectangular flux channels, ASME J. Electron. Pack. 125 (2003) 178–185.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal performance improvement based on the partial heating position of a heat sink Youngchan Yoon a, Seung-Jae Park a,b, Dong Rip Kim a, Kwan-Soo Lee a,⇑ a b
School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Korea Institute for Defense Analyses, 37, Hoegi-ro, Dongdaemun-gu, Seoul 02455, Republic of Korea
a r t i c l e
i n f o
Article history: Received 10 January 2018 Received in revised form 22 March 2018 Accepted 23 March 2018
Keywords: Electronic cooling Heat sink Forced convection Partial heating
a b s t r a c t The thermal performance of a heat sink is analyzed according to the position of the partially heated surface. Numerical models for simulating forced convection were used to analyze the heat transfer between the heat sink and ambient air. The optimal partial heating position was discussed in terms of the effects of total heat transfer rate, air velocity, the ratio of total heat sink length to partially heated surface width, the thermal conductivity of the heat sink, and the thickness of the heat sink base. Finally, a correlation was suggested to determine the partial heating position that maximizes thermal performance by using the experimental design method. It was thus possible to reduce the thermal resistance of the heat sink by up to approximately 30% by finding the optimal partial heating position. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction As the performance of electronic devices improves, the amount of heat generation increases, which negatively impacts their performances. For the effective cooling of electronic devices, Joo et al. [1] optimized the fin geometry and compared the thermal performance, and Li et al. [2] promoted natural convective air flow by using a perforated heat sink. Many researchers have also improved thermal performance by changing the geometry of the heat sink [3–7] and by using surrounding structures [8–11]. The heating conditions of the studies described above are the case where heat is applied to the bottom parts of the heat sink. However, in the case of power electronic devices, the size of the heat sink is typically larger than the size of the heating element due to high heat generation. An insulated gate bipolar mode transistor (IGBT) is a typical example, as shown in Fig. 1. In the case of this partial heating condition, the above-mentioned geometric shape change or the use of surrounding structures cannot be directly applied because the temperature distribution and heat transfer characteristics of the heat sink are different. The effective cooling method of partial heating conditions has been studied by several researchers, mainly using microchannel heat sinks. In microchannel heat sinks, since the heat exchanging area is relatively small, nanofluids are mainly used as a working fluid to ensure heat transfer performance [12]. Toh et al. [13] ⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee). https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.080 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
studied the position of the maximum temperature in the microchannel heat sink under partial heating conditions. Sudhakar et al. [14] studied the transient temperature response of the microchannel heat sink under partial heating conditions, and Yoon et al. [15] found that the thermal performance was better in pin-fin than in strip-fin of the microchannel heat sink for the partial heating case. However, none of them investigated how the thermal performance can vary with the partial heating position in spite of their importance in improving the cooling performance. According to Cho et al. [16], a microchannel heat sink with a trapezoidal header has the highest temperature when the heater is located upstream. However, this is due to the flow distribution difference according to the header shape. Therefore, it cannot be generalized that the thermal performance is always poor when the heater is located at the upstream of the heat sink. In the studies by Anbumeenakshi et al. [17] and Lelea et al. [18], the thermal resistance had the smallest value when the heater was located at the upstream of the microchannel heat sink. However, the base thickness used in these studies was on the microscale, and the effects of axial heat conduction of the heat sink base are different in macroscale heat sinks. Therefore, in a macroscale heat sink, the thermal resistance is not always low when the heater is located at the upstream. In addition, all of the studies mentioned above utilized water or various nanofluids as the working fluid. Therefore, it is necessary to study the cooling system of a macroscale heat sink that uses air as a working fluid in the partial heating condition.
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
753
Nomenclature A Dh H h k L N p
q_ Q_ Rth s T t u
surface area [mm2] hydraulic diameter [mm] height [mm] convective heat transfer coefficient [W/m2 K] kinetic energy of turbulence [m2/s2]/thermal conductivity [W/m K] length [mm] number of fin arrays pressure [Pa] heat flux [W/m2] heat transfer rate [W] thermal resistance [°C/W] space [mm] temperature [°C] thickness [mm] velocity [m/s]
Greek symbols g normal direction vector q density [kg/m3]
dynamic viscosity [N s/m2] specific dissipation rate [s1]
l x
Subscripts a air avg average b base bot bottom ch channel eff effective f fin h heat sink in in p polyethylene t turbulent top top u upstream 1 ambient
Finally, a correlation was suggested to predict the optimal partial heating position to minimize the thermal resistance of the heat sink under various operating conditions by using the design of experiments method.
2. Mathematical modeling 2.1. Numerical model
Fig. 1. IGBT cooling system in an industrial inverter.
Emekwuru et al. [19] performed a numerical analysis by dividing the position of the partially heated surface into three positions (upstream, center, and downstream) for an air-cooled heat sink. The study found that the thermal resistance of the heat sink was the lowest when the partially heated surface was located at the center. However, since the partial heating position was limited to only three positions, the central position cannot be the optimum position. In addition, the average temperature of the entire heat sink was used as a measure of thermal performance. However, this limits the accurate evaluation of the optimal cooling of a macroscale heat sink for the partial heating condition because the heat sink typically has a large temperature distribution. In this study, the thermal performance of an air-cooled macroscale heat sink was numerically investigated in terms of the position of partial heating in the heat sink after verifying the numerical model with experiments. Here, the temperature used to calculate the thermal resistance of the heat sink is not the average temperature of the heat sink but the average temperature of the partially heated surface, which is suitable for power electronic device cooling in industrial fields. The effects of various factors, such as the total heat transfer rate, the velocity of the air, the ratio of total heat sink length to partially heated surface width, the thermal conductivity of the heat sink, and the thickness of the heat sink base, on the optimal partial heating position were investigated.
Fig. 2 illustrates the heat sink and the heater used in this study. The heat sink consisted of a fin and a base, with the top, left, and right sides making a physically closed system. The following assumptions were applied for the numerical analysis. (1) (2) (3) (4)
The flow is three-dimensional and steady state. The air properties do not change with temperature. Radiative heat transfer of the heat sink can be neglected. Heat transfer occurs only in the air and the heat sinks, and there is no heat transfer on the top and the sides surrounding the heat sink.
The governing equations used in the numerical analysis were as follows, and the shear stress transport (SST) k x model was used for turbulent flow. Validation of the numerical analysis and selection of the turbulence model are described in Section 2.3.
Fig. 2. Schematic of the heat sink.
754
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
Continuity:
2.2. Numerical method
@ðqui Þ ¼0 @xi
ð1Þ
Momentum:
@ @p @ @ui ðqui uj Þ ¼ þ ðl þ lt Þ @xi @xi @xj @xj Turbulent kinetic energy:
@ @ ðqkui Þ ¼ @xj @xj
lþ
lt @k þ Gk Y k rk @xj
Specific dissipation rate:
@ @ ðqxuj Þ ¼ @xj @xj
lþ
ð2Þ
ð3Þ
lt @ x þ Gx Y x þ Dx rx @xj
ð4Þ
Energy:
@ @ @T ðui qcp TÞ ¼ keff þ ui ðsij Þeff @xi @xj @xj
ð5Þ
where rk and rx are the turbulent Prandtl numbers for k and x. Gk and Gx are the production of turbulence kinetic energy and generation of x, respectively. Y k and Y x are the dissipation terms of k and x, and Dx is the cross diffusion term [20].
Gk ¼ qu0i u0j
@uj aa 0 0 @uj ; Gx ¼ qui uj @xi mt @xi
Y k ¼ qb kx; Y x ¼ qbf b x Dx ¼ 2ð1 F 1 Þq
lt ¼
1
xrx;2
2
@k @ x @xj @xj
qk 1 h i x max 1 ; SF 2 a
ðsij Þeff ¼ leff
Fig. 3 shows the model used for the numerical analysis. The geometric parameters were N = 14, tf = 3 mm, tb = 8 mm, L = 150 mm, Hh = 50 mm, and w = 60 mm. A partial heat flux condition was applied to the bottom surface of the base to simulate the heater. Considering the required computational time and number of grids, only half of the heat sink was used as the computational domain based on the symmetry condition. ANSYS MESH was used to generate hexahedral meshes. The grid dependence changed the number of meshes from 200,075 to 2,622,815, and the air domain changed from 0.5 L to 1.5 L for the heat sink air inlet and outlet, respectively. At this time, the reference mesh number was set to 1,416,000, where the relative error of the heat sink average temperature change was within 1%, and the air domain in the inlet/ outlet direction was set to 1 L. Numerical analysis was performed using ANSYS Fluent release 17.0, a commercial computational fluid dynamics (CFD) analysis program, using a finite volume method. The SIMPLE algorithm was chosen to solve the flow field by combining velocity and pressure during the numerical analysis. The convective terms and energy equations of each governing equation were discretized using a second-order upwind scheme to improve accuracy. The dependent variables in the iterative calculation were determined to have converged when the maximum relative error
ð6Þ ð7Þ ð8Þ
Table 1 Boundary conditions of numerical method. Boundary conditions
Momentum
Thermal
Air domain
Velocity inlet/pressure outlet condition ui = 0
Tin = 25 °C
Heat sink domain
ð9Þ
Insulated wall domain Symmetric face
a1 x
ui = 0 (no-slip condition) @u ¼0 @ g symmetric face
@uj @ui 2 @uk leff þ dij 3 @xi @xj @xk
ð10Þ
Interface between air and heat sink domain
Fig. 3. Domain for the numerical analysis.
ui = 0 (no-slip condition)
h _ kh @T @ g b;heating region ¼ q @T ¼ 0 (adiabatic) @g
wall
@T @ gsymmetric face
¼0
Ta,wall = Th,wall a h ka @T ¼ kh @T @g @g wall
wall
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
of the dependent variable was less than 105 for all governing equations. The boundary conditions used in the numerical analysis are shown in Table 1. 2.3. Experiment and validation As shown in Fig. 4, a chamber was used for forced convection, and air with a constant temperature and velocity was flown into the test section. The test section consisted of a heat sink, a heater, and a duct surrounding the heat sink, as shown in Fig. 5. The heat sink was an extruded heat sink made of aluminum alloy 6063 (kh = 200 W/m K). The geometry of the heat sink was the same as that used for the numerical analysis, and the duct around the heat sink was insulated using polyethylene insulation (kp = 0.03 W/m K). In order to maximize the amount of heat transferred from the heater to the heat sink, insulation (kp = 0.03 W/m K, tp = 20 mm) was installed around the heater, and the amount of heat transferred to the heat sink (Q_ h ) was calculated using the following equation by measuring the top and bottom temperature of the insulation.
T p;top T p;bot Q_ h ¼ Q_ in kp Ap tp
ð11Þ
The temperature was measured using a thermocouple (type-T, gauge 36) and a data acquisition device (NI 9213, cDAQ-9178). The steady state temperature was considered to be when the temperature change of the heat sink was less than 0.1 °C. The heater power was controlled by a Slidac transformer, and the power consumption was measured using a wattmeter (CLAMP ON POWER HiTESTER, HIOKI). Here, the accuracy of the thermocouple and wattmeter is ±0.5 °C and ±0.5% rdg., respectively. The numerical and experimental results were compared using the thermal resistance of the heat sink according to the Reynolds number variation when the heater is located at the center of the heat sink base. In addition, Q_ h = 100 W was applied to simulate medium size power electronics.
Rth;b ¼
T b;av g T 1 Q_ h
ð12Þ
ReDh ¼
qa uch;av g Dh la
755
ð13Þ
When a thermocouple is installed between the heater and the contact surface of the heat sink, an air gap can be formed due to the thickness of the thermocouple, which leads to the issue that the heat from the heater cannot be effectively transferred to the heat sink. Therefore, as shown in Fig. 5, the average temperature measured at the upper surface of the base where the heater was installed (Tb,avg) was used to calculate the thermal resistance. qa is the density of the air, la is the viscosity coefficient of the air, uch;av g is the average velocity of air in the heat sink channel, and Dh is the hydraulic diameter of the heat sink channel and is equivalent to
2ðsf Hf Þ sf þHf
in Fig. 3. The maximum uncertainty of the thermal
resistance in this experiment is approximately 5.1% [21]. As shown in Table 2, among the turbulence models used for the numerical analysis, the smallest error was found for the k-x SST model. This agrees well with the fact that the k-x SST model is commonly used for forced convection conditions in heat sinks [22,23]. Therefore, this was used as the reference model. Fig. 6 shows the verification results of the numerical model with experiments. The maximum error was within approximately 5%, showing that the numerical analysis was in good agreement with the experimental results. 3. Results and discussion The thermal performance of the heat sink under partial heating was investigated by combining the results of conduction in the heat sink and convective heat transfer to the air. The conductive and convective heat transfers are maximized when the partial heating is applied to different locations within the limited dimensions of rectangular heat sinks Therefore, there will be an optimal position for maximizing the thermal performance with respect to both the conductive and convective heat transfer. The optimal partial heating positions were suggested for a variety of operating conditions. To find this optimal position, the thermal performance of the heat sink was investigated based on the partial heating position. The average temperature of the partially heated surface, not the
Fig. 4. Constant temperature and velocity chamber.
756
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
Fig. 5. Test section.
Table 2 Numerical results according to turbulent models (Q_ h = 100 W, w/L = 0.4, ReDh = 9289). Model
Rth,b (°C/W)
Error (%)
Experiment k-e-standard k-e RNG k-x standard k-x SST
0.116 0.076 0.074 0.124 0.121
– 30 32 7 5
heat sink average temperature, was used as the index of thermal performance. This is because the temperature of the surface where the electronic device is actually installed directly affects the lifetime of the electronic device. Numerical analysis was performed by increasing the distance x from the upstream edge of the heat sink to the center of the partially heated surface by 1% of the total length (L) of the heat sink, as shown in Fig. 7. In order to determine the optimal partial heating position under various operating conditions, the thermal performance of the heat sink was investigated in terms of the total heat transfer rate (Q_ h ), the ReDh , the ratio of the partially heated surface width to the total heat sink length (w/L), the thermal conductivity of the heat sink (kh), and the ratio of the base thickness to the heat sink height (tb/Hh). Using these results and the design of experiments method, a correlation equation was suggested that can predict the optimal
Fig. 6. Validation of the numerical results (T1 = 25 °C, Q_ = 100 W).
Fig. 7. Schematic of the partially heated surface.
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
757
partial heating position to minimize thermal resistance under various operating conditions. 3.1. Thermal performance with variation in the partial heating position The partial heating problem is based on the local heat flux unlike the entire heating problem, so conductive heat transfer in the x direction is important, as shown in Fig. 8. Lee et al. [24] and Yovanovich et al. [25] calculated the heat spreading resistance in a plate when a partially heated surface was located at the center. Muzychka et al. [26] found that the spreading resistance increases as the partially heated surface is farther away from the center under the condition that the edges of the heat sink were insulated. Therefore, considering only conductive heat transfer, it is preferable that the partially heated surface is located at the center of the heat sink. However, the thermal design of the heat sink should consider both conductive and convective heat transfer with an air flow direction. If forced convection in the x direction is considered, the optimum partial heating position is influenced by convective heat transfer. Therefore, numerical analysis is performed to see the convective heat transfer effect, and the average NuDh is calculated as shown in Fig. 9. The average NuDh was obtained by using the following equation. Here, kh = 200 W/m °C, w/L = 0.4, Q_ h = 100
Fig. 9. Average NuDh as a function of x/L.
W, tb/Hh = 0.16, and the values of ReDh are 3096 and 9289 with uin = 2 m/s and 6 m/s.
NuDh ¼
hav g Dh ka
RL hav g ¼
0
hx dx L
ð14Þ
ð15Þ
In general, hx is the largest at the edge of the heat sink due to the leading edge effect, and it is expected that the average NuDh also increases when the partially heated surface is located upstream. However, when considering the entire heat sink, the average NuDh tends to decrease as the partial heating position goes upstream. This is attributed to the fact that the air passes through a high-temperature heating zone located upstream, rapidly raising the temperature and consequently reducing the capacity for heat exchange with the rear part of the heat sink. On the other hand, when the partially heated surface is located downstream, the direction of conduction through the base and the cold air flow direction are reversed. As a result, the heat exchange efficiency increases and the average NuDh increases. Fig. 10 shows the thermal resistance as a function of x/L, using the average temperature of the partially heated surface. Here, the optimal position Xopt, the position with the smallest thermal resistance, is located about 0.52–0.54 relative to the entire length from the upstream side. This is because considering the convection heat
Fig. 10. Thermal resistance as a function of x/L.
transfer, the average NuDh increases and the best thermal performance is shown when the partially heated surface is located behind the center. Also, Xopt increases as the Reynolds number increases.
X opt ¼
xopt L
ð16Þ
In addition, when the partial heating position is located at the optimal position, the thermal resistance decreases by about 7% at ReDh ¼ 3096 and by about 13% at ReDh ¼ 9289 compared to the case when it is located upstream (x/L = 0). 3.2. A parametric study of the optimal partial heating position In this study, Xopt can be expressed as a function of five parameters as follows.
X opt ¼ f ðQ_ h ; ReDh ; w=L; kh ; tb =Hh Þ
Fig. 8. Heat transfer schematic in partial heating conditions.
ð17Þ
Here, these parameters were selected for the following reasons: depending on the heat transfer rate, Q_ h may affect the temperatures of the heat sink and the air, thus causing the optimal position to vary. In the case of ReDh , the convective heat transfer coefficient varies with the rate of air flow through the channel of the heat sink. This affects the optimal position of the partially heated surface. The
758
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
spreading resistance of the heat sink is predominantly determined by w/L, kh and tb/Hh. Hence, these parameters were included because of their potential to affect the optimal partial heating position. The range of each factor is as follows.
50 W 6 Q_ h 6 200 W 3096 6 ReDh 6 9289 0:2 6 w=L 6 0:8
ð18Þ
20 W=m C 6 kh 6 220 W=m C 0:04 6 t b =Hh 6 0:22 First, to investigate the change in Xopt as a function of Q_ h , ReDh = 6192, w/L = 0.4, kh = 100 W/m °C, and tb/Hh = 0.1 were fixed, while the design parameter Q_ h was varied between 50 W and 200 W. As
a result, the change in Q_ h did not affect Xopt. The effects of ReDh , w/L, kh, and tb/Hh on Xopt at a fixed Q_ h = 100 W are shown in Fig. 11.
First, as w/L increased, Xopt decreased. As w/L increased, it became similar to the case of a uniform heat flux being applied to the entire base and the partial heating effect was reduced. Also, as kh decreased, Xopt increased because the conductive thermal resistance of the heat sink increased, which increased the relative influence of convection. Finally, Xopt decreased as the base thickness (tb) increased because as tb increased, the conductive thermal resistance in the x direction decreased. 3.3. Correlation The equation for determining Xopt was proposed using the parameters (ReDh , w/L, kh/kref, tb/Hh) mentioned above. Here, the thermal conductivity kh of the heat sink is non-dimensionalized using the thermal conductivity of Al 6061 (kref = 167 W/m °C), which is generally used as the material for extrusion-type heat sinks. Numerical analysis was performed on the Full Factorial Design model (480 points) using the design of experiments method based on the design range of each factor as shown in Table 3. Then, an equation of correlation (R2 ¼ 0:96) was generated, as shown below. As shown in Fig. 12, the predicted values were within 10% of the numerical analysis results, demonstrating that the correlation equation predicted the results of the numerical analysis well.
X opt ¼ C 1 þ C 2 ðReDh ÞC 3
wC 4 k C 5 t C6 h b L kref Hh
ð19Þ
where
C 1 ¼ 4:859 101 ; C 2 ¼ 2:020 104 ; C 3 ¼ 4:564 101 ; C 4 ¼ 4:399 101 ; C 5 ¼ 2:207 101 C 6 ¼ 3:471 101 ; kref ¼ 167 W=m C: The reduction in thermal resistance when the partial heating was located at the optimal point based on the correlation was investigated. For each parameter, the thermal resistance improvement was investigated when the partial heating was located at the upstream edge and at the optimal position. The improvements of the thermal resistance with kh, ReDh , and tb changes were 18%, 17% and 16%, respectively. In particular, the improvement in thermal resistance was most sensitive to the width of the partially heated surface relative to the heat sink length, and the degree of thermal resistance reduction as a function of the width ratio is shown in Fig. 13. The thermal performance was improved by approximately 30% at the maximum. This result indicates that the heat performance can be improved simply by placing the heating element at the optimal position without changing the shape of the heat sink.
Fig. 11. Results of the parametric study for Xopt.
Table 3 Design parameters and ranges. Design parameter
ReDh w/L kh/kref tb/Hh
Range
Level
Min.
Max.
3096 0.20 0.12 0.04
9289 0.80 1.32 0.22
5 4 6 4
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
759
3.4. Comparison between optimal positions under non-uniform/ uniform heat flux conditions The difference in the optimal partial heating positions was investigated under non-uniform and uniform heat flux conditions. For this, numerical analysis was performed at the heat flux condition where the heat flux decreases linearly from the center to both ends as shown in Fig. 14. The total heat transfer rate Q_ h was equal to 100 W under both non-uniform and uniform heat flux conditions, and the numerical analysis was performed with kh=200 W/m °C, w/L = 0.4, ReDh = 9289, and tb/Hh = 0.16. The optimal position, Xopt, with respect to minimizing the thermal resistance, was 0.54 in both cases. Therefore, the correlation proposed in Section 3.3 was valid under strip-shaped partial heating conditions, regardless of the non-uniformity of the heat flux.
4. Conclusions Fig. 12. Comparison of the numerical results with the predicted results for Xopt.
Fig. 13. Thermal resistance ratio between the optimal position and upstream edge, as functions of w/L and ReDh (Q_ h ¼ 100 W; kh = 100 W/m °C, tb/Hs = 0.1).
The thermal performance of a heat sink according to the partial heating position was investigated, and the parameters affecting the optimal position were analyzed. Based on this analysis, a correlation was proposed through the design of experiments method to determine the optimal partial heating position. Specifically, numerical analysis was performed for a heat sink with partial heat and forced convection, and an experiment was conducted to verify the results. Thermal resistance was used as an indicator for thermal performance. By calculating the thermal resistance in terms of the partial heating position, the thermal performance of the heat sink was the lowest when the partial heating was located behind the center of the heat sink. The effects of various parameters, including the total heat transfer rate, the partially heated surface width, the heat sink thermal conductivity, and the thickness of the heat sink base, on the optimum heating position were also analyzed. The optimum position was farther from the upstream of the heat sink for larger ReDh and smaller partial heating surface width, lower thermal conductivity, and smaller base thickness. On the other hand, the total heat transfer rate had no effect on the optimum position. Therefore, an equation for predicting the optimal partial heating position was presented using four parameters, excluding the total heat transfer rate. The predicted results showed good agreement with the numerical results within an error of 10%. Based on the optimal partial heating position, the thermal
Fig. 14. Non-uniform/uniform heat flux contour under heat sink base.
760
Y. Yoon et al. / International Journal of Heat and Mass Transfer 124 (2018) 752–760
performance improved by up to 30% compared to when the partial heating was located at the upstream edge. Finally, the effects of nonuniform/uniform heat flux conditions on the optimal positions were compared. As a result, there was no difference in the optimal positions for both cases. Therefore, the optimal position could be determined by applying the correlation regardless of the nonuniformity. It is expected that the thermal performance can be improved by changing the installation position of the heating element on the heat sink for effective cooling of power electronic devices. Conflict of interest No conflict of interest. Acknowledgements This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20162010103830, No. 20164010200860). References [1] Y. Joo, S.J. Kim, Comparison of thermal performance between plate-fin and pinfin heat sinks in natural convection, Int. J. Heat Mass Transf. 83 (2015) 345– 356. [2] B. Li, S. Jeon, C. Byon, Investigation of natural convection heat transfer around a radial heat sink with a perforated ring, Int. J. Heat Mass Transf. 97 (2016) 705– 711. [3] D. Jang, S.J. Yook, K.S. Lee, Optimum design of a radial heat sink with a finheight profile for high-power LED lighting applications, Appl. Energy 116 (2014) 260–268. [4] C.H. Huang, Y.H. Chen, H.Y. Li, An impingement heat sink module design problem in determining optimal non-uniform fin widths, Int. J. Heat Mass Transf. 67 (2013) 992–1006. [5] W. Wan, D. Deng, Q. Huang, T. Zeng, Y. Huang, Experimental study and optimization of pin fin shapes in flow boiling of micro pin fin heat sinks, Appl. Therm. Eng. 114 (2017) 436–449. [6] X. Yu, J. Feng, Q. Feng, Q. Wang, Development of a plate-pin fin heat sink and its performance comparisons with a plate fin heat sink, Appl. Therm. Eng. 25 (2) (2005) 173–182. [7] K.S. Lee, W.S. Kim, J.M. Si, Optimal shape and arrangement of staggered pins in the channel of a plate heat exchanger, Int. J. Heat Mass Transf. 44 (17) (2001) 3223–3231.
[8] H.Y. Li, W.R. Liao, T.Y. Li, Y.Z. Chang, Application of vortex generators to heat transfer enhancement of a pin-fin heat sink, Int. J. Heat Mass Transf. 112 (2017) 940–949. [9] S.J. Park, D. Jang, K.S. Lee, Thermal performance improvement of a radial heat sink with a hollow cylinder for LED downlight applications, Int. J. Heat Mass Transf. 89 (2015) 1184–1189. [10] P. Suzana, B.C. Avram, ‘‘Heat Shield”—an enhancement device for an unshrouded, forced convection heat sink, J. Electron. Packag. 128 (2) (2006) 172–176. [11] H. Jonsson, B. Moshfegh, Modeling of the thermal and hydraulic performance of plate fin, strip fin, and pin fin heat sinks-influence of flow bypass, IEEE Trans. Compon. Packag. Technol. 24 (2) (2001) 142–149. [12] H. Li, Y. He, Y. Hu, B. Jiang, Y. Huang, Thermophysical and natural convection characteristics of ethylene glycol and water mixture based ZnO nanofluids, Int. J. Heat Mass Transf. 91 (2015) 385–389. [13] K.C. Toh, X.Y. Chen, J.C. Chai, Numerical computation of fluid flow and heat transfer in microchannels, Int. J. Heat Mass Transf. 45 (26) (2002) 5133–5141. [14] S. Sudhakar, J.A. Weibel, Transient analysis of nonuniform heat input propagation through a heat sink base, J. Electron. Packag. 139 (2) (2017), 020901-020901-020907. [15] S.H. Yoon, N. Saneie, Y.J. Kim, Two-phase flow maldistribution in minichannel heat-sinks under non-uniform heating, Int. J. Heat Mass Transf. 78 (2014) 527– 537. [16] E.S. Cho, J.W. Choi, J.S. Yoon, M.S. Kim, Experimental study on microchannel heat sinks considering mass flow distribution with non-uniform heat flux conditions, Int. J. Heat Mass Transf. 53 (9) (2010) 2159–2168. [17] C. Anbumeenakshi, M.R. Thansekhar, On the effectiveness of a nanofluid cooled microchannel heat sink under non-uniform heating condition, Appl. Therm. Eng. 113 (2017) 1437–1443. [18] D. Lelea, The heat transfer and fluid flow of a partially heated microchannel heat sink, Int. Commun. Heat Mass Transf. 36 (8) (2009) 794–798. [19] N.G. Emekwuru, F.R. Hall, P.J. Spence, Partially heated heat sinks in a zerobypass, Int. Commun. Heat Mass Transf. 39 (3) (2012) 343–349. [20] Ansys, Ansys Fluent 17.0 Theory Guide, 2016. [21] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm Fluid Sci. 1 (1988) 3–17. [22] F. Zhou, I. Catton, Numerical evaluation of flow and heat transfer in plate-pin fin heat sinks with various pin cross-sections, Numer. Heat Transf., Part A: Appl. 60 (2) (2011) 107–128. [23] C.S. Sharma, M.K. Tiwari, B. Michel, D. Poulikakos, Thermofluidics and energetics of a manifold microchannel heat sink for electronics with recovered hot water as working fluid, Int. J. Heat Mass Transf. 58 (1) (2013) 135–151. [24] S. Lee, V.A. Seaho Song, K.P. Moran, Constriction/spreading resistance model for electronics packaging, ASME/JSME Therm. Eng. Conf. 4 (1995) 109–206. [25] M.M. Yovanovich, Y.S. Muzychka, J.R. Culham, Spreading resistance of isoflux rectangles and strips on compound flux channels, J. Thermophys. Heat Transf. 13 (4) (1999) 495–500. [26] Y.S. Muzychka, J.R. Culham, M.M. Yovanovich, Thermal spreading resistance of eccentric heat sources on rectangular flux channels, ASME J. Electron. Pack. 125 (2003) 178–185.