- Email: [email protected]
Orientation effect of a radial heat sink with a chimney for LED downlights
International Journal of Heat and Mass Transfer 110 (2017) 416–421
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Orientation effect of a radial heat sink with a chimney for LED downlights Seung-Jae Park, Kwan-Soo Lee ⇑ School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
a r t i c l e
i n f o
Article history: Received 3 January 2017 Received in revised form 28 February 2017 Accepted 17 March 2017
Keywords: Heat sink Orientation effect Natural convection Chimney
a b s t r a c t The orientation effect of a radial heat sink with a chimney was investigated in an attempt to design safer cooling systems for LED downlights. The natural convective and radiative heat transfer were simulated with a numerical model to analyze the heat transfer and flow around the cooling system, and the model was experimentally validated. The causes of the orientation effect were determined by analyzing the numerical results. The influence of the geometric parameters of the cooling system on the orientation effect was analyzed. A parametric study was conducted to select the three geometric parameters that have the largest influence on the orientation effect. The numerical analysis was carried out on the design points, which were selected according to the design of experiments. A correlation was obtained that can predict the orientation effect factor depending on the geometric factors and installation angle of the cooling system. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction LED lightings have the advantages of being eco-friendly and long-lasting. Therefore, these lightings are being used to replace conventional lighting. However, if the temperature of the LED chip is increased, the lifetime will be reduced, and the emitted light will become unstable. Since LED downlights are normally embedded in the ceiling of a room, it is preferable to install a natural convection type heat sink that has the advantages of a semi-permanent lifetime and noiselessness operation compared to forced convection type cooling systems, such as fans [1]. However, the thermal performance of natural convection type heat sinks is inferior to other cooling systems. Therefore, studies seeking to enhance the thermal performance by changing the shape of the fins or installing a surrounding structure have been actively pursued. The radial heat sink, which has plate fins that are aligned radially on a circular base, is used for circular electrics, such as LED downlights. The cooling performance of long fin (L) type, long and middle fin (LM) type, and long, middle, and short fin (LMS) type radial heat sinks [2]. As a result, it was observed that the LM type heat sink, which can increase the heat transfer surface without overlapping of thermal boundary layers, was the optimum shape. The same research team improved the heat transfer rate of the radial heat sink by optimizing the shape and array of the pin ⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.03.062 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
fins [3–5]. However, the mass-production of heat sinks that contain complex-shaped fins is expensive; therefore, it is difficult to make these adjustments in commercial products. Therefore, practical LED downlights utilize the LM type radial heat sink [6]. Park et al. [7] suggested the installation of a hollow cylinder-shaped surrounding structure to maximize the cooling performance without changing the fin shape. Utilizing the hollow cylinder-shaped surrounding structure could enhance the performance of the heat sink by 40%, because the air flow at the region where the heat exchange did not occur was restricted and the air velocity around the fin was increased. Park et al. [6] developed a chimney-shaped surrounding structure to minimize the mass increase in cooling systems that is caused by the installation of surrounding structure. The optimized chimney was 60% lighter than the hollow cylinder. Because of the horizontal part of the chimney, the cooled air could penetrate into the central part of the radial heat sink, which caused a 20% enhancement in the cooling performance. Heat sinks are installed within electronic devices at different angles. Therefore, many researchers have studied the orientation effect, which is a change in the cooling performance depending on the installation angle. Tari and Mehrtash [8] studied the thermal performance of a square heat sink depending on the installation angle, found the causes of the orientation effect, and suggested a correlation that can calculate the Nu of the heat sink depending on the installation angle. Shen et al. [9] calculated the thermal performance of a square heat sink in relation to the installation angle and the fin direction with a numerical method and analyzed
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
417
Nomenclature A cp g h k l N _ m p Q_ q_ Rth r T t u
surface area (m2) specific heat (J/kg°C) gravity acceleration (m/s2) height (mm) kinetic energy of turbulence (m2/s2)/thermal conductivity (W/m°C) length (mm) number of fin arrays mass flow rate (g/s) pressure (Pa) heat generation rate (W) heat flux (W/m2) thermal resistance (°C/W) radius (mm) temperature (°C) thickness (m/s) velocity component (m/s)
the flow pattern around the fin to find the cause of the orientation effect. However, the flow patterns in square heat sinks and radial heat sinks are different; thus, it is difficult to apply their results to a radial heat sink. The orientation effect of a radial heat sink that had a concentric ring in the central part was studied [10,11]. The influence of the number of fin arrays on the orientation effect was studied and a correlation that could predict the orientation effect factor was suggested in their study. However, the equipment of the surrounding structure changed the flow pattern. Therefore, we cannot predict the orientation effect of the cooling system with a chimney above a radial heat sink using the existing research results. In this study, the orientation effect of a radial heat sink with chimney, as shown in Fig. 1, is analyzed. A numerical model to simulate the natural convective and radiative heat transfer is adopted,
Greek symbols e emissivity/dissipation rate of turbulent kinetic energy (m2/s3) l dynamic viscosity (m2/s) h installation angle (°) Subscripts a air acr acrylic ave average b base c chimney eff effective h heat sink i inner l long fin m middle fin o outer
and a validation experiment is conducted. The influence of the geometric parameters of the cooling system on the orientation effect is analyzed. Finally, the correlation that can predict the orientation effect factor depending on the geometric factors and installation angle of the cooling system was suggested. 2. Model description 2.1. Numerical model Fig. 2 shows the boundary conditions and the computational domain containing a radial heat sink, chimney-shaped surrounding structure, and air. Only half of the region was calculated with the symmetry boundary condition to reduce the computational effort. An LM type radial heat sink [2] was considered in this study. To retain the independence of the computational domain from the installation angle of the cooling system, a spherical control volume was adjusted for the air domain. To calculate the thermal flow, the following assumptions were conducted: (1) The air is an ideal gas. (2) The flow is three dimensional and steady state. (3) The material properties are independent of the temperature, except the density of air. (4) The surfaces of the cooling system are gray and diffuse. The renormalization group (RNG) k-e turbulence model and discrete ordinates (DO) radiation model were selected as the numerical models for this study. The general transport equation was used as follows [12]:
@ @ @/ þ S/ ðquj /Þ ¼ C/ @xj @xj @xj
ð1Þ
where the terms for /, C/ , and S/ were listed in Table 1. 2.2. Numerical methodology
Fig. 1. The configuration of the cooling system with a chimney and a radial heat sink.
The radial heat sink and chimney have the following parameters: N = 20, ll = 50 mm, lm = 20 mm, hh = 20 mm, th = 2 mm, rh = 75 mm, hc = 200 mm, tc = 2 mm, rc_i = 45 mm, and rc_o = 75 mm. The radius of the air domain (ra) was changed from 1.2(hc + hh) to 2.4(hc + hh) to obtain the size of the computational domain that produced a less than 1% change in the temperature. Consequently,
418
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
Fig. 2. Computational domain and boundary conditions.
Table 1 Arbitrary scalar parameters (/), diffusivity coefficients (C/ ), and source terms (S/ ) in general transport equation (Eq. (1)). Equation
/
C/
S/
Continuity Momentum
1 ui
0
0 @p=@xi þ F (for z-direction F = –qg)
Turbulent kinetic energy
k
Dissipation rate of turbulence kinetic energy
e
Energy
T
leff ak leff ae leff aleff
lt S2 qe C 1e ðe=kÞðlt S2 C 3e g i lt =qPrt @ q=@xi Þ ðC 2e þ 0:085g3 ð1 g=4:38Þ=ð1 þ 0:012g3 ÞÞðqe2 =kÞ 1=cp @ðui ðsij Þeff Þ=@xj
we set ra to 1.5(hc + hh). The number of tetrahedral meshes was changed from 1,026,054 to 11,287,916 to test the grid dependency. As a result, 5,257,829 meshes were selected as a reference meshes that produced a less than 1% change in the temperature of the heat sink. The heights of meshes were decreased around the solids where the boundary layers were developed. ANSYS ICEM and FLUENT release 17.0 were used to generate the grid and discretize and calculate the general equation. A maximum relative error less than 105 was defined for the convergence criterion for dependent variables. 3. Experiments and validation Fig. 3 shows the configuration of the experimental setup consisting of a cooling system, film heater, acrylic plate, and rotating frame. The acrylic (k = 0.2 W/m°C, e = 0.85) was used to make the chimney. The chimney parameters were as follows: hc = 200 mm, tc = 2 mm, rc_i = 55 mm, and rc_o = 75 mm. The aluminum alloy 6061 (k = 171 W/m°C, e = 0.25) was used to make the heat sink. The heat sink parameters were as follows: N = 20, ll = 50 mm, lm = 20 mm, hh = 20 mm, th = 2 mm, and rh = 75 mm. The heat sink and chimney were fixed in place by a hot melt adhesive. The film heater was employed to apply the heat flux, and a slidacs and wattmeter were utilized to control and measure the power of the film heater. To make the heat flux uniform, an aluminum plate (1 mm) was placed under the base of the heat sink.
Fig. 3. Experimental setup.
The acrylic plate was positioned under the film heater and thermocouples were set at the top and bottom faces of the acrylic plate to measure the rate of heat transfer through the acrylic plate. All inter-
419
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The thermal resistance of the cooling system was calculated using following equation:
Rth ¼
T h av e T a q_ h b Ah b
ð3Þ
The experiments were conducted six times repeatedly, and the uncertainty of the thermal resistance of the heatsink was calculated as less than 7.6%. Fig. 4 is the comparison between the numerical and experimental results at Q_ film heater ¼ 10 W and Ta = 25 °C. The experimental results show the error was less than 10% as compared with the numerical results. 4. Results and discussion 4.1. Orientation effect and flow pattern
Fig. 4. The results of the numerical analysis and validation experiment (Q_ film heater ¼ 10 W, Ta = 25 °C).
faces were plastered with thermal grease to minimize the thermal contact resistance. Binder clips were installed to fix the heat sink, film heater, and acrylic plate. The cooling system was established on the rotating frame to measure the orientation effect. To ensure that measurements were performed at steady state, we obtained the value of the temperatures when the change of temperature was less than 0.1 °C. The heat flux was obtained as follows:
q_ h
b
¼
T Q_ film heater kacr Aacr acr
top T acr bottom
t acr
ð2Þ
Aacr
Fig. 4 shows the thermal resistance depending on the installation angle of the cooling system. The power of the film heater was 10 W, and the temperature of the air was 25 °C. The air flow around the cooling system, the temperature contours on the symmetry faces, and the inlet mass flow rate with respect to the Table 3 The ranges and references of the geometric parameters for the parametric study. Geometric parameters
N ll lm hc rc_i
Ranges for parametric study Min.
Ref.
Max.
12 40 mm 10 mm 100 mm 35 mm
20 50 mm 20 mm 200 mm 55 mm
28 60 mm 30 mm 300 mm 75 mm
Table 2 The flow pattern, the temperature contour, and the mass flow rate of the inlet air depending on the installation angle. (a) h = 0°
(b) h = 90°
(c) h = 180°
Side face _ sideface ¼ 0:879 g=s m
Side face 1, upper face _ sideface1 ¼ 0:140 g=s, m _ upperface ¼ 0:140 g=s m
Upper face _ upperface ¼ 0:106 g=s m
Streamline around heat sink
Temperature contour on symmetry faces
Location of side face and upper face
Air inlet surface Mass flow rate of inlet air
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S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
installation angle are shown in Table 2. At h = 0°, air entered through the side face and exited through the upper surface, thereby generating a chimney-shaped flow pattern. Installing the chimney increased the flow rate of the inlet air and caused the air to penetrate into the center of the radial heat sink, as shown by Park et al. [6]. As h was increased, the flow rate of inlet air
through the side face was decreased, and the cooling performance deteriorated rapidly. Thus, beyond h = 90°, the cooling performance of the cooling system was not further enhanced by the chimney installation. At h = 90°, the air started to enter both side face 1 and the upper face. Therefore, the cooling performance degenerated gradually compared to the previous installation angles. At h = 180°, the flow pattern was changed again; air entered through the upper surface and exited through the side face. 4.2. Parametric study
(a) The effect of the number of fins (N)
The influences of the parameters of the cooling system (i.e., the number of fins N, the length of the long fin ll, the length of the middle fin lm, the height of the chimney hc, and the inner radius of the chimney rc_i) on Nurh h =Nurh h¼0 (i.e., the orientation effect performance factor) were analyzed. Table 3 shows the range and reference value of the geometric parameters in the parametric study. Among the five parameters, the length of the long fin (ll) and inner radius of the chimney (rc_i) had relatively weak influence (less than 10%), while the number of fins (N), the length of the middle fin (lm), and the height of the chimney (hc) had greater influence (more than 10%). Fig. 5 shows the value of Nurh h =Nurh h¼0 depending on N, lm, and hc. N had the greatest influence, followed by hc and lm. As the values of N, lm, and hc increased, the values of Nurh h =Nurh h¼0 decreased, implying that the orientation effect became stronger. In the case of hc, the position of the inflection point was changed, unlike the other factors. This is because, as hc was increased, the flow resistance of the chimney to the air entering into the upper surface of the heat sink was increased; therefore, a change in the flow pattern (air inlet surface: side face ? side face 1 and upper face) occurred at a larger h. 4.3. Correlation
(b) The effect of the length of the middle fin (lm)
A correlation is proposed that is able to calculate the orientation effect of a radial heat sink with a chimney. The correlation is a function of the geometric parameters and installation angle of the cooling system. Based on the parametric study, the three geometric parameters (i.e., the number of fins N, the length of the middle fin lm, and the height of the chimney hc) that had a large effect on Nurh h =Nurh h¼0 (i.e., the orientation effect factor) were considered in order to develop the correlation. In the ranges of 12 N 28, 10 mm lm 30 mm, and 100 mm hc 300 mm,
(c) The effect of the height of the chimney (hc) Fig. 5. The results of the parametric study (Q_ film heater ¼ 10 W, Ta = 25 °C).
Fig. 6. Comparison of the orientation effect factor of the numerical analysis and correlation.
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
each parameter was divided into five levels, and 25 experimental points were selected using an orthogonal array (OA). We also considered five installation angles (h = 0°, 45°, 90°, 135°, and 180°), allowing us to obtain a total of 125 design points. The correlation that can predict the value of Nurhx h =Nurhx h¼0 depending on the installation angle and geometric parameters of the cooling system by performing a regression analysis of the 125 design points is described as follows:
Nurh h rh ¼ 1 C 1 ln ð1 þ C 2 hÞC3 C 4 þ C 5 2pr h Nurh h¼0 th N C 9 C 12 lm hc C7 þ C8 C 10 þ C 11 rh rh
!C 6
ð4Þ
will help design safer cooling system by considering the installation angle. Conflicts of interest We declare no conflicts of interest in this paper. Acknowledgement 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
where
C 1 ¼ 0:94 C 5 ¼ 0:24
421
C 2 ¼ 0:0091 C 6 ¼ 0:35
C 9 ¼ 0:211 C 10 ¼ 0:0986
C 3 ¼ 0:573 C 4 ¼ 0:271 C 7 ¼ 0:175 C 8 ¼ 0:301 C 11 ¼ 0:12
ð5Þ
C 12 ¼ 0:267
The coefficient of determination of Eq. (4) was R2 = 0.94. Fig. 6 shows the graph that compares the Nurh h =Nurh h¼0 values of the numerical analysis and correlation. The correlation is able to predict the orientation effect with a maximum error of less than 20%. 5. Conclusions The orientation effect of a radial heat sink with a chimney was analyzed in this study. The heat transfer and flow around the cooling system were simulated with the RNG k-e turbulence model and DO radiation model, and the models were validated experimentally. The orientation effect with respect to the installation angle was calculated, and the cause of the orientation effect was determined by analyzing the flow pattern. As a result, we found that the orientation effect was caused by changes in the mass flow rate and flow pattern of air. The influences of the parameters of the cooling system on Nurh h =Nurh h¼0 , i.e., the performance factor of the orientation effect, were investigated, and the three parameters that had the largest influence were selected. Finally, the correlation that can predict the value of Nurh h =Nurh h¼0 was suggested by regression analysis of 125 design points. The results of this study
[1] V.A.F. Costa, A.M.G. Lopes, Improved radial heat sink for led lamp cooling, Appl. Therm. Eng. 70 (2014) 131–138. [2] S.H. Yu, K.S. Lee, S.J. Yook, Optimum design of a radial heat sink under natural convection, Int. J. Heat Mass Transfer 54 (2011) 2499–2505. [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] D. Jang, S.H. Yu, K.S. Lee, Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications, Int. J. Heat Mass Transfer 55 (2012) 515– 521. [5] S.J. Park, D. Jang, S.J. Yook, K.S. Lee, Optimization of a staggered pin-fin for a radial heat sink under free convection, Int. J. Heat Mass Transfer 87 (2015) 184–188. [6] S.J. Park, D. Jang, S.J. Yook, K.-S. Lee, Optimization of a chimney design for cooling efficiency of a radial heat sink in a LED downlight, Energy Convers. Manage. 114 (2016) 180–187. [7] 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 Transfer 89 (2015) 1184–1189. [8] I. Tari, M. Mehrtash, Natural convection heat transfer from inclined plate-fin heat sinks, Int. J. Heat Mass Transfer 56 (2013) 574–593. [9] Q. Shen, D. Sun, Y. Xu, T. Jin, X. Zhao, Orientation effects on natural convection heat dissipation of rectangular fin heat sinks mounted on LEDs, Int. J. Heat Mass Transfer 75 (2014) 462–469. [10] B. Li, C. Byon, Orientation effects on thermal performance of radial heat sinks with a concentric ring subject to natural convection, Int. J. Heat Mass Transfer 90 (2015) 102–108. [11] 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 Transfer 97 (2016) 705–711. [12] S.H. Yu, D. Jang, K.S. Lee, Effect of radiation in a radial heat sink under natural convection, Int. J. Heat Mass Transfer 55 (2012) 505–509.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Technical Note
Orientation effect of a radial heat sink with a chimney for LED downlights Seung-Jae Park, Kwan-Soo Lee ⇑ School of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
a r t i c l e
i n f o
Article history: Received 3 January 2017 Received in revised form 28 February 2017 Accepted 17 March 2017
Keywords: Heat sink Orientation effect Natural convection Chimney
a b s t r a c t The orientation effect of a radial heat sink with a chimney was investigated in an attempt to design safer cooling systems for LED downlights. The natural convective and radiative heat transfer were simulated with a numerical model to analyze the heat transfer and flow around the cooling system, and the model was experimentally validated. The causes of the orientation effect were determined by analyzing the numerical results. The influence of the geometric parameters of the cooling system on the orientation effect was analyzed. A parametric study was conducted to select the three geometric parameters that have the largest influence on the orientation effect. The numerical analysis was carried out on the design points, which were selected according to the design of experiments. A correlation was obtained that can predict the orientation effect factor depending on the geometric factors and installation angle of the cooling system. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction LED lightings have the advantages of being eco-friendly and long-lasting. Therefore, these lightings are being used to replace conventional lighting. However, if the temperature of the LED chip is increased, the lifetime will be reduced, and the emitted light will become unstable. Since LED downlights are normally embedded in the ceiling of a room, it is preferable to install a natural convection type heat sink that has the advantages of a semi-permanent lifetime and noiselessness operation compared to forced convection type cooling systems, such as fans [1]. However, the thermal performance of natural convection type heat sinks is inferior to other cooling systems. Therefore, studies seeking to enhance the thermal performance by changing the shape of the fins or installing a surrounding structure have been actively pursued. The radial heat sink, which has plate fins that are aligned radially on a circular base, is used for circular electrics, such as LED downlights. The cooling performance of long fin (L) type, long and middle fin (LM) type, and long, middle, and short fin (LMS) type radial heat sinks [2]. As a result, it was observed that the LM type heat sink, which can increase the heat transfer surface without overlapping of thermal boundary layers, was the optimum shape. The same research team improved the heat transfer rate of the radial heat sink by optimizing the shape and array of the pin ⇑ Corresponding author. E-mail address: [email protected] (K.-S. Lee). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.03.062 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
fins [3–5]. However, the mass-production of heat sinks that contain complex-shaped fins is expensive; therefore, it is difficult to make these adjustments in commercial products. Therefore, practical LED downlights utilize the LM type radial heat sink [6]. Park et al. [7] suggested the installation of a hollow cylinder-shaped surrounding structure to maximize the cooling performance without changing the fin shape. Utilizing the hollow cylinder-shaped surrounding structure could enhance the performance of the heat sink by 40%, because the air flow at the region where the heat exchange did not occur was restricted and the air velocity around the fin was increased. Park et al. [6] developed a chimney-shaped surrounding structure to minimize the mass increase in cooling systems that is caused by the installation of surrounding structure. The optimized chimney was 60% lighter than the hollow cylinder. Because of the horizontal part of the chimney, the cooled air could penetrate into the central part of the radial heat sink, which caused a 20% enhancement in the cooling performance. Heat sinks are installed within electronic devices at different angles. Therefore, many researchers have studied the orientation effect, which is a change in the cooling performance depending on the installation angle. Tari and Mehrtash [8] studied the thermal performance of a square heat sink depending on the installation angle, found the causes of the orientation effect, and suggested a correlation that can calculate the Nu of the heat sink depending on the installation angle. Shen et al. [9] calculated the thermal performance of a square heat sink in relation to the installation angle and the fin direction with a numerical method and analyzed
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
417
Nomenclature A cp g h k l N _ m p Q_ q_ Rth r T t u
surface area (m2) specific heat (J/kg°C) gravity acceleration (m/s2) height (mm) kinetic energy of turbulence (m2/s2)/thermal conductivity (W/m°C) length (mm) number of fin arrays mass flow rate (g/s) pressure (Pa) heat generation rate (W) heat flux (W/m2) thermal resistance (°C/W) radius (mm) temperature (°C) thickness (m/s) velocity component (m/s)
the flow pattern around the fin to find the cause of the orientation effect. However, the flow patterns in square heat sinks and radial heat sinks are different; thus, it is difficult to apply their results to a radial heat sink. The orientation effect of a radial heat sink that had a concentric ring in the central part was studied [10,11]. The influence of the number of fin arrays on the orientation effect was studied and a correlation that could predict the orientation effect factor was suggested in their study. However, the equipment of the surrounding structure changed the flow pattern. Therefore, we cannot predict the orientation effect of the cooling system with a chimney above a radial heat sink using the existing research results. In this study, the orientation effect of a radial heat sink with chimney, as shown in Fig. 1, is analyzed. A numerical model to simulate the natural convective and radiative heat transfer is adopted,
Greek symbols e emissivity/dissipation rate of turbulent kinetic energy (m2/s3) l dynamic viscosity (m2/s) h installation angle (°) Subscripts a air acr acrylic ave average b base c chimney eff effective h heat sink i inner l long fin m middle fin o outer
and a validation experiment is conducted. The influence of the geometric parameters of the cooling system on the orientation effect is analyzed. Finally, the correlation that can predict the orientation effect factor depending on the geometric factors and installation angle of the cooling system was suggested. 2. Model description 2.1. Numerical model Fig. 2 shows the boundary conditions and the computational domain containing a radial heat sink, chimney-shaped surrounding structure, and air. Only half of the region was calculated with the symmetry boundary condition to reduce the computational effort. An LM type radial heat sink [2] was considered in this study. To retain the independence of the computational domain from the installation angle of the cooling system, a spherical control volume was adjusted for the air domain. To calculate the thermal flow, the following assumptions were conducted: (1) The air is an ideal gas. (2) The flow is three dimensional and steady state. (3) The material properties are independent of the temperature, except the density of air. (4) The surfaces of the cooling system are gray and diffuse. The renormalization group (RNG) k-e turbulence model and discrete ordinates (DO) radiation model were selected as the numerical models for this study. The general transport equation was used as follows [12]:
@ @ @/ þ S/ ðquj /Þ ¼ C/ @xj @xj @xj
ð1Þ
where the terms for /, C/ , and S/ were listed in Table 1. 2.2. Numerical methodology
Fig. 1. The configuration of the cooling system with a chimney and a radial heat sink.
The radial heat sink and chimney have the following parameters: N = 20, ll = 50 mm, lm = 20 mm, hh = 20 mm, th = 2 mm, rh = 75 mm, hc = 200 mm, tc = 2 mm, rc_i = 45 mm, and rc_o = 75 mm. The radius of the air domain (ra) was changed from 1.2(hc + hh) to 2.4(hc + hh) to obtain the size of the computational domain that produced a less than 1% change in the temperature. Consequently,
418
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
Fig. 2. Computational domain and boundary conditions.
Table 1 Arbitrary scalar parameters (/), diffusivity coefficients (C/ ), and source terms (S/ ) in general transport equation (Eq. (1)). Equation
/
C/
S/
Continuity Momentum
1 ui
0
0 @p=@xi þ F (for z-direction F = –qg)
Turbulent kinetic energy
k
Dissipation rate of turbulence kinetic energy
e
Energy
T
leff ak leff ae leff aleff
lt S2 qe C 1e ðe=kÞðlt S2 C 3e g i lt =qPrt @ q=@xi Þ ðC 2e þ 0:085g3 ð1 g=4:38Þ=ð1 þ 0:012g3 ÞÞðqe2 =kÞ 1=cp @ðui ðsij Þeff Þ=@xj
we set ra to 1.5(hc + hh). The number of tetrahedral meshes was changed from 1,026,054 to 11,287,916 to test the grid dependency. As a result, 5,257,829 meshes were selected as a reference meshes that produced a less than 1% change in the temperature of the heat sink. The heights of meshes were decreased around the solids where the boundary layers were developed. ANSYS ICEM and FLUENT release 17.0 were used to generate the grid and discretize and calculate the general equation. A maximum relative error less than 105 was defined for the convergence criterion for dependent variables. 3. Experiments and validation Fig. 3 shows the configuration of the experimental setup consisting of a cooling system, film heater, acrylic plate, and rotating frame. The acrylic (k = 0.2 W/m°C, e = 0.85) was used to make the chimney. The chimney parameters were as follows: hc = 200 mm, tc = 2 mm, rc_i = 55 mm, and rc_o = 75 mm. The aluminum alloy 6061 (k = 171 W/m°C, e = 0.25) was used to make the heat sink. The heat sink parameters were as follows: N = 20, ll = 50 mm, lm = 20 mm, hh = 20 mm, th = 2 mm, and rh = 75 mm. The heat sink and chimney were fixed in place by a hot melt adhesive. The film heater was employed to apply the heat flux, and a slidacs and wattmeter were utilized to control and measure the power of the film heater. To make the heat flux uniform, an aluminum plate (1 mm) was placed under the base of the heat sink.
Fig. 3. Experimental setup.
The acrylic plate was positioned under the film heater and thermocouples were set at the top and bottom faces of the acrylic plate to measure the rate of heat transfer through the acrylic plate. All inter-
419
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
The thermal resistance of the cooling system was calculated using following equation:
Rth ¼
T h av e T a q_ h b Ah b
ð3Þ
The experiments were conducted six times repeatedly, and the uncertainty of the thermal resistance of the heatsink was calculated as less than 7.6%. Fig. 4 is the comparison between the numerical and experimental results at Q_ film heater ¼ 10 W and Ta = 25 °C. The experimental results show the error was less than 10% as compared with the numerical results. 4. Results and discussion 4.1. Orientation effect and flow pattern
Fig. 4. The results of the numerical analysis and validation experiment (Q_ film heater ¼ 10 W, Ta = 25 °C).
faces were plastered with thermal grease to minimize the thermal contact resistance. Binder clips were installed to fix the heat sink, film heater, and acrylic plate. The cooling system was established on the rotating frame to measure the orientation effect. To ensure that measurements were performed at steady state, we obtained the value of the temperatures when the change of temperature was less than 0.1 °C. The heat flux was obtained as follows:
q_ h
b
¼
T Q_ film heater kacr Aacr acr
top T acr bottom
t acr
ð2Þ
Aacr
Fig. 4 shows the thermal resistance depending on the installation angle of the cooling system. The power of the film heater was 10 W, and the temperature of the air was 25 °C. The air flow around the cooling system, the temperature contours on the symmetry faces, and the inlet mass flow rate with respect to the Table 3 The ranges and references of the geometric parameters for the parametric study. Geometric parameters
N ll lm hc rc_i
Ranges for parametric study Min.
Ref.
Max.
12 40 mm 10 mm 100 mm 35 mm
20 50 mm 20 mm 200 mm 55 mm
28 60 mm 30 mm 300 mm 75 mm
Table 2 The flow pattern, the temperature contour, and the mass flow rate of the inlet air depending on the installation angle. (a) h = 0°
(b) h = 90°
(c) h = 180°
Side face _ sideface ¼ 0:879 g=s m
Side face 1, upper face _ sideface1 ¼ 0:140 g=s, m _ upperface ¼ 0:140 g=s m
Upper face _ upperface ¼ 0:106 g=s m
Streamline around heat sink
Temperature contour on symmetry faces
Location of side face and upper face
Air inlet surface Mass flow rate of inlet air
420
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
installation angle are shown in Table 2. At h = 0°, air entered through the side face and exited through the upper surface, thereby generating a chimney-shaped flow pattern. Installing the chimney increased the flow rate of the inlet air and caused the air to penetrate into the center of the radial heat sink, as shown by Park et al. [6]. As h was increased, the flow rate of inlet air
through the side face was decreased, and the cooling performance deteriorated rapidly. Thus, beyond h = 90°, the cooling performance of the cooling system was not further enhanced by the chimney installation. At h = 90°, the air started to enter both side face 1 and the upper face. Therefore, the cooling performance degenerated gradually compared to the previous installation angles. At h = 180°, the flow pattern was changed again; air entered through the upper surface and exited through the side face. 4.2. Parametric study
(a) The effect of the number of fins (N)
The influences of the parameters of the cooling system (i.e., the number of fins N, the length of the long fin ll, the length of the middle fin lm, the height of the chimney hc, and the inner radius of the chimney rc_i) on Nurh h =Nurh h¼0 (i.e., the orientation effect performance factor) were analyzed. Table 3 shows the range and reference value of the geometric parameters in the parametric study. Among the five parameters, the length of the long fin (ll) and inner radius of the chimney (rc_i) had relatively weak influence (less than 10%), while the number of fins (N), the length of the middle fin (lm), and the height of the chimney (hc) had greater influence (more than 10%). Fig. 5 shows the value of Nurh h =Nurh h¼0 depending on N, lm, and hc. N had the greatest influence, followed by hc and lm. As the values of N, lm, and hc increased, the values of Nurh h =Nurh h¼0 decreased, implying that the orientation effect became stronger. In the case of hc, the position of the inflection point was changed, unlike the other factors. This is because, as hc was increased, the flow resistance of the chimney to the air entering into the upper surface of the heat sink was increased; therefore, a change in the flow pattern (air inlet surface: side face ? side face 1 and upper face) occurred at a larger h. 4.3. Correlation
(b) The effect of the length of the middle fin (lm)
A correlation is proposed that is able to calculate the orientation effect of a radial heat sink with a chimney. The correlation is a function of the geometric parameters and installation angle of the cooling system. Based on the parametric study, the three geometric parameters (i.e., the number of fins N, the length of the middle fin lm, and the height of the chimney hc) that had a large effect on Nurh h =Nurh h¼0 (i.e., the orientation effect factor) were considered in order to develop the correlation. In the ranges of 12 N 28, 10 mm lm 30 mm, and 100 mm hc 300 mm,
(c) The effect of the height of the chimney (hc) Fig. 5. The results of the parametric study (Q_ film heater ¼ 10 W, Ta = 25 °C).
Fig. 6. Comparison of the orientation effect factor of the numerical analysis and correlation.
S.-J. Park, K.-S. Lee / International Journal of Heat and Mass Transfer 110 (2017) 416–421
each parameter was divided into five levels, and 25 experimental points were selected using an orthogonal array (OA). We also considered five installation angles (h = 0°, 45°, 90°, 135°, and 180°), allowing us to obtain a total of 125 design points. The correlation that can predict the value of Nurhx h =Nurhx h¼0 depending on the installation angle and geometric parameters of the cooling system by performing a regression analysis of the 125 design points is described as follows:
Nurh h rh ¼ 1 C 1 ln ð1 þ C 2 hÞC3 C 4 þ C 5 2pr h Nurh h¼0 th N C 9 C 12 lm hc C7 þ C8 C 10 þ C 11 rh rh
!C 6
ð4Þ
will help design safer cooling system by considering the installation angle. Conflicts of interest We declare no conflicts of interest in this paper. Acknowledgement 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
where
C 1 ¼ 0:94 C 5 ¼ 0:24
421
C 2 ¼ 0:0091 C 6 ¼ 0:35
C 9 ¼ 0:211 C 10 ¼ 0:0986
C 3 ¼ 0:573 C 4 ¼ 0:271 C 7 ¼ 0:175 C 8 ¼ 0:301 C 11 ¼ 0:12
ð5Þ
C 12 ¼ 0:267
The coefficient of determination of Eq. (4) was R2 = 0.94. Fig. 6 shows the graph that compares the Nurh h =Nurh h¼0 values of the numerical analysis and correlation. The correlation is able to predict the orientation effect with a maximum error of less than 20%. 5. Conclusions The orientation effect of a radial heat sink with a chimney was analyzed in this study. The heat transfer and flow around the cooling system were simulated with the RNG k-e turbulence model and DO radiation model, and the models were validated experimentally. The orientation effect with respect to the installation angle was calculated, and the cause of the orientation effect was determined by analyzing the flow pattern. As a result, we found that the orientation effect was caused by changes in the mass flow rate and flow pattern of air. The influences of the parameters of the cooling system on Nurh h =Nurh h¼0 , i.e., the performance factor of the orientation effect, were investigated, and the three parameters that had the largest influence were selected. Finally, the correlation that can predict the value of Nurh h =Nurh h¼0 was suggested by regression analysis of 125 design points. The results of this study
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