International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 04, April 2019, pp. 65-76, Article ID: IJMET_10_04_009
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=4
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
OPTIMAL PLATE-FIN DESIGN FOR
IMPROVING HEAT DISSIPATION
PERFORMANCE OF AUTOMOBILE LAMP
REFLECTORS
Young Shin Kim
Industrial Technology Research Institute, Kongju National University, Korea
Seung Jun Na
Department of Mechanical Engineering, Graduate School, Kongju National University, Korea
Euy Sik Jeon
Department of Mechanical Engineering, Graduate School (Industrial Technology Research
Institute), Kongju National University, Korea
ABSTRACT
Automobile headlamp reflectors are subjected to high temperatures owing to heat
produced by the lamp and their sealed structure. Such high temperatures reduce light
quantity and shorten service life in lamps. Therefore, this study designed and analyzed
radiating fin designs, integrated into these reflectors, aiming to improve headlamp heat
dissipation performance. Basic analyses were conducted upon an existing headlamp,
and the validity of the analytical model was verified by testing existing reflector
temperatures under conditions similar to those modeled during the analyses. Based on
this verification, three types of radiating fins were modeled and analyzed. The vertical
fin type exhibited the highest heat dissipation performance. Subsequently, design
variables were selected for the vertical fin type and size optimization was performed
using the design of the experiment model. Results confirmed a heat dissipation
performance increase of 4.5% relative to the existing model.
Key words: Optimal design, Plate-fin, Heat dissipation, Lamp reflector
Cite this Article: Young Shin Kim, Seung Jun Na, Euy Sik Jeon, Optimal Plate-Fin
Design for Improving Heat Dissipation Performance of Automobile Lamp Reflectors,
International Journal of Mechanical Engineering and Technology 10(4), 2019, pp. 6576.
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Optimal Plate-Fin Design for Improving Heat Dissipation Performance of Automobile Lamp
Reflectors
1. INTRODUCTION
Nomenclature
L
W
H
k
P
T
T∞
RI
x, y, z
u, v, w
t
h
𝜀
ρ
g
vertical length of reflector (m)
horizontal length of reflector (m)
heat transfer coefficient (W/m2℃)
thermal conductivity (W/m℃)
pressure (Pa)
temperature (℃)
temperature of the fluid sufficiently far from the surface (℃)
refractivity
axial coordinate (m)
velocity in x, y and z-directions, respectively (m/s)
fin thickness (m)
fin height (m)
emissivity
density (kg/m3)
gravity (m/s2)
Automobile headlamps, located near the engine compartment, experience temperature
increases due to heat generated by lamp bulbs and their sealed structure. Such temperature
increases degrade the contained bulb, reducing light quantity and shortening service life. At
higher temperatures, nearby components can experience thermal shock deformation. Among
such components, reflectors (which reflect light from the bulb out of the headlamp structure)
are subjected to the most heat. To minimize reflector deformation due to thermal shock,
domestic and international studies have actively investigated heat dissipation design and heatreleasing plastic materials [1-3].
Heat dissipation design studies have adopted various perspectives. Many studies have
investigated LED lamp design following the increased use of such lamps. Sokmen et al. [4]
conducted numerical analyses and experiments to define thermal deformations inside
headlamps. Park [5] analyzed the heat dissipation performance characteristics according to
major design variables, including the heat sink shape, number of fins, and fin thickness. Jones
and Smith [6] presented a heat transfer relation formula for fin arrangement and reported that
fin spacing and height are the most important variables for the heat transfer of fins. Dipankar
Bhanja et al. [7] applied nonlinear equations using the Adomian decomposition method to
determine the temperature distribution in a T-shaped fin resulting from heat transfer, and thus
demonstrated T-shaped fin performance according to thickness and length as well as the effect
of heat transfer on optimal design. Studies aiming to reduce the heat dissipation effect by
increasing surface area and the number of radiating fins, however, remain lacking.
This study analyzed how reflector temperature is affected by lamp heat by modeling an
existing reflector. These analytical results were verified through a comparison with temperature
measurements taken from an existing reflectors and lamps. Based on this analysis, the heat
dissipation performance characteristics of radiating fin designs (plate- and pin-fin types) were
further investigated. To find an effective heat dissipation structure, arrangements and forms
were proposed for radiating fins integrated into the reflector. The heat dissipation performance
of these reflectors was then examined in accordance with the heat source using thermal analysis
software. This investigation of fin shape and dimension was expected to improve the heat
dissipation performance of reflectors.
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2. AUTOMOBILE LAMP REFLECTOR
2.1. Reflector Heat Flow Analysis Condition
A three-dimensional (3D) heat flow analysis was conducted to compare the heat transfer of an
existing reflector with three types of reflector-radiating fin integrations. This analysis was
validated by comparing the analytical and experimental results of the existing reflector. Further
analyses were then conducted based on these results. Heat flow analyses for the radiating fins
were conducted using ANSYS Fluent, a commercial software program. Analyses were
conducted under the following assumptions:
•
Air density was calculated by treating air as an ideal gas.
•
The discrete ordinates (DO) radiation model was used to analyze the radiation characteristics of
integrated reflectors, and all heat from the bulb was assumed to be radiant heat.
•
The atmospheric condition was set at 25 °C, and the thermal conductivity of the reflector was
set to 0.25 [W/m℃] (the thermal conductivity coefficient of the PBT material).
When 3D Cartesian coordinates are applied under the above assumptions, the principal
equations are as follows:
Continuity:
𝜕(𝜌𝑢)
𝜕𝑥
+
𝜕(𝜌𝑣)
𝜕𝑦
𝜕(𝜌𝑤)
+
𝜕𝑧
=0
(1)
Momentum:
𝜕(𝜌𝑢2 )
𝜕𝑥
𝜕(𝜌𝑣𝑢)
𝜕𝑥
𝜕(𝜌𝑤𝑢)
𝜕𝑥
+
+
+
𝜕(𝜌𝑢𝑣)
𝜕𝑦
𝜕(𝜌𝑣 2 )
𝜕𝑦
+
+
𝜕(𝜌𝑤𝑣)
𝜕𝑦
𝜕(𝜌𝑤𝑢)
𝜕𝑧
𝜕(𝜌𝑣𝑤)
𝜕𝑧
+
𝜕2 𝑢
𝜕2 𝑢
𝜕2 𝑢
𝜕𝑃
𝜕2 𝑣
𝜕2 𝑣
𝜕2 𝑣
(2)
= − 𝜕𝑦 + 𝜇 (𝜕𝑥 2 + 𝜕𝑦 2 + 𝜕𝑧 2 ) − 𝜌𝑔
𝜕(𝜌𝑤 2 )
𝜕𝑧
𝜕𝑃
= − 𝜕𝑥 + 𝜇 (𝜕𝑥 2 + 𝜕𝑦 2 + 𝜕𝑧 2 )
𝜕2 𝑤
𝜕𝑃
𝜕2 𝑤
= − 𝜕𝑧 + 𝜇 ( 𝜕𝑥 2 + 𝜕𝑦 2 +
𝜕2 𝑤
𝜕𝑧 2
)
(3)
(4)
Fluid energy:
𝜕(𝜌𝑢𝑇)
𝜕𝑥
+
𝜕(𝜌𝑣𝑇)
𝜕𝑦
+
𝜕(𝜌𝑤𝑇)
𝜕𝑧
𝑘
𝜕2 𝑇
𝜕2 𝑇
𝜕2 𝑇
= 𝐶 + 𝜇 (𝜕𝑥 2 + 𝜕𝑦 2 + 𝜕𝑧 2 )
𝑝
(5)
Solid:
𝜕2 𝑇
𝜕2 𝑇
𝜕2 𝑇
𝑘 (𝜕𝑥 2 + 𝜕𝑦 2 + 𝜕𝑧 2 ) + 𝑆𝑇 = 0
(6)
Figure 1 shows the boundary conditions used in 3D heat flow analysis. A control volume
of 0.17×0.17×0.17 m3 was used to model the air chamber around the lamp housing.
Conditions are shown in Table 1.
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Optimal Plate-Fin Design for Improving Heat Dissipation Performance of Automobile Lamp
Reflectors
Figure 1 Simulated boundary conditions
Table 1 Initial conditions of 3D model
No.
Name
Emissivity
Setting value
1
Bulb
0.1
400 [℃]
2
Reflector inner
0.1
0.25 [W/m℃]
3
Air
Convection
5 [W/m2℃]
Temperature
25 [℃]
2.2. Comparison with Experimental Results
The basic simulation of the existing reflector indicated the highest temperature of the reflector
to be 115.6 ℃ with a heat flow inside the chamber of 0.34 [m/s]. To verify and validate the
analytical results, the temperature of an existing reflector was measured and the experimental
results were compared with the calculated ones for the analysis. Figure 2 shows the schematic
diagram of the experimental setup, and Fig. 3 shows the experimental setup for reflector
temperature measurements. A 0.17 * 0.17 * 0.17 m air chamber was fabricated from acrylic to
set the same boundary conditions as were used for calculations. A K-type thermocouple sensor
was attached to the surface of the reflector, and temperature measurements were taken.
The temperature of the reflector was measured at three points on the lens unit at regular
horizontal intervals, and these results were compared to those calculated during thermal
analysis at the same positions. Both calculated and measured results are shown in Fig. 4. This
comparison indicated the temperature of the central portion to be approximately equivalent
between methods, with similar results at both the left and right points.
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Young Shin Kim, Seung Jun Na, Euy Sik Jeon
Temp.(℃)
Figure 2 Schematic diagram
Figure 3 Reflector heat dissipation experiment
130
125
120
115
110
105
100
95
90
85
80
Left
Middle
Experiment
Right
Simulation
Figure 4 Results comparison
2.3. Analysis of Integrated Reflector and Radiating Fins
The radiating fin shapes in Fig. 5 were designed for reflector temperature comparison. Three
types of fins were designed, all maintaining the heat transfer area and weight of the existing
reflector: vertical plate, horizontal plate, and pin fins.
(a) Type 1-Vertical plate fin
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Optimal Plate-Fin Design for Improving Heat Dissipation Performance of Automobile Lamp
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(b) Type 2-Horizontal plate fin
Temp.(℃)
(c) Type 3-Pin fin
Figure 5 Reflector models
130
125
120
115
110
105
100
95
90
85
80
Left
initial model
Type2
Type1
Type3
Middle
Right
Figure 6 Maximum temperature by type
The three types of reflector-fin integration were each analyzed following the same
methodology as the basic analysis. Figure 6 is a graph of temperature changes in the reflectorfin integrations. Type 1 was found to demonstrate the lowest thermal analysis temperatures,
whereas types 2 and 3 displayed temperatures higher than those of the existing model. This
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Young Shin Kim, Seung Jun Na, Euy Sik Jeon
appears to be because the air flow was interrupted by the position of the radiating fins, creating
a thermal interference phenomenon that decreased the air flow because of the change in the
pressure between the radiating fins. This was caused by an increase in the surface area of the
radiating fins. Type 1 was thus selected as the optimal model because it exhibited the lowest
temperature results. It was postulated that heat dissipation performance could be improved
through size optimization.
3. SIZE OPTIMIZATION
3.1. Design Variable Setting and Range Derivation
To optimize the heat conduction of the vertical plate pin model, improving its heat dissipation
performance, design variables were set as shown in Fig. 7. The thickness (t), height (h), and
number (n) of radiating fins were selected as design variables and based on the fixed horizontal
(W) and vertical (L) lengths of the heat transfer area of the reflector. Variable values were
selected as follows. Thickness was based on the minimum thickness that could be obtained
from general plastic injection. Height was set by considering the gap between the housing and
reflector. The number of radiating fins was selected by considering the horizontal length of the
reflector and the thickness of the radiating fins. After configuring the three variables, the
radiating fins underwent size optimization using DOE to minimize the temperature of the
housing. Table 2 contains the values for each variable.
(a) Top view
(b) Front view
Figure 7 Rotated diagrams of the fin installed vertically
Table 2 Design variables and levels
Parameters
Level
1
2
3
h [mm]
8
10
12
t [mm]
0.5
0.75
1
n [ea]
24
28
32
3.2. Design of experiment (DOE)
The Box-Behnken method, a commonly used method in response surface design, can be used
to efficiently estimate first-order and second-order terms. In this study, DOE was performed
using the Box-Behnken method in Minitab 17 software. A total of 15 analyses were conducted
based on the design conditions table, and Table 3 shows the results analyzed for each condition.
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Optimal Plate-Fin Design for Improving Heat Dissipation Performance of Automobile Lamp
Reflectors
Table 3 Experimental and predicted results
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Level
h [mm]
t [mm]
n [ea]
Results
[℃]
10
12
10
8
8
8
10
10
10
12
12
10
10
8
12
0.5
1
1
0.75
0.5
0.75
0.75
0.5
1
0.75
0.5
0.75
0.75
1
0.75
24
28
24
32
28
24
28
32
32
24
28
28
28
28
32
132.711
129.875
131.881
128.532
129.152
128.825
129.014
130.711
129.224
129.216
130.4
129.014
129.014
127.625
128.759
3.3. Results and analysis
ANOVA analysis results, shown in Table 4, demonstrated that each design variable
significantly affected the heat dissipation performance and confirmed each second-order term
also had significant effects. Equation (7) represents the regression equation derived for
temperature prediction. Figure 8 shows a surface plot of the maximum reflector temperature by
variable. Curvature effect was confirmed to occur due to the design variables.
Table 4 Analysis of variance
Source
Model
Linear
h
t
n
Square
h*h
t*t
n*n
Error
Lack-of-Fit
Pure Error
Total
DF
6
3
1
1
1
3
1
1
1
8
6
2
14
Adj SS
21.7130
8.3057
2.1177
2.4520
3.7360
13.4074
3.9353
6.0625
2.6763
3.3640
3.3640
0.0000
25.0770
Adj MS
3.61884
2.76857
2.11768
2.45201
3.73601
4.46912
3.93525
6.06248
2.67633
0.42050
0.56066
0.0000
F-Value
8.61
6.58
5.04
5.83
8.88
10.63
9.36
14.42
6.36
P-Value
0.004
0.015
0.055
0.042
0.018
0.004
0.016
0.005
0.036
temp. = 160.3 + 5.42h − 32.97t − 3.15n − 0.2581h ∗ h + 20.50t ∗ t + 0.0532n ∗ n
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.
(6)
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Young Shin Kim, Seung Jun Na, Euy Sik Jeon
(a)
(b)
(c)
Figure 8 Main effect plot
The suitability of the model was determined by analyzing the residual plots obtained
through the Box-Behnken method. Figure 9 shows the residual plots of the model as follows.
Figure 9(a) shows the normal probability plot, in which the straight line values confirmed
normality. Figure 9(b) plots residuals versus fitted values and confirms model validity through
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Optimal Plate-Fin Design for Improving Heat Dissipation Performance of Automobile Lamp
Reflectors
the randomly scattered values. Figure 9(c) is a histogram, depicting the results in an
approximate bell shape. Figure 9(d) shows residuals versus orders, thus confirming the
experiment was performed randomly.
Figure 9 Residual plot of model for error values (temp.)
A reaction optimization tool was used to derive the optimal values of the independent
radiating fin design variables. Figure 10 shows the results of the optimization conditions for
each design variable. The objective function was derived to minimize the maximum
temperature.
Figure 10 Optimization conditions
After modeling was performing by applying the radiating fin optimization conditions
derived using the Box-Behnken method, a thermal analysis simulation was performed. The
results from the initial and type 1 models, those from DOE, and the optimized results were all
compared and analyzed.
Table 4 shows these results. The optimization results confirmed that reflector heat
dissipation performance was improved by 4.5% relative to the existing model.
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Table 4 Optimization results
Level
Parameters
t [mm]
h [mm]
n [ea]
temperature [℃]
Initial
Type 1
DOE
Results of
simulation
132.97
1
10
24
128.56
0.8081
8.0
30.4
126.93
0.8
8.0
30
127.02
4. CONCLUSIONS
In this study, a radiating fin design was optimized via thermal analysis simulation to improve
the heat dissipation performance of automobile lamp reflectors, and design performance was
examined. Three types of radiating fins with different shapes and arrangements were designed,
and their heat dissipation performances were compared and analyzed using thermal analysis
simulation. After selecting the optimal model, the heat dissipation performance of the resulting
reflector was optimized via radiating fin size optimization using the Box-Behnken method.
1) Thermal analysis was conducted based on modeling of an automobile lamp reflector. The
validity of the analytical model was verified by performing a temperature measurement
experiment on the lamp reflector under conditions similar to the analysis conditions.
2) A thermal analysis simulation was performed to compare the heat dissipation
performances of the vertical plate, horizontal plate, and pin fins, and it was confirmed that
the vertical plate fin shape exhibited the highest heat dissipation performance.
3) To improve the heat dissipation performance of the selected vertical plate fin, the height,
thickness, and number of the fins were optimized using DOE in the Box-Behnken method.
As a result, it was confirmed that heat dissipation performance was improved by 4.5%
relative to the existing model.
ACKNOWLEDGEMENT
This research was supported by the Ministry of Trade, Industry and Energy, Korea Institute for
Advancement of Technology through the Encouragement Program for The Industries of
Economic Cooperation Region(P0006067)
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Optimal Plate-Fin Design for Improving Heat Dissipation Performance of Automobile Lamp
Reflectors
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