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Effects of Ambient Temperatures on Natural
Convection Heat Transfer from Finned Heat Sinks
Lian-Tuu Yeh, Ph D & PE
ASME Fellow
Dallas, Texas, USA
Email: jjyeh2@aol.com
Keywords: Ambient Temperatures, Natural Convection Heat Transfer, Finned Heat
Sinks
Abstract: The electronic equipment is often required to operate at various ambient
temperatures in the real world conditions, especially for an outdoor system. A cfd
analysis is performed to study the effects of the ambient temperatures for the finned heat
sink on the heat transfer coefficient under the natural convection conditions. Four
different ambient temperatures, 100, 120, 140 and 160 ºF are considered for the
continuous fin, staggered fin and in-line fin heat sinks. The overall heat transfer
coefficient of individual finned heat sinks is determined to facilitate the thermal analysis
and design of the equipment
1. Introduction
The electronic equipment is often required operating at various ambient temperatures in the
real world applications such as the outdoor electronics. Therefore, there is an urgent need to
address these issues for the practical engineering applications.
Heat transfer by natural (or free) convection has long been considered as one of the most cost
effective and reliable cooling methods. Natural convection with air has many practical
engineering applications and is of special interest to the cooling of outdoor electronic equipment
such as those shown in Figure 1. The advantages of air cooling by natural convection are simple,
safe and cost effective.
Electronic box
Continuous fins
Staggered fins
Electronic box
Continuous fins
Staggered fins
Figure 1 Finned Heat Sink for Outdoor Electronics
Figure 2 shows a typical configuration of a vertically continuous fin array. The flow field
over a finned heat sink is much complicated than the typical flow over a single plate or in
parallel plates because of the involvement of the third surface (fin base). The finned heat sink as
presented in Figure 2 consists of a number of U-shaped channels. Little flow through corner
regions which are formed by the heat sink base and fins results in a significant reduction in the
heat transfer.
Figure 2 A Vertical Straight Fin Heat Sink
For vertically straight- fin heat sinks as shown in Figure 2, several experimental data (1-3)
are available. Among them, Izume and Nakamure (3) developed a mathematical relationship
describing heat transfer from the finned heat sink, however, their equation does not hold in the
limiting cases of very large or very small ratios of the channel depth to channel width. To
overcome this problem, Van De Pol and Tierney (4) developed an empirical equation which is
applicable to any channel depth to width ratios to compute the U-channel heat transfer
coefficient. The correlation is limited to the constant wall temperature condition and is only
applicable to the continuous straight fins.
Yeh et al. (5) performed a CFD analysis on the continuous fin, staggered fin and in-line fin
heat sinks as illustrated in Figure 3 at the constant wall temperature conditions. The results
indicate that the continuous fin configuration is the most efficient thermally, and is followed by
the staggered fins and then by the in-line fins. Though the in-line fin array has the greatest
surface area, it has the least heat loss because of the smallest fin spacing choking the flow.
Continuous fins Staggered fins In -Li n e fins
Continuous fins Staggered fins In -Li n e fins
Figure 3 Three Types of Finned Heat Sinks
Yeh (6) extended the analysis to examine the effects of the cover/shroud on the heat transfer.
To further understand the effect of the distance between the cover and the fin tip of the heat sink,
this distance is varied from zero to 99”. The results indicate that there will be no effect of the
cover on the heat loss and entrant flow rate as long as the distance between the cover and the
heat sink tip is greater than 4.36” with the fin height of 2.0”. Based on the limited data in this
work, it is concluded that there is no effect of the cover on the heat transfer of a finned heat sink
if the distance between the heat sink and the cover is greater than 2.5 times of the fin height.
Thermal Analysis
The previous analyses (5, 6) are limited to the case with a vertical heat sink at the ambient
temperature of 120 ºF (40 ºC). Those analyses were made to meet specific product development
needs then. However, the electronic equipment is often required to operate at various ambient
temperatures for the indoor and outdoor applications. Therefore, the thermal analysis is further
extended to all three types of finned heat sinks at various ambient conditions (from 100ºF to
160ºF).
The overall dimensions of the finned heat sink are listed as follows:
Fin width (in) : 10.341
Fin length (in) : 15
Fin thickness (in) : 0.1
Fin height (in) : 2.0
Fin base plate thickness (in) : 0.2
Fin numbers : 20
In order to maintain the component junction temperature below 100ºC, the maximum
temperature of the heat sink base must not be over 80ºC and thus it is assumed to be uniform at
176 F (80 C). In addition, the air density is considered to be constant and at the sea level.
Because of light weight and high thermal conductivity, aluminum is often a preferred choice to
be used in cooling of electronics. The thermal conductivity of the heat sink is assumed to be 80
Btu/hr-F-ft (137 W/m-C).
Results and Discussions
The heat losses from the heat sink versus the ambient air temperatures for various types of
finned heat sinks are given in Figure 4. With the fixed temperature (176 F or 80 C) at the heat
sink base, the heat loss decreases when the ambient temperature increases. As can been seen in
Figure 4, the continuous fin heat sink with the least heat loss is the most effective thermally, then
is followed by the staggered fin heat sink. On other hand, the in-line fin configuration has the
worst thermal performance even though it has largest convection surface area. This is because
the fin spacing of the heat sink is too small to be effective by chocking the air flow through the
fins. Table 1 lists the geometrical data of each type of fin configurations.
Heat Loss from Heat Sinks
0
20
40
60
80
100
120
140
160
80 100 120 140 160 180
Ambient Temperature, (F)
Heat Loss, (Watts)
continuous
staggered
in-line
Figure 4 Natural Convection Heat Losses versus Ambient Air Temperatures
Table 1 Comparison among Various Types of Fin Configurations
Continuous Staggered In-Line
Number of fins 20 20/19 39/0
Fin spacing (in) 0.439 0.439 0.1695
Convection area (in2 ) 1373.2 1454.4 1537.9
The heat transfer coefficients for various types of fin configurations as functions of the ambient
temperatures are calculated and presented in Figure 5. The heat transfer coefficient, h, which is
defined as h = Q/(A ∆T) is computed based on the total convection (exposed) surface area as listed
in Table 1 and the total heat loss from Figure 4. Figure 5 clearly shows the nonlinear functions of
the temperature for the natural convection heat transfer coefficient. Based on the limited data
available from the present analysis, the following correlation is developed.
h1/h2 = (ΔT1/ΔT2)0.5 (1)
Where hi is the heat transfer coefficient at ΔTi = Tsurface - Tambient .
The following equation exists for the most cases of the natural convection in laminar flow,
including the flow over a vertical plate or horizontal plates,
Nu α RaH 0.25 = (Gr Pr)0.25 (2a)
where
Nu = Nusselt number, h H /k,
RaH = Rayleigh number, Gr Pr,
Pr = Prandtl number, cp / k,
Gr = Grashof number, 2g H3 T/ 2 ,
H = Characteristic length (Plate height for vertical plate),
T = temperature difference between the wall and ambient,
Equation (2a) implies
h α (∆T)0.25 (2b)
As can be seen from Equations (1) and (2b), one can conclude that the flow through individual U-
channels of the finned heat sinks is not a laminar flow. This is due to the fact that the U-channel
flow field is complicated. For vertical heat sinks, the flow entering the heat sink from the bottom
side is relatively uniform. However, combining the entrant flow between the fin tips at the front
side of the heat sink as illustrated in Figure 6 makes the flow field relatively complicated. The flow
distributions for the heat sinks operating at the ambient of 49ºC (120ºF) are listed on Table 2.
Natural Convection Heat Transfer
Coefficients
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
80 100 120 140 160 180
Ambient Temperature, (F)
Heat Transfer
Coefficient, (Btu/hr-
ft**2)
continuous
staggered
in-line
Figure 5 Heat Transfer Coefficients of Finned Heat Sinks
Entrant
Flow
In le t
Flow
Exit
Flow
Entrant
Flow
In le t
Flow
Exit
Flow
Figure 6 Flow Field for a Vertical Finned Heat Sink
The heat sink thermal resistance which is defined as ∆T/Q (=1/ (h A)) (ºC/W) is often used to
measure the thermal efficiency of the heat sink. The thermal resistance of the heat sink as a
function of the ambient temperatures is presented in Figure 7. The thermal resistance basically
represents an inverse of the heat transfer coefficient.
Table 2 Average flow rate to heat sink (CFM)
Continuous Staggered In-Line
- Entering from bottom 1.8004 1.6026 1.2237
- Entering from fin tip (net entrant) 5.0825 3.4805 1.3625
- Exiting from top 6.9209 5.3127 3.0548
Heat Sink Thermal Resistan ce
0
0.2
0.4
0.6
0.8
1
1.2
80 100 120 140 160 180
Ambient Temperature, (F)
Thermal Resistance, (C/W)
continuous
stagger ed
in-line
Figure 7 Thermal Resistance of Various Heat Sinks
The system thermal design generally utilizes the ambient temperature based on the worst
case condition and it is industry dependent. In other words, individual industry has its standards
to follow. For the outdoor equipment, the ambient temperature of 49 ºC (120 ºF) is applied to the
system thermal design. The ambient temperature of 71 ºC (160 ºF) is employed if the equipment
is located inside a non-air conditioning building which is also subjected to solar heating.
Therefore, the temperature range of the ambient from 100ºF to 160ºFare chosen for this study.
Table 3 listed the operating and non-operating environments for a wide range of components
installations.
Table 3 Electronic Equipment Environments and Heat Sinks
Summary and Conclusion
The electronics are often required operate at various ambient temperature ranges in the real
world applications. The air cooling by the natural convection is the most simple, safe and cost-
effective method. Therefore, the present study is focusing at the analysis of natural convection
heat transfer over the wide range of ambient temperatures from 100ºF to 160ºF.
The continuous fin is the most efficient thermally, and is followed by the staggered fins and
then by the in-line fins. The in-line fin array has the greatest surface area but it has the least heat
transfer coefficient because of the smallest fin spacing choking the flow. As given in Figure 5, it
clearly shows the nonlinear functions of the temperature for the natural convection heat transfer
coefficient. Based on the limited data available from the present analysis, the heat transfer
coefficient is a function of (ΔT)0.5 where ΔT is the temperature difference between the heat sink
base and the ambient.
The radiation heat transfer must always be included in the analysis and design of any system
under the natural convection (passive cooling method). This is especially true for the system
operating at high altitudes where the radiation becomes even more important because the air
density is smaller. In addition, the solar heating must also be considered for cooling of the outdoor
equipment.
References
[1] Starner, K.E., and McManus, H. N, “An Experimental Investigation of Free Convection Heat Transfer from
Rectangular Fin Arrays”, J Heat Transfer 85, 1963
[2] Welling, J.R. and Wooldridge, C. R., “Free Convection Heat Transfer Coefficients from Rectangular Vertical
Fins”, J Heat Transfer 87, 1965
[3] Izume, K, and Nakamura, H, “Heat Transfer by Convection on Heated surface with Parallel Fins”, Jap. Soc.
Mech. Eng., 34, 1969
[4] Van De Pol, D. W., and Tierney, J.K., “Free Convection Nusselt Number for Vertical U-Shaped Channels”, J
Heat Transfer, 95, 1973
[5] Yeh, L.T., Yeh, Joseph and Chung, B.T. F., “Natural Convection from Finned Heat Sinks”, IPack2007-33036,
Vancouver, BC, Canada, July 8-12, 2007
[6] Yeh, L.T., “Natural Convection from Finned Heat Sinks with/without Cover/Shroud”, 19th International
Symposium on Transport Phenomena, Reykjavik, Iceland, August 17th – 21st, 2008
[7] Yeh, L. T., and Chu, R., C, Thermal Management of Microelectronic Equipment, ASME Press, 2002
[8] Yeh, L. T., and Chu, R., C, Thermal Management of Telecommunications Equipment, ASME Press, 2013
[9] Yeh, L. T., Thermal Management of Microelectronic Equipment, 2nd Edition, ASME Press, 2017