Thermal Management

Application Note - Interpoint
Crane Aerospace & Electronics Power Solutions
Thermal Management
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
Although the concepts stated are universal, this application note was written specifically for Interpoint products.
Switching Power Supplies are devices which transform power
from an input voltage level to one or more output voltages, generally different from that at the input. The conversion efficiency can
range from less than 50% to more than 90% depending on the
particular device and its type, the input voltage, and the percent
of full load to which the outputs are loaded. The internal power
dissipation, the difference between input and output power can
cause a significant rise in the device case temperature unless
some means are provided to remove all or part of this energy.
The following will discuss the various options available to solve
this Thermal Management problem.
into the maximum output load power to arrive at the input power.
Subtract the output power from the input power to determine the
internal power dissipation.
PDISS = (Pin - POUT) = POUT
Interpoint metal packaged power converters are generally
intended to have thermal energy removed by conduction from the
baseplate as indicated in Figure 1. A metal surface or cold wall
in contact with the mounting base, with a thermal grease or elastomer to fill air voids, is recommended. The removal of thermal
energy by convection in still or moving air is possible for low
power applications where the air temperature is not very high.
Heat transfer by radiation, where the heat transfer rate varies
as the 4th power of the absolute temperature is also possible
particularly where convection is ineffective. In this case, all of the
case surface not in contact with a thermal sink should be painted
a dull black to raise the emissivity as close to unity as possible.
Mounting base and
thermal surface
The Interpoint power converters of the first generation have full
load case temperature ratings of 85°C maximum, with derating
along a straight line to zero at 125°C. Parts which fall into this
category are MHE, MTW, MTO, MRH, and MFW. Second generation parts have full load case temperature ratings of 125°C, with
derating along a straight line to zero at 135°C case temperature.
Parts which fall into this category are MSA, MGA, MHF+, MHD,
MTR, MFL, MFLHP, MOR, MHV, MHP, MCH, and MGH. The
individual data sheets should be consulted for each part contemplated for use.
The first step in assessing the magnitude of a thermal problem
is to determine the internal power dissipation, the magnitude of
the heat source. First, determine the maximum output power to
the load in watts. Once this is known, the efficiency can be determined from the minimum full load value and the typical performance curves on the data sheet. Divide the decimal efficiency
Crane Aerospace & Electronics
Crane Electronics Group (Interpoint Brand)
PO Box 97005 • Redmond WA 98073-9705
425.882.3100 • [email protected]
www.interpoint.com
( Eff1 -1)
Mounting base and
thermal surface
Figure 1: Mounting Base and Thermal Surface
For example, assume we are going to use an MSA2805S with
a maximum load power of 2.0 watts. From the datasheet’s
Electrical Characteristics table (see Figure 2) the minimum
full load efficiency is found to be 66%. Assume that extended
periods of operation are required at an input voltage of 40 volts.
Although 28 volts is the normal value. Referring to the Typical
Performance Curves (see Figure 2) we see that the efficiency will
be minimum at 40 rather than 28 volts, so we should use the 40
volt curve to be safe. From Figure 2, we get a typical efficiency
of 55% at a 2.0 watt output load. This should be adjusted by the
Page 1 of 9
Rev D - 20090312
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
ratio of minimum to typical full load efficiency, 0.66/0.71 as found
in the data sheet performance tables. See Figure 2 again. The
minimum efficiency for this example is then 55%(0.66/0.71) =
51.1%. Then, the internal power dissipation is,
PDISS = POUT
1 -1
( Eff
)
= 2.0 W
1
-1 = 1.91 W
( 0.511
)
TRISE = (PDISS)/((Kc) (A))= (PDISS) (Thermal Resistance)
The various means by which temperature rise can be minimized
are examined in the following.
CONDITION
INPUT
VOLTAGE
Tc = - 55°C to + 125°C
NO LOAD TO FULL
NORMAL
TRANSIENT 1
INPUT
CURRENT
Tc = - 55°C to + 125°C
NO LOAD
FULL LOAD
INHIBITED
OUTPUT VOLTAGE
FULL LOAD
OUTPUT
CURRENT 2
VIN = 16 TO 40 Vdc
Tc = -55°C to + 125°C
OUTPUT
POWER 2
VIN = 16 TO 40 Vdc
Tc = -55°C to + 125°C
EFFICIENCY
FULL LOAD
16
0
28
40
50
27
250
3
40
TYPICAL PERFORMANCE CURVE
80
16V
5
4.95 5.00 5.05
0
5
66
71
10
LOAD
REGULATION
NO LOAD TO FULL
Tc = - 55°C TO + 125°C
10
OUTPUT
RIPPLE VOLTAGE
FULL LOAD, 10 kHz-2 MHz
125 350
INPUT RIPPLE
CURRENT
FULL LOAD, 10 kHz-2 MHz
Tc = 25°C
Tc = - 55°C to + 125°C
25 100
30 150
LOAD FAULT POWER
4
DISSIPATION
SHORT CIRCUIT
1.5
2.0
LOAD FAULT
RECOVERY5
SHORT CIRCUIT
TO FULL LOAD
12.5
25
STEP LOAD
RESPONSE
TRANSIENT
50% to 100%; 100% to 50%
10% to 100%
100% to 10%
100
220
150
250
550
375
50% to 100%; 100% to 50%
10% to 100%
100% to 10%
100
100
200
250
250
500
50
3
50
STEP LINE RESPONSE
6
TRANSIENT
16 TO 40 Vdc
40 to 16 Vdc
50
50
150
150
STEP LINE RESPONSE
5
RECOVERY
16 TO 40 Vdc
40 to 16 Vdc
100
200
250
500
INPUT/OUTPUT
CAPACITANCE
START UP DELAY
OVERSHOOT
70
1000
Tc = - 55°C to + 125°C
FULL LOAD
V IN MIN TO MAX
5
Where KC is the convection coefficient, and A is the total surface
area of the heat source. Temperature rise is an inverse propor-
MSA2805S
MIN TYP MAX
LINE
REGULATION
STEP LOAD
RESPONSE
RECOVERY
KC has units of W/(in2 • °C); A has units of inch2
EFFICIENCY (%)
PARAMETER
1) Convection
The term convection applies to heat transfer due to the motion
of the heated material due to differences in density. The material
can be a fluid or gas, and in the case being discussed, it is air.
The heat source is the internal dissipation of the power converter.
The temperature rise above the free air temperature can be
expressed as,
60
40V
50
40
30
1
2
3
FULL LOAD
FULL LOAD
10
0
5
MSA2805S EFFICIENCY
50
6
4
OUTPUT POWER (Watts)
25
50
Figure 2: Msa Specification Table
www.interpoint.com
28V
and
Performance Curve
Page 2 of 9
Rev D - 20090312
6
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
single sided copper clad vector board 1.8” x 2.8”, with the copper
on the opposite side in traces and ground plane, and with filter
components on the MSA side and the MSA and components
connected thru to the copper, the following was observed:
tion of surface area and Kc, and Kc will also vary as a function
of orientation such as horizontal, vertical, etc. Table 1 shows
the convection coefficients for various Interpoint metal package
type power converters in °C/watt. The value of the coefficients
have been determined empirically and apply in still air with the
package thermal surface horizontal but oriented down. This
is pins down for all but MFL style cases. For cases where the
thermal surface is in a vertical plane or horizontal on the top, Kc
is slightly larger, giving a slightly smaller temperature rise.
With the MSA having a spacing of 0.05” above the board, the
thermal coefficient from case to ambient was measured as 29°C/
watt. The board was horizontal with the MSA on the upside.
For the MSA2805S example, where Pdiss was found to be 1.91
W, the case temperature rise from Table 1 will be on the order of,
TRISE = (1.91 W)(32°C/W) = 61.1°C.
Since the maximum case temperature for this part is +125°C,
the maximum ambient air temperature should not exceed +64°C.
However, since the MTBF varies as an inverse exponential of
case temperature, some other means of conducting thermal
energy away, such as conduction and/or radiation, should be
looked at to help lower case temperature rise. Each 20° to 30°C
rise in case temperature, will reduce the MTBF by roughly a
factor of 2. Refer to the following paragraphs.
Some additional thermal information for the MSA, also determined by measurement is as follows. For an MSA centered on a
With the MSA in contact with the vectorboard, 0.05” spacing
removed, the thermal coefficient from case to ambient was
measured as 22°C/watt. The reduced thermal rise is due to some
conduction in the epoxy glass board, and convection from the
increased area immediately surrounding the MSA.
2) Conduction
Removing thermal energy by conduction is analogous to the
conduction of electrical current in a wire, usually of copper.
Copper is used because it is an excellent and economical electrical conductor. Silver is the best but not generally used because
of cost and problems with migration. Good electrical conductors are also good thermal conductors. For thermal conduction,
aluminum may sometimes be preferable because of its low
density, 2.7 grams/cubic centimeter, as compared to 8.9 for
copper. Aluminum has about 1.6 times the resistivity of copper.
thermal resistance - Case / ambient
Model
convection only, in free air
ΘCA
°C/Watt
in inches2
MCH, MGH
45
2.32
MSA, MGA
32
3.28
MSR
29
4.50
MHF, MHF+, MHF+ T
26
5.01
24
5.6
FM704A, MHV,
19
7.34
MHE, MHD, MTR
19
7.34
17
8.14
MRH, MTO,
18
7.9
MTW, MTR T, MHV T
18
7.9
16
9.02
13.5
12.0
8.0
22.0
SAME WITH FLANGES
SAME WITH FLANGES
SAME WITH FLANGES
MFL, MHP, MOR, MFLHP
MFW
Table 1: Convection Coefficients
www.interpoint.com
~Surface Area
and
Thermal Resistance
Page 3 of 9
Rev D - 20090312
Kc
W / (inch2 • °C)
9.57 x 10 -3
9.53 x 10 -3
7.66 x 10 -3
7.68 x 10 -3
7.44 x 10 -3
7.17 x 10 -3
7.17 x 10 -3
7.22 x 10 -3
7.03 x 10 -3
7.03 x 10 -3
6.93 x 10 -3
6.17 x 10 -3
5.68 x 10 -3
in
Free Air Convection
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
Figure 3 shows a Thermal-Electrical Analog which may be helpful
in understanding thermal conduction. The circuit is a single loop
driven by a current source and consisting of a series of 3 resistors terminating at the ground reference to complete the loop.
The electrical current, which flows in the direction of the arrow,
causes a series of voltage drops in the resistors, V3 being the
lowest and V1 the highest, with respect to the ground reference.
The units involved are Amperes, Ohms, and Volts respectively.
For the thermal model, the current source is replaced by a heat
source which becomes the rate at which thermal energy is generated, and has units of joules/second, or watts. Heat flows in the
direction of the arrow as with the electrical case.
The electrical resistances are replaced by thermal resistances
having units of °C/watt, and the voltage drops are replaced by
thermal differences having units of °C. The electrical resistors
are replaced by mechanical components such as the metal case,
thermal interface pad, metal thermal ladder, and heatsink. The
analog example shown has a power semiconductor in a metal
case as the heat source. The metal case is in turn mounted
on a heatsink with a thermal interface pad used to fill air voids.
The highest temperature, TJ, is the semiconductors junction
temperature, and the lowest the ambient air, TA. In between are
the case, TC, and heatsink temperatures, TS. Heat flows from the
highest to the lowest temperature with intermediate temperatures
in between as defined by the various thermal resistances (Θ).
The thermal resistance for convection could also be added as a
(V2)
TC
(V1)
TJ
ΘJC
(R1)
HEATSOURCE
(CURRENT
SOURCE)
(V3)
TS
ΘCS
(R2)
HEATFLOW = PD
(CURRENT = AMPS = I)
parallel path in the thermal circuit model, where the area is modified to exclude that portion in contact with another surface for
conduction.
The thermal resistance of a material is determined from the reciprocal of its thermal conductivity multiplied by the ratio of length to
cross sectional area. This is shown on Figure 3, with some materials properties shown on Tables 2 and 3. For materials listed in
Table 3, copper has the best conductivity, and air the worst. The
Sil Pad 1500 has a conductivity in the middle of the former two,
and is about 100 times better than air. It is available in sheets or
pre-cut pads in a thickness of 0.01”. It can be used to fill air voids
between the power converter thermal surface and a thermal
sink or other surface. Air voids in thermal interfaces can result
in hot spots and serious problems down the road if they are not
filled. Thermal grease is another alternative to the Sil Pad for this
purpose.
THERMAL:
HEATSOURCE IS INTERNAL PD IN WATTS
Θ
ΘSA
(R3)
A
TA
(GRND
(REF.)
∆ TJC = PD ΘJC∼ (V1–V2) = I R1
∆ TJA = PD (ΘJC+ΘCS+ΘSA) ∼ V1 = I (R1+R2+R3)
∆ TJA = (TJ–TA) = TEMP. DIFF. – JUNCTION TO AMBIENT
~ (V1 – 0) = TOTAL VOLTAGE DROP
TJ
TC
TS
TA
= THERMAL RESISTANCE IN °C/WATT
=
( K1 )( A ), K = THERMAL CONDUCTIVITY IN WATTS
=
=
=
=
=
=
CROSS SECTIONAL AREA OF PATH IN cm2
LENGTH OF THERMAL PATH IN cm
JUNCTION TEMP IN °C
CASE TEMP IN °C
HEATSINK TEMP IN °C
AMBIENT TEMP IN °C
ELECTRICAL:
I
R
= CURRENT IN AMPS
= RESISTANCE IN OHMS
= “ρ”
( A ),
“ρ” = RESISTIVITY IN Ohm-cm
“ρ” = the Greek letter Rho
V
= VOLTAGE IN VOLTS
Figure 3: Thermal Electrical Analog
www.interpoint.com
Page 4 of 9
Rev D - 20090312
cm °C
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
BERQUIST THERMAL INTERFACE PADS
SIL-PAD SIL-PAD SIL-PAD SIL-PADSIL-PAD
400(.009) 400(.007) 600(.009) 1000 1500
Color
Gray
Gray
Green
Pink
Green
Thermal Resistance, ˚C/watt
.50
.45
0.35
0.35
0.23
Dielectric Constant, 1000 (Hz)
5.5
5.5
5.0
4.5
4.0
Continuous Use
Temp. ˚C
-60 to -60 to
+180 +180
Thermal Conductivity
W/m-k nominal
Thickness
Inches
(mm)
0.9
0.9
-60 to -60 to
+180
+180
0.9
INTERPOINT'S "TMP" ACCESSORY
SIL - PAD 1500 MATERIAL
W
K (1500) = 0.02 c m˚C
-60 to
+180
0.9
0.9
~ 100 x Better than air
Assume Pad Dimensions are:
Area = 2.5 cm x 5.0 cm = 12.5 cm2
Thickness = Length = 0.025 cm
.009±.001 .007±.001 .009±.001 .009±.001. 010±.001
(.23±.025)(.18±.025)(.23±.025)(.23±.025)(.25±.025)
Volume Resistivity, Ohm Metre Typical
11
11
12
11
11
1.0 x 10 1.0 x 10 8 1.0 x 10 1.0 x 10 8 1.0 x 10
Normal
8
1.5 x 10
Moist
1.5 x 10 1.5 x 10
Breakdown Voltage (minimum AC) 4500
3500
Thermal Vacuum Weight Loss Percent
.40
.25
.40
.25
(TML) Max. As Manufactured
Post Cure 24 HRS. 440˚F, 225˚C
4500
.07
.07
Hardness, Shore A
85
85
85
ASSUME
85
Tcs
80
11
(75)
14
(100)
11
(75)
11
(75)
6
(40)
Breaking Strength, Lbs/inch
kN/m
100
18
100
18
100
18
100
18
65
11
Elongation Percent Nominal
4
4
4
4
4
Silicone/ Silicone/ Silicone/ Silicone/ Silicone/
Fiberglass Fiberglass Fiberglass Fiberglass Fiberglass
TMP-006
TMP-001
TMP-003
TMP-002
TMP-005
Table 2: Thermal Interface Pads
www.interpoint.com
1
K1500
.025cm
)
) ( 12.5cm
[ [ AL [ = ( 50cm˚C
W
2
P = 11.0 WATTS
D
= P
D
cs
= (11w)
( 0.1˚C
) = 1.1˚C
W
Si conversions are approximations and are not intended to be exact.
1.5
Tensile Strength, K Psi, Typical
(MPa)
Construction
[
CS = 0.10 ˚C
W
.08
2.0 - 2.1 2.0 - 2.1
Specific Gravity
CS =
4000
.22
Volatile Condendsable a Material, Percent
.11
.11
Maximum (CVCM) As Manufactured
Post Cure 24 HRS. 440˚F, 225˚C
4500
Page 5 of 9
Rev D - 20090312
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
THERMAL
Conductivity
K (Watts/cm - ˚C)
MATERIAL
ALUMINA (96%)
ALUMINUM
ALUMINUM SILICATE
BERYLLIA
BRASS
COPPER
EPOXY (INSUL.)
EPOXY (COND.)
FUSED SILICA
GRAPHITE 2
KOVAR
LEAD
MOLYBDENUM
NICKEL
SILICON
STEEL (C.R.S.)
STEEL (S.S. #316)
TUNGSTEN
SIL PAD 1500
AIR
0.30 1
1
2.14
0.013
1
2.20
0.85
3.21
≈ 0.014
≈ 0.08
≈ 0.014
1.4
0.15
0.38
1.34
0.58
1
0.84
0.55
0.15
1.56
0.02
0.00024
THERMAL
Expansion
Coefficient
α(10-6/ ˚C)
6.4
23.0
3.2
6.0
18.5
17.0
≈ 30.0
≈ 35
0.55
≈ 5.4
62
29.0
4.9
13.0
4.2
13
16.5
5.0
Density
Specific Heat
c (joules/gm/ ˚C) d (gm/cm3)
1.13
0.9
1.04
1.25
0.38
0.39
0.75
≈ 1.67
0.50
0.14
0.25
0.44
0.70
0.45
0.50
0.13
1. STRONG FUNCTION OF TEMPERATURE
2. APPROXIMATION ONLY
Table 3: Thermal Properties
www.interpoint.com
of
Common Material
Page 6 of 9
Rev D - 20090312
4.0
2.7
2.3
2.9
8.4
8.9
2.3
2.6
2.2
1.8
8.0
11.3
10.2
8.9
2.33
7.8
8.0
19.3
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
MPO = 30W & EFF = 82%
5
0
0
50
60
70
TC – °C
80
MFW EXAMPLE
90
100
110
( P – P �� ) Θ
30
= 125° C – �( 0.82 – 30� ) 2.7
�
�
MTC MAX = 125° C – �
O
� EFF
120 130
125
MTC MAX
MAX. AVG.
JUNC. TEMP.
O
�
�
PD – WATTS
EXAMPLE:
�
�
ΘJC = 2.7
PD = 6.6 Watts
MAX CASE TEMP. = 125° C – (PD) (ΘJC)
°C
W
�
�
ΘJC
15W
=
40° C
�
�
10
SLOPE =
� PO P = P – P
PD =MMMMI–
O
IN
O
� EFF
�
�
PD max at full load
15
-1
JC
MTC MAX = 125° C – (6.6W) (2.7 °C ) = 107° C
W
Figure 4: Thermal Considerations
Figure 4 is an example of how to determine ΘJC from the
derating curve for an MFW power converter, and then the
maximum allowable case temperature for an assumed load of
30 watts. At full load, 70 W, the internal dissipation will be about
15 watts. Since derating to zero occurs along a straight line from
85°C to 125°C, the thermal resistance, ΘJC , is equal to (125 85) °C/15 watts = 2.7°C/watt. Based on an internal dissipation
of 6.6 watts, the max allowable case temp is found to be 107°C.
This procedure can be used to determine ΘJC on any Interpoint
power converter. On the second generation parts, the derating
to zero occurs over 10°C rather than 40°C, so the thermal resistances will be smaller than in the former case.
Figure 5 is an example of an MFW power converter with a 30
watt load but now mounted on a heatsink. The heatsink could
just as well have been a thermal ladder with the other end
connected to a cold wall. For simplicity, flat surfaces with no air
voids are assumed without fillers. In reality a thermal pad would
EXAMPLE:
TC
ΘJC
TJ
TA
ΘSA
TA = 55°C, PO = 30W and EFFICIENCY = 82%
WHAT IS MAX. ΘSA FOR HEATSINK?
TC max = 107° C from Figure 4 above


Figure 5: Case Mounted
www.interpoint.com
on


ΘSA max = 52°C
6.6W
= 7.9° C / W
Thermal Sink
Page 7 of 9
Rev D - 20090312
°C

– 30 WATTS  ΘSA W
°C

 ΘSA W




ΘCS = 0 FOR SIMPLIFIED EXAMPLE


∆ TJA = PD (ΘJC+ ΘSA) = PDΘJA= °C
Δ TSA max = PD (ΘSA max)
 30

107°C – 55°C =  0.82

52°C = 6.6W


= °C


∆ TJC = PD ΘJC= W  °C
 W
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
step is to find a heatsink which meets this among other requirements, either by design or in a manufacturers catalog.
be used resulting in an additional thermal resistance in the equations. The ΘJC of 2.7°C/watt from Figure 4 is used here. The
ambient temperature is 55°C, and the object of the calculation is
to determine the largest allowable heatsink thermal resistance,
Ɵ. The maximum case temp from Figure 4 is 107°C, and the
delta T over which derating occurs is found to be 52°C. From the
calculation of Figure 5, the maximum allowable heatsink thermal
resistance to ambient, ΘSA, is found to be 7.9°C/watt. The next
Figure 6 shows an example of a real problem. A three output
power converter, MTO28515T, is used in a small avionics system
where there was a thermal problem follows:
The system is in a small metal box of the type having perforations in the walls to allow air circulation from the outside environ-
MTO
0.3"
0.01" interface
pad on top of Cu
0.7"
2.0"
Tin Plated Cu Bracket Under MTO
0.04"
Cu
0.85"
( A) =(
1
ΘBRACKET = K
CU
1
ΘPAD = KPAD
1 cm° C
3.2 W
cm° C
)
) ( 2.54
0.22 cm2
cm° C
( A ) = ( 1102
) (
W
∆T = 1.9 W
(
3.6° C + 0.11° C
W
W
)
)
0.025 cm
11.0 cm 2
=
= 3.6° C
W
=
0.11° C
W
7.03° C
WHERE:
BRACKET
ABRACKET
PAD
APAD
= 1" = 2.54 cm
= 0.85" X 0.04" = 0.034"2 = 0.22 cm2
= 0.01" = 0.025 cm
= 2" x 0.85" = 1.72"2 = 11 cm2
Figure 6: MTO Heat Sink Design
www.interpoint.com
and
Page 8 of 9
Rev D - 20090312
Calculations
Crane Aerospace & Electronics Power Solutions
Thermal Management
Application Note
ment. The power output was about 6.0 watts, input power 7.9
watts at 76% efficiency, and internal PD of (7.9 - 6.0) = 1.9 watts.
From Table 1, temperature rise of the MTO case due to only
convection is predicted to be about (1.9 watts)(18°C/watt) = 34°C.
The maximum system case temperature spec is + 85°C, about
what the ambient air will also be. Adding 34°C to this figure, the
MTO case is predicted to rise to about 119°C, as verified by
measurement, and too hot for this part, which derates to zero at
+125°C. The solution was to find an additional thermal path to
lower the case temperature.
The MTO was mounted on the top PC card just below the metal
top cover of the box, and mounted about 0.05” above the PC
card to allow inspection of solder joints. Here the solution was
simple. A tin plated copper bracket, 0.04” thick, was attached to
the PC card to form a thermal path between the mounting base
and the system box cover. The MTO was seated on the bracket
with an interface pad, the other end attached to the system box
cover with mechanical fasteners. The part under the MTO is a
heat spreader, and the thermal ladder is about 1.0” long. The
calculation of Figure 6 indicates the predicted MTO case temp
rise is lowered to about 7°C due to conduction through the
bracket. Convection from the cover surface area will also still
occur, but will have a minimal effect. Radiation should also be
considered as an alternate means of heat transfer. Measuring
the actual temperature is always recommended. A small thermocouple or glass junction diode should be attached to the thermal
surface for this purpose wherever possible. Alternately, attach to
the sidewall of the case as close to the base as possible.
3) Radiative Cooling
Radiation refers to the continual radiation of energy from a body
and is referred to as radiant energy. It is in the form of electromagnetic waves, predominantly in the 1 to 10 micron area of the
spectrum. The rate at which radiation occurs can be expressed
by Stefan’s law as in the formula,
R = e • c • T4 where,
a rectangular shape with a dull black finish on a smooth surface,
the emissivity will be less, and unknown at this point. The
following experiment was conducted to determine the value.
The case temperature of an MSA power converter dissipating
1.05 watts internally was found to be 55°C when suspended
with cover up in an ambient of 22°C. The thermal coefficient by
convection is then calculated to be,
(55 - 22)/(1.05) = 31.4°C/watt.
The cover was then spray-painted a dull black. The label could
still be read through the paint. The experiment was repeated and
the case temperature rose to only 47°C, with the ambient temperature still 22°C. Since the temperature rise was lowered by 8°C,
about 0.25 watts must have been removed by means other than
convection - in this case radiation. Then, since everything else is
known, the emissivity is calculated as,
e=
P
A • c • T4
where A is the cover area = 0.0013 meters
e=
(0.25)
(0.0013)(5.7x10-8)(3204)
= 0.32,
or about one third. The remainder of the case was painted dull
black with the result that the temperature rise was reduced an
additional 3°C. The surface area in this case is 0.0019 meters
squared. Our conclusion is that radiation should be considered as
a means of heat transfer. It would have been of further benefit in
the example of Figure 6.
e = emissivity having a range of 0 to 1, where a perfect blackbody = 1.
c = 5.7 x 10-8 in MKS units.
T = absolute Kelvin temperature.
R = Rate of emission of radiant energy in Joules/Second/
square meter, or Watts/square meter.
The square meters refer to the surface area of the body emitting
the radiant energy. In an application where the cover is painted
a dull black, it will be the total cover area in square meters. The
radiation calculation is simple except for determining what the
emissivity is. An ideal blackbody might be a sphere having a dull
black and rough surface, and an emissivity approaching one. For
Thermal Management Rev D - 20090312 All information is believed to be accurate, but no responsibility is assumed for errors or
omissions. Interpoint reserves the right to make changes in products or specifications without notice. Copyright © 1999 - 2009
Interpoint Corporation. All rights reserved. www.interpoint
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