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Thermal Modeling
© M. T. Thompson, 2009
1
Power Electronics Notes 29Thermal Circuit Modeling and Introduction
to Thermal System Design
Marc T. Thompson, Ph.D.
Thompson Consulting, Inc.
9 Jacob Gates Road
Harvard, MA 01451
Phone: (978) 456-7722
Email: [email protected]
Website: http://www.thompsonrd.com
Jeff W. Roblee, Ph.D.VP of EngineeringPrecitech, Inc.Keene, NHwww.ametek.com
Thermal Modeling
© M. T. Thompson, 2009
2
Summary
• Basics of heat flow, as applied to device sizing and heat sinking
• Use of thermal circuit analogies– Thermal resistance– Thermal capacitance
• Examples– Picture window examples– Magnetic brake– Plastic tube in sunlight
Thermal Modeling
© M. T. Thompson, 2009
• All components (capacitors, inductors and transformers, semiconductor devices) have maximum operating temperatures specified by manufacturer• High operating temperatures have undesirable effects on components:
Need for Component Temperature Control
Capacitors• Electrolyte evaporation rate increases significantly with temperature increases and thus shortens lifetime
Magnetic Components• Losses (at constant power input) increase above 100 °C• Winding insulation (lacquer or varnish) degrades above 100 °C
Semiconductors• Unequal power sharing in parallel or series devices• Reduction in breakdown voltage in some devices• Increase in leakage currents• Increase in switching times
3
Thermal Modeling
© M. T. Thompson, 2009
• Control voltages across and current through components via good design practices
• Snubbers may be required for semiconductor devices.• Free-wheeling diodes may be needed with magnetic
components• Maximize heat transfer via convection and radiation from component to ambient
• Short heat flow paths from interior to component surface and large component surface area.• Component user has responsibility to properly mount temperature-critical components on heat sinks.
• Apply recommended torque on mounting bolts and nuts and use thermal grease between component and heat sink.
• Properly design system layout and enclosure for adequate air flow
Temperature Control Methods
4
Thermal Modeling
© M. T. Thompson, 2009
Heat Transfer• Heat transfer (or heat exchange) is the flow of thermal
energy due to a temperature difference between two bodies
• Heat transfers from a hot body to a cold one, a result of the second law of thermodynamics
• Heat transfer is slowed when the difference in temperature between the two bodies reduces
5
Thermal Modeling
© M. T. Thompson, 2009
6
Intuitive Thinking about Thermal Modeling
• Heat (Watts) flows from an area of higher temperature to an area of lower temperature
• Heat flow is by 3 mechanisms– Conduction - transferring heat through a solid
body– Convection - heat is carried away by a moving
fluid• Free convection• Forced convection - uses fan or pump
– Radiation• Power is radiated away by electromagnetic
radiation• You can think of high- thermal conductivity
material such as copper and aluminum as an easy conduit for conductive power flow…. i.e. the power easily flows thru the material
Thermal Modeling
© M. T. Thompson, 2009
7
Thermal Circuit Analogy• Use Ohm’s law analogy to model thermal
circuits
• Thermal resistance
• k = thermal conductivity (W/(mK))• Thermal capacitance: analogy isn’t as
straightforward• cp = heat capacity of material (Joules/(kg-K))
TH
TH
CC
RR
PI
TV
kA
lR
A
lR TH
ELECTRICAL THERMAL Forcing variable Voltage (V) Temperature (K) Flow variable Current (A) Power (W) Resistance Resistance (V/A) Thermal resistance (K/W) Capacitance Capacitance (V/C) Thermal capacitance (J/K)
pTH McC
Thermal Modeling
© M. T. Thompson, 2009
8
Thermal Circuit Analogy
ELECTRICAL THERMAL
Forcing variable Voltage (V) Temperature (K)
Flow variable Current (A) Heat (W)
Resistance Resistance (V/A) Thermal resistance (K/W)
Capacitance Capacitance (V/C) Thermal capacitance (J/K)
• Heat transfer can be modeled by thermal circuits• Using Ohm’s law analogy:
Reference: M. T. Thompson, Intuitive Analog Circuit Design, Newnes, 2006.
thV R I T R P
Thermal Modeling
© M. T. Thompson, 2009
9
Thermal Circuit Analogy
• Elementary thermal network
Reference: M. T. Thompson, Intuitive Analog Circuit Design, Newnes, 2006.
Thermal Modeling
© M. T. Thompson, 2009
10
Thermal Resistance
• Thermal resistance quantifies the rate of heat transfer for a given temperature difference
• k = thermal coefficient (W/(mK))• A = cross section (m2)• l = length (m)
TH
l l KR ( ) R
A kA W
T 2T 1
Area A
l
P cond
Thermal Modeling
© M. T. Thompson, 2009
11
Thermal Capacitance
• Thermal capacitance is an indication of how well a material stores thermal energy
• It is used when transient phenomena are considered• Analogy isn’t as straightforward• M = mass (kg)• cp = heat capacity of material (Joules/(kg-K))
pTH McC TH
dTP C
dt
Thermal Modeling
© M. T. Thompson, 2009
12
Heat Flow Mechanisms
• Heat flows by 3 mechanisms; the driving force for heat transfer is the difference in temperature
1. Conduction
2. Convection • Free convection• Forced convection
3. Radiation
Reference: R. E. Sonntag and C. Borgnakke, Introduction to Engineering Thermodinamics, John Wiley, 2007
Thermal Modeling
© M. T. Thompson, 2009
13
Conduction• Heat is transferred through a solid from an area of
higher temperature to lower temperature
• To have good heat conduction, you need large area, short length and high thermal conductivity
• Example: aluminum plate, l = 10 cm, A=1 cm2, T2 = 25C (298K), T1 = 75C (348K), k = 230 W/(m-K)
condTH
cond R
TT
kA
lTT
P,
2121
WattCkA
lR o
condTH /35.4)10(230
)1.0(4,
WattsPcond 5.11
35.4
50
T 2T 1
Area A
l
P cond
Thermal Modeling
© M. T. Thompson, 2009
14
Thermal Conductivity of Selected Materials
Material Thermal conductivity @ 300K k, W/(m-K)
Copper 400 Aluminum 200
Iron 25-75 Steel (1008) 50
Stainless steel 12-35 Brick 0.4-0.5 Cork 0.04
Epoxies 0.16-1.4 Glass-epoxy 3
Window glass 0.78 Still air 0.027
References: 1. B. V. Karlekar and R. M. Desmond, Engineering Heat Transfer, pp. 8, West Publishing, 1977
2. Burr Brown, Inc., “Thermal and Electrical Properties of Selected Packaging Materials”
Thermal Modeling
© M. T. Thompson, 2009
Thermal Equivalent Circuits
• Heat flow through a structure composed of layers of different materials
• Thermal equivalent circuit simplifies calculation of temperatures in various parts of structure.
P
R sacsR
jcR
Junction Case Sink Ambient
jT cT sT aT++++
----
Chip T j
Case Tc
Isolation pad
Heat sink T s
Ambient Temperature T a
• Ti = Pd (Rjc+ Rcs + Rsa) + Ta
• If there parallel heat flow paths, then thermal resistances combine as do electrical resistors in parallel.
15
Thermal Modeling
© M. T. Thompson, 2009
16
Thermal Conductivity of Selected Materials
Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
17
Heat Capacity of Selected Materials
Reference: B. V. Karlekar and R. M. Desmond, Engineering Heat Transfer, West Publishing, 1977
• Heat capacity is an indication of how well a material stores thermal energy
Thermal Modeling
© M. T. Thompson, 2009
18
Heat Capacity of Alloys
Reference: http://www.engineeringtoolbox.com/specific-heat-metal-alloys-d_153.html
Thermal Modeling
© M. T. Thompson, 2009
19
Convection
Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”
• Convection can be free (without a fan) or forced (with a fan)
Thermal Modeling
© M. T. Thompson, 2009
20
Free Convection
Reference: http://www.freestudy.co.uk/heat%20transfer/convrad.pdf
Thermal Modeling
© M. T. Thompson, 2009
21
Heat Transfer Coefficient for Convection
• Heat is transferred via a moving fluid• Convection can be described by a heat transfer
coefficient h and Newton’s Law of Cooling:
• Heat transfer coefficient depends on properties of the fluid, flow rate of the fluid, and the shape and size of the surfaces involved, and is nonlinear
• Equivalent thermal resistance:
)( as TThAP
hAR convTH
1,
Test condition h, W/m2oC Air, free convection 5-15
Air, forced convection 15-50 Water, forced convection 300-12,000
Water, boiling 5,500-100,000
Reference: B. V. Karlekar and R. M. Desmond, Engineering Heat Transfer, pp. 14, West Publishing, 1977
Thermal Modeling
© M. T. Thompson, 2009
22
Free Convection• Heat is drawn away from a surface by a free gas
or fluid• Buoyancy of fluid creates movement• For vertical fin:
• A in m2, dvert in m• Example: square aluminum plate, A=1 cm2, Ta =
25C (298K), Ts = 75C (348K)
asvert
asconv TThA
d
TTAP
25.0
25.1
34.1T sT a
Area A
d vert
)/(2.11
56)01.0(
50)10(34.1
2
25.0
25.14
KmWh
mWP
eq
conv
Thermal Modeling
© M. T. Thompson, 2009
23
Free Convection Heat Transfer Coefficient (h)• For vertical fin:
• Area A in m2, fin vertical height dvert in m
T sT a
Area A
d vert
25.0
35.1
vert
As
d
TTh
Thermal Modeling
© M. T. Thompson, 2009
24
Forced Convection• With a fan
Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
25
Forced Convection
• In many cases, heat sinks can not dissipate sufficient power by natural convection and radiation
• In forced convection, heat is carried away by a forced fluid (moving air from a fan, or pumped water, etc.)
• Forced air cooling can provide typically 3-5 increase in heat transfer and 3-5 reduction in heat sink volume– In extreme cases you can do 10x better by using big
fans, convoluted heat sink fin patterns, etc.
Thermal Modeling
© M. T. Thompson, 2009
26
Thermal Performance Graphs for Heat Sinks
Reference: http://electronics-cooling.com/articles/1995/jun/jun95_01.php
• Curve #1: natural convection (P vs. Tsa)• Curve #2: forced convection curve (Rsa vs. airflow)
12
Thermal Modeling
© M. T. Thompson, 2009
27
Radiation
• Energy is transferred through electromagnetic radiation
Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
28
Radiation
• Energy is lost to the universe through electromagnetic radiation
• = emissivity (0 for ideal reflector, 1 for ideal
radiator “blackbody”); = Stefan-Boltzmann constant = 5.6810-8 W/(m2K4)
• Example: anodized aluminum plate, = 0.8, A=1 cm2, Ta = 25C (298K), Ts = 75C (348K)
P rad
T s
T a
Area A
Material Emissivity Aluminum
Polished Oxidized Anodized
0.04-0.06 0.2-0.33 0.7-0.9
Copper Polished Dull
0.02 0.15
Glass 0.8-0.95
44asrad TTAP
mWPrad 31)298348)(10)(107.5)(8.0( 4448
Thermal Modeling
© M. T. Thompson, 2009
29
Radiation
• Incident, reflected and emitted radiation; e.g. body in sunlight
Reference: http://www.energyideas.org/documents/factsheets/PTR/HeatTransfer.pdf
Thermal Modeling
© M. T. Thompson, 2009
30
Emissivity
Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
31
Emissivity
Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
32
Comments on Radiation• In multiple-fin heat sinks with modest temperature
rise, radiation usually isn’t an important effect– Ignoring radiation results in a more conservative
design• Effective heat transfer coefficient due to radiation for
ideal blackbody ( = 1) at with surface temperature 350K radiating to ambient at 300K is hrad = 6.1 W/(m2K), which is comparable to free convection heat transfer coefficient– However, radiation between heat sink fins is
usually negligible (generally they are very close in temperature)
Thermal Modeling
© M. T. Thompson, 2009
33
IC Mounted to Heat Sink
• Interfaces– Heat sink-ambient: convection (free or forced)– Heat sink-case of IC: conduction– Case – junction: conduction
Thermal Modeling
© M. T. Thompson, 2009
Multiple Fin Heat Sink
Reference: http://www.oldcrows.net/~patchell/AudioDIY/AudioDIY.html
34
Thermal Modeling
© M. T. Thompson, 2009
35
IC Mounted to Heat Sink
Reference: International Rectifier, Application Note AN-997
Thermal Modeling
© M. T. Thompson, 2009
36
IC Mounted to Heat Sink --- Close-up
Reference: International Rectifier, Application Note AN-997
• Thermal compound is often used to fill in the airgap voids
Thermal Modeling
© M. T. Thompson, 2009
37
IC Mounted to Heat Sink --- Contact Resistance vs. Torque (TO-247)
Reference: International Rectifier, Application Note AN-997
Thermal Modeling
© M. T. Thompson, 2009
38
IC Mounted to Heat Sink --- Contact Resistance vs. Interface Material (TO-247)
Reference: International Rectifier, Application Note AN-997
Thermal Modeling
© M. T. Thompson, 2009
39
IC Mounted to Heat Sink --- Contact Resistance vs. Interface Material (TO-247)
Reference: International Rectifier, Application Note AN-997
• Dry vs. thermal compound vs. electrically-insulating pad
Thermal Modeling
© M. T. Thompson, 2009
40
Thermal Grease
Thermal Modeling
© M. T. Thompson, 2009
41
Heat Sink Pad
Thermal Modeling
© M. T. Thompson, 2009
Transient Thermal Impedance
• Heat capacity per unit volume Cv = dQ/dT [Joules /oC] prevents short duration high power dissipation surges from raising component temperature beyond operating limits.
• Transient thermal equivalent circuit. Cs = CvV where V is the volume of the component.
P(t)R
jT (t)
aT
Cs
P(t)
t
RPo
tSlope = 0.5
log Z (t)
• Transient thermal impedance Z(t) = [Tj(t) - Ta]/P(t) •= π R Cs /4 =
thermal time constant
• Tj(t = ) = 0.833 Po R
42
Thermal Modeling
© M. T. Thompson, 2009
Use of Transient Thermal Impedance• Response for a rectangular power dissipation pulse P(t) = Po {u(t) - u(t - t1)}.
P(t)
t
RPo
tt1 t1
Z (t)
1-Z (t - t )
net response
-R
• Tj(t) = Po { Z(t) - Z(t - t1) }
• Symbolic solution for half sine power dissipation pulse.
•P(t) = Po {u(t - T/8) - u(t - 3T/8)} ; area under two curves identical.
•Tj(t) = Po { Z(t - T/8) - Z (t - 3T/8) }T/8 3T/8
T/2
Po
t
P(t)
Equivalent rectangular pulse
Half sine pulse
43
Thermal Modeling
© M. T. Thompson, 2009
Multilayer StructuresP(t)
Silicon
Copper mountHeat sink
Tj
CuT
cT
aT
• Multilayer geometry
• Transient thermal equivalent circuit
Tj CuTcT
aT
C (Si)s C (Cu)sC (sink)sP(t)
R (sink)R (Cu)R (Si)
R (Si)
R (Cu)R (Si)
+
R (sink)R (Cu)R (Si)
+ +
log(t)
log[Z (t)]
(Si) (sink) (Cu)
• Transient thermal impedance (asymptotic) of multilayer structure assuming widely separated thermal time constants.
44
Thermal Modeling
© M. T. Thompson, 2009
Heat Sinks• Aluminum heat sinks of various shapes and sizes widely available for cooling components.
• Often anodized with black oxide coating to reduce thermal resistance by up to 25%.
• Sinks cooled by natural convection have thermal time constants of 4 - 15 minutes.
• Forced-air cooled sinks have substantially smaller thermal time constants, typically less than one minute.
• Choice of heat sink depends on required thermal resistance, Rsa, which is determined by several factors.
• Maximum power, Pdiss, dissipated in the component mounted on the heat sink.
• Component's maximum internal temperature, Tj,max
• Component's junction-to-case thermal resistance, Rjc. • Maximum ambient temperature, Ta,max.
• Rsa = {Tj,max - Ta,max}Pdiss - Rjc • Pdiss and Ta,max determined by particular application.• Tj,max and Rjc set by component manufacturer.
45
Thermal Modeling
© M. T. Thompson, 2009
Heat Conduction Thermal Resistance
• Generic geometry of heat flow via conduction
Pcond
Temperature = T1Temperature = T2
d
h
b
T > T12
heat flow direction
• Heat flow Pcond [W/m2] =kA (T2 - T1) / d = (T2 - T1) / R cond
• Thermal resistance R cond = d / [k A]
• Cross-sectional area A = hb
• k = Thermal conductivity has units of W-m-1-oC-1 (kAl = 220 W-m-1-oC-1 ).• Units of thermal resistance are oC/W
46
Thermal Modeling
© M. T. Thompson, 2009
Radiative Thermal Resistance
• Stefan-Boltzmann law describes radiative heat transfer.
• Prad = 5.7x10-8 EA [( Ts)4 -( Ta)4 ] ; [Prad] = [Watts]
• E = emissivity; black anodized aluminum E = 0.9 ; polished aluminum E = 0.05
• A = surface area [m2] through which heat radiation emerges.
• Ts = surface temperature [K] of component. Ta = ambient temperature [K].
• (Ts - Ta )/Prad = R ,rad = [Ts - Ta][5.7x10-8EA {( Ts/100)4 -( Ta/100)4 }]-1
• Example - black anodized cube of aluminum 10 cm on a side. Ts = 120 C and Ta = 20 C
• R,rad = [393 - 293][(5.7) (0.9)(6x10-2){(393/100)4 - (293/100)4 }]-1
• R,rad = 2.2 C/W
47
Thermal Modeling
© M. T. Thompson, 2009
Convective Thermal Resistance
• Pconv = convective heat loss to surrounding air from a vertical surface at sea level having height dvert [in meters] less than one meter.
• Pconv = 1.34 A [Ts - Ta]1.25 dvert-0.25
• A = total surface area in [m2]
• Ts = surface temperature [K] of component. Ta = ambient temperature [K].
• [Ts - Ta ]/Pconv = R,conv = [Ts - Ta ] [dvert]0.25[1.34 A (Ts - Ta )1.25]-1
• R,conv = [dvert]0.25 {1.34 A [Ts - Ta]0.25}-1
• Example - black anodized cube of aluminum 10 cm on a side. Ts = 120C and Ta = 20 C.
• R,conv = [10-1]0.25([1.34] [6x10-2] [120 - 20]0.25)-1
• R,conv = 2.2 C/W
48
Thermal Modeling
© M. T. Thompson, 2009
Combined Effects of Convection and Radiation
• Heat loss via convection and radiation occur in parallel.
• Steady-state thermal equivalent circuit
• R,sink = R,rad R,conv / [R,rad + R,conv]
• Example - black anodized aluminum cube 10 cm per side
• R,rad = 2.2 C/W and R,conv = 2.2 C/W
• R,sink = (2.2) (2.2) /(2.2 + 2.2) = 1.1 C/W
P R,conv,rad
R
sT
aT
49
Thermal Modeling
© M. T. Thompson, 2009
50
Cost for Various Heat Sink Systems
Reference: http://www.electronics-cooling.com/Resources/EC_Articles/JUN95/jun95_01.htm
• Note: heat pipe and liquid systems require eventual heat sink
Thermal Modeling
© M. T. Thompson, 2009
51
Comparison of Heat Sinks
Reference: http://www.ednmag.com/reg/1995/101295/21df3.htm
STAMPED EXTRUDED “CONVOLUTED” FAN
Thermal Modeling
© M. T. Thompson, 2009
52
2N3904 Static Thermal Model
Thermal Modeling
© M. T. Thompson, 2009
53
Liquid Cooling
• Advantages– Best performance per unit volume– Typical thermal resistance 0.01-0.1 C/W
• Disadvantages– Need a pump– Heat exchanger– Possibility of leaks – Cost
Thermal Modeling
© M. T. Thompson, 2009
54
Heat Pipe
• Heat pipe consists of a sealed container whose inner surfaces have a capillary wicking material
• Boiling heat transfer moves heat from the input to the output end of the heat pipe
• Heat pipes have an effective thermal conductivity much higher than that of copper
Thermal Modeling
© M. T. Thompson, 2009
55
Thermoelectric (TE) Cooler
• “Cooler” is a misnomer; a TE cooler is a heat pump• Peltier effect: uses current flow to pump heat from
cold side to warm side• Pumping is typically 25% efficient; to pump 2 Watts
of waste heat takes 8 Watts or more of electrical power
• However, device cooled device can be at a lower temperature than ambient
• TE coolers can heat or cool, depending on current flow
Thermal Modeling
© M. T. Thompson, 2009
56
Thermoelectric (TE) Cooler
Thermal Modeling
© M. T. Thompson, 2009
57
Fan
Thermal Modeling
© M. T. Thompson, 2009
58
Example 1: Picture Window
• Consider picture window with A = 1 m2, 2.5 mm thick
• Ti = 70F (25C); Approximate To = 32F (0C) for 6 months (long winter !)
• What is total cost for heat loss at $0.10/kW-hr
T iT o
wR iw R w R ow
glass
P
T i T o
Thermal Modeling
© M. T. Thompson, 2009
59
Example 1: Picture Window
• Assumptions:– Window glass k = 0.78 W/(m-K)– Inside and outside window, heat
transfer dominated by free convection; h = 10 W/(m2K)
• Riw = Row = 1/(hA) = 0.1 C/Watt• Rw = w/(kA) =0.0025/(0.78)(1) = 0.0032
C/Watt• Rtotal = 0.2032 C/Watt• P = DT/Rtotal = 25C/0.2032C/Watt =
123 Watts• E = 3 kW-hr/day or 539 kW-hr for winter• Cost = $53.9
T iT o
wR iw R w R ow
glass
P
T i T o
Thermal Modeling
© M. T. Thompson, 2009
60
Example 2: Picture Window with Double Pane
• Assumptions:– Still air in airgap k = 0.027
W/(m-K)– Ignore radiation
• 1 cm airgap: Rairgap = g/(kA) =0.01/(0.027)(1) = 0.37 C/Watt
• Rtotal = 0.58 C/Watt• P = DT/Rtotal = 25C/0.58C/Watt =
43 W• E = 1 kW-hr/day or 188 kW-hr for
winter• Cost = $18.80
– Cost will be lower if gap has vacuum
T i T airgap
wR iw R w R ow
P
T i T o
g
glass glass T o
R wR airgap
Thermal Modeling
© M. T. Thompson, 2009
61
Example 3: Temperature Rise in Magnetic Brake
Aluminum reaction rail (4 mm thick)
Steel back plate (11 mm thick)v
N
S
N
S
N
S
N
S
• Train mass M = 12,300 kg• Initial speed = 16 meters/second• Brake aluminum fin length 10 meters• Stopping time: a few seconds• Cycle time: 1200 seconds• What is temperature rise in aluminum fin and in
steel ?
Thermal Modeling
© M. T. Thompson, 2009
62
Example 3: Magnetic Brake Thermal Model
• Model for 1 meter long section of brake• Guesstimated dominant time constant = 4,500
seconds (0.5 x 9000 F) based on thermal model above
Thermal Modeling
© M. T. Thompson, 2009
63
Example 3: Magnetic Brake Temperature Profile
• PSPICE simulation
Thermal Modeling
© M. T. Thompson, 2009
64
Example 4: White Pipe in the Hot Sun
• How hot does the surface of a white pipe get? Assume R = 0.565 m, pipe length = 1m, sunlight = 1200 W/m2, h = 8 W/m2-K, = 0.9 and solar absorption coeff. solar = 0.26
• Assume no conductive heat transfer
Thermal Modeling
© M. T. Thompson, 2009
65
Example 4: Pipe in the Hot Sun
convradreflsun QQQQ
Qsun = 1356 WQrefl = (1-solar)Qsun = 1003 W
• Therefore, 353 Watts is absorbed by the pipe, then dissipated via radiation and convection
Thermal Modeling
© M. T. Thompson, 2009
66
Example 4: Pipe in the Hot Sun
• Given these assumptions, temperature rise above ambient (Ts – TA) 7 degrees C with Qconv = 195 W and Qrad = 158 W
For radiation:
)( 44Asrad TTAQ
with = 0.9, = 5.6810-8 W/(m2K4) and surface area A = 1.0 m2 .
For free convection:
Asconv TThA
Q
1
with free convection heat transfer coefficient estimated as h 8 W/(m2-K).
Thermal Modeling
© M. T. Thompson, 2009
67
Example 5: What Happens if Pipe is Black?
Qrefl goes way down (solar energy absorption goes up, as solar = 0.9)
Thermal Modeling
© M. T. Thompson, 2009
68
Other Important Thermal Design Issues• Contact resistance
– How to estimate it– How to reduce it
• Thermal pads, thermal grease, etc.• Proper torque for mounting screws
• Geometry effects– Vertical vs. horizontal fins– Fin efficiency (how close together can you put
heat sink fins ?)
Thermal Modeling
© M. T. Thompson, 2009
69
Some Heat Sinks
• TO-92 (small transistor package)
Reference: Aavid-Thermalloy
Thermal Modeling
© M. T. Thompson, 2009
70
Some Heat Sinks• TO-220
Reference: Aavid-Thermalloy
Thermal Modeling
© M. T. Thompson, 2009
71
Some Heat Sinks
• TO-247
Reference: Aavid-Thermalloy
Thermal Modeling
© M. T. Thompson, 2009
72
Some Heat Sinks
• Vicor power brick
Reference: Aavid-Thermalloy
Thermal Modeling
© M. T. Thompson, 2009
73
Some Heat Sinks
• Liquid cooled plate
Reference: Aavid-Thermalloy
Thermal Modeling
© M. T. Thompson, 2009
74
Extrusions
Reference: Aavid-Thermalloy
Thermal Modeling
© M. T. Thompson, 2009
75
Cooling Fins
References: J H. Lienhard IV and J H. Lienhard V, “A Heat Transfer Textbook,” 3 rd edition, Phlogiston Press, Cambridge, MA 2008
Thermal Modeling
© M. T. Thompson, 2009
76
Improving Conductive Heat Transfer
References: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
77
Improving Forced Convection Heat Transfer
References: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
78
Improving Forced Convection Heat Transfer
References: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
79
Improving Radiation Heat Transfer
References: International Rectifier, Application note N-1057, “Heatsink Characteristics”
Thermal Modeling
© M. T. Thompson, 2009
80
Conversion Factors
References: J H. Lienhard IV and J H. Lienhard V, “A Heat Transfer Textbook,” 3 rd edition, Phlogiston Press, Cambridge, MA 2008