Title: Power Electronics Notes 29 Thermal Circuit Modeling and Introduction to Thermal System Design
1Power 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) 4567722
 Email marctt_at_thompsonrd.com
 Website http//www.thompsonrd.com
 Jeff W. Roblee, Ph.D.
 VP of Engineering
 Precitech, Inc.
 Keene, NH
 www.ametek.com
2Summary
 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
3Need for Component Temperature Control
All components (capacitors, inductors and
transformers, semiconductor devices) have maximum
operating temperatures specified by
manufacturer High operating temperatures have
undesirable effects on components
3
4Temperature Control Methods
Control voltages across and current through
components via good design practices Snubbers
may be required for semiconductor
devices. Freewheeling 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 temperaturecritical 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
4
5Heat 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
6Intuitive 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
7Thermal Circuit Analogy
 Use Ohms law analogy to model thermal circuits
 Thermal resistance
 k thermal conductivity (W/(mK))
 Thermal capacitance analogy isnt as
straightforward  cp heat capacity of material (Joules/(kgK))
8Thermal Circuit Analogy
 Heat transfer can be modeled by thermal circuits
 Using Ohms law 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)
Reference M. T. Thompson, Intuitive Analog
Circuit Design, Newnes, 2006.
8
9Thermal Circuit Analogy
 Elementary thermal network
Reference M. T. Thompson, Intuitive Analog
Circuit Design, Newnes, 2006.
9
10Thermal 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)
10
11Thermal Capacitance
 Thermal capacitance is an indication of how well
a material stores thermal energy  It is used when transient phenomena are
considered  Analogy isnt as straightforward
 M mass (kg)
 cp heat capacity of material (Joules/(kgK))
11
12Heat Flow Mechanisms
 Heat flows by 3 mechanisms the driving force for
heat transfer is the difference in temperature  Conduction
 Convection
 Free convection
 Forced convection
 3. Radiation
Reference R. E. Sonntag and C. Borgnakke,
Introduction to Engineering Thermodinamics, John
Wiley, 2007
12
13Conduction
 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, A1 cm2, T2
25C (298K), T1 75C (348K), k 230 W/(mK)
14Thermal Conductivity of Selected Materials
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
15Thermal Equivalent Circuits
Thermal equivalent circuit simplifies
calculation of temperatures in various parts of
structure.
Heat flow through a structure composed of
layers of different materials
Case
Junction
Sink
Ambient
P




Isolation pad
Ti Pd (R?jc R?cs R?sa) Ta If there
parallel heat flow paths, then thermal
resistances combine as do electrical resistors in
parallel.
15
16Thermal Conductivity of Selected Materials
Reference International Rectifier, Application
note N1057, Heatsink Characteristics
17Heat Capacity of Selected Materials
 Heat capacity is an indication of how well a
material stores thermal energy
Reference B. V. Karlekar and R. M. Desmond,
Engineering Heat Transfer, West Publishing, 1977
18Heat Capacity of Alloys
Reference http//www.engineeringtoolbox.com/speci
ficheatmetalalloysd_153.html
19Convection
 Convection can be free (without a fan) or forced
(with a fan)
Reference International Rectifier, Application
note N1057, Heatsink Characteristics
20Free Convection
Reference http//www.freestudy.co.uk/heat20tran
sfer/convrad.pdf
20
21Heat Transfer Coefficient for Convection
 Heat is transferred via a moving fluid
 Convection can be described by a heat transfer
coefficient h and Newtons 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
Reference B. V. Karlekar and R. M. Desmond,
Engineering Heat Transfer, pp. 14, West
Publishing, 1977
22Free 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, A1 cm2, Ta
25C (298K), Ts 75C (348K)
23Free Convection Heat Transfer Coefficient (h)
 For vertical fin
 Area A in m2, fin vertical height dvert in m
24Forced Convection
Reference International Rectifier, Application
note N1057, Heatsink Characteristics
25Forced 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 35?
increase in heat transfer and 35? reduction in
heat sink volume  In extreme cases you can do ?10x better by using
big fans, convoluted heat sink fin patterns, etc. 
26Thermal Performance Graphs for Heat Sinks
 Curve 1 natural convection (P vs. ?Tsa)
 Curve 2 forced convection curve (Rsa vs.
airflow)
1
2
Reference http//electronicscooling.com/article
s/1995/jun/jun95_01.php
26
27Radiation
 Energy is transferred through electromagnetic
radiation 
Reference International Rectifier, Application
note N1057, Heatsink Characteristics
28Radiation
 Energy is lost to the universe through
electromagnetic radiation 
 ? emissivity (0 for ideal reflector, 1 for
ideal radiator blackbody) ? StefanBoltzmann
constant  5.68?108 W/(m2K4)
 Example anodized aluminum plate, ? 0.8, A1
cm2, Ta 25C (298K), Ts 75C (348K)
29Radiation
 Incident, reflected and emitted radiation e.g.
body in sunlight
Reference http//www.energyideas.org/documents/f
actsheets/PTR/HeatTransfer.pdf
29
30Emissivity
Reference International Rectifier, Application
note N1057, Heatsink Characteristics
31Emissivity
Reference International Rectifier, Application
note N1057, Heatsink Characteristics
32Comments on Radiation
 In multiplefin heat sinks with modest
temperature rise, radiation usually isnt 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)
33IC Mounted to Heat Sink
 Interfaces
 Heat sinkambient convection (free or forced)
 Heat sinkcase of IC conduction
 Case junction conduction
34Multiple Fin Heat Sink
Reference http//www.oldcrows.net/patchell/Audi
oDIY/AudioDIY.html
34
35IC Mounted to Heat Sink
Reference International Rectifier, Application
Note AN997
36IC Mounted to Heat Sink  Closeup
 Thermal compound is often used to fill in the
airgap voids
Reference International Rectifier, Application
Note AN997
37IC Mounted to Heat Sink  Contact Resistance
vs. Torque (TO247)
Reference International Rectifier, Application
Note AN997
38IC Mounted to Heat Sink  Contact Resistance
vs. Interface Material (TO247)
Reference International Rectifier, Application
Note AN997
39IC Mounted to Heat Sink  Contact Resistance
vs. Interface Material (TO247)
 Dry vs. thermal compound vs. electricallyinsulati
ng pad 
Reference International Rectifier, Application
Note AN997
40Thermal Grease
40
41Heat Sink Pad
41
42Transient 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)
Transient thermal impedance Z?(t) Tj(t) 
Ta/P(t)
??? p R? Cs /4 thermal time
constant Tj(t ??) 0.833 Po R?
42
43Use of Transient Thermal Impedance
Response for a rectangular power dissipation
pulse P(t) Po u(t)  u(t  t1).
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)
43
44Multilayer Structures
Multilayer geometry
Transient thermal equivalent circuit
Transient thermal impedance (asymptotic) of
multilayer structure assuming widely separated
thermal time constants.
44
45Heat 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. Forcedair cooled sinks
have substantially smaller thermal time
constants, typically less than one minute.
Choice of heat sink depends on required thermal
resistance, R?sa, 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
junctiontocase thermal resistance, R?jc.
Maximum ambient temperature, Ta,max.
R?sa Tj,max  Ta,maxPdiss  R?jc
Pdiss and Ta,max determined by particular
application. Tj,max and R?jc set by
component manufacturer.
45
46Heat Conduction Thermal Resistance
Generic geometry of heat flow via conduction
Heat flow Pcond W/m2 ???k?A (T2  T1) / d
(T2  T1) / R ?cond
Thermal resistance R ? cond d / k A
Crosssectional area A hb k Thermal
conductivity has units of Wm1oC1 (kAl
220 Wm1oC1 ). Units of thermal resistance
are oC/W
46
47Radiative Thermal Resistance
StefanBoltzmann law describes radiative heat
transfer. Prad 5.7x108 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 
Ta5.7x108EA ( 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)(6x102)(393/100)4  (293/100)4 1
R?,rad 2.2 ?C/W
47
48Convective 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  Ta1.25
dvert0.25 A total surface area in
m2 Ts surface temperature ?K of
component. Ta ambient temperature ?K.
Ts  Ta /Pconv R?,conv Ts  Ta
dvert0.251.34 A (Ts  Ta )1.251 R?,conv
dvert0.25 1.34 A Ts  Ta0.251
Example  black anodized cube of aluminum 10 cm
on a side. Ts 120??C and Ta 20
?C. R?,conv 1010.25(1.34 6x102
120  200.25)1 R?,conv 2.2 ?C/W
48
49Combined Effects of Convection and Radiation
Heat loss via convection and radiation occur in
parallel. Steadystate 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
49
50Cost for Various Heat Sink Systems
 Note heat pipe and liquid systems require
eventual heat sink 
Reference http//www.electronicscooling.com/Res
ources/EC_Articles/JUN95/jun95_01.htm
51Comparison of Heat Sinks
STAMPED
EXTRUDED
CONVOLUTED
FAN
Reference http//www.ednmag.com/reg/1995/101295/
21df3.htm
522N3904 Static Thermal Model
53Liquid Cooling
 Advantages
 Best performance per unit volume
 Typical thermal resistance 0.010.1 C/W
 Disadvantages
 Need a pump
 Heat exchanger
 Possibility of leaks
 Cost
54Heat 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
55Thermoelectric (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 
56Thermoelectric (TE) Cooler
56
57Fan
57
58Example 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/kWhr
59Example 1 Picture Window
 Assumptions
 Window glass k 0.78 W/(mK)
 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 kWhr/day or 539 kWhr for winter
 Cost 53.9
60Example 2 Picture Window with Double Pane
 Assumptions
 Still air in airgap k 0.027 W/(mK)
 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 kWhr/day or 188 kWhr for winter
 Cost 18.80
 Cost will be lower if gap has vacuum
61Example 3 Temperature Rise in Magnetic Brake
 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 ?
62Example 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
63Example 3 Magnetic Brake Temperature Profile
64Example 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/m2K, ? 0.9 and solar
absorption coeff. ?solar 0.26  Assume no conductive heat transfer
64
65Example 4 Pipe in the Hot Sun
Qsun 1356 W Qrefl (1?solar)Qsun 1003 W
 Therefore, 353 Watts is absorbed by the pipe,
then dissipated via radiation and convection
65
66Example 4 Pipe in the Hot Sun
For radiation
with ? 0.9, ? 5.68?108 W/(m2K4) and surface
area A 1.0 m2 . For free convection
with free convection heat transfer coefficient
estimated as h ? 8 W/(m2K).
 Given these assumptions, temperature rise above
ambient (Ts TA) ? 7 degrees C with Qconv 195
W and Qrad 158 W
66
67Example 5 What Happens if Pipe is Black?
Qrefl goes way down (solar energy absorption goes
up, as ?solar 0.9)
67
68Other 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 ?)
69Some Heat Sinks
 TO92 (small transistor package)
Reference AavidThermalloy
70Some Heat Sinks
Reference AavidThermalloy
71Some Heat Sinks
Reference AavidThermalloy
72Some Heat Sinks
Reference AavidThermalloy
73Some Heat Sinks
Reference AavidThermalloy
74Extrusions
Reference AavidThermalloy
75Cooling Fins
References J H. Lienhard IV and J H. Lienhard
V, A Heat Transfer Textbook, 3rd edition,
Phlogiston Press, Cambridge, MA 2008
75
76Improving Conductive Heat Transfer
References International Rectifier, Application
note N1057, Heatsink Characteristics
77Improving Forced Convection Heat Transfer
References International Rectifier, Application
note N1057, Heatsink Characteristics
78Improving Forced Convection Heat Transfer
References International Rectifier, Application
note N1057, Heatsink Characteristics
79Improving Radiation Heat Transfer
References International Rectifier, Application
note N1057, Heatsink Characteristics
80Conversion Factors
References J H. Lienhard IV and J H. Lienhard
V, A Heat Transfer Textbook, 3rd edition,
Phlogiston Press, Cambridge, MA 2008
80