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Power Electronics Notes 29 Thermal Circuit Modeling and Introduction to Thermal System Design

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Title: Power Electronics Notes 29 Thermal Circuit Modeling and Introduction to Thermal System Design


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 marctt_at_thompsonrd.com
  • Website http//www.thompsonrd.com
  • Jeff W. Roblee, Ph.D.
  • VP of Engineering
  • Precitech, Inc.
  • Keene, NH
  • www.ametek.com

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

3
Need 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
4
Temperature Control Methods
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
4
5
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
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

7
Thermal 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/(kg-K))

8
Thermal 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
9
Thermal Circuit Analogy
  • Elementary thermal network

Reference M. T. Thompson, Intuitive Analog
Circuit Design, Newnes, 2006.
9
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)

10
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 isnt as straightforward
  • M mass (kg)
  • cp heat capacity of material (Joules/(kg-K))

11
12
Heat 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
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, A1 cm2, T2
    25C (298K), T1 75C (348K), k 230 W/(m-K)

14
Thermal 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
15
Thermal 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
16
Thermal Conductivity of Selected Materials
Reference International Rectifier, Application
note N-1057, Heatsink Characteristics
17
Heat 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
18
Heat Capacity of Alloys
Reference http//www.engineeringtoolbox.com/speci
fic-heat-metal-alloys-d_153.html
19
Convection
  • Convection can be free (without a fan) or forced
    (with a fan)

Reference International Rectifier, Application
note N-1057, Heatsink Characteristics
20
Free Convection
Reference http//www.freestudy.co.uk/heat20tran
sfer/convrad.pdf
20
21
Heat 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
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, A1 cm2, Ta
    25C (298K), Ts 75C (348K)

23
Free Convection Heat Transfer Coefficient (h)
  • For vertical fin
  • Area A in m2, fin vertical height dvert in m

24
Forced Convection
  • With a fan

Reference International Rectifier, Application
note N-1057, Heatsink Characteristics
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.

26
Thermal Performance Graphs for Heat Sinks
  • Curve 1 natural convection (P vs. ?Tsa)
  • Curve 2 forced convection curve (Rsa vs.
    airflow)

1
2
Reference http//electronics-cooling.com/article
s/1995/jun/jun95_01.php
26
27
Radiation
  • Energy is transferred through electromagnetic
    radiation

Reference International Rectifier, Application
note N-1057, Heatsink Characteristics
28
Radiation
  • Energy is lost to the universe through
    electromagnetic radiation
  • ? emissivity (0 for ideal reflector, 1 for
    ideal radiator blackbody) ? Stefan-Boltzmann
    constant
  • 5.68?10-8 W/(m2K4)
  • Example anodized aluminum plate, ? 0.8, A1
    cm2, Ta 25C (298K), Ts 75C (348K)

29
Radiation
  • Incident, reflected and emitted radiation e.g.
    body in sunlight

Reference http//www.energyideas.org/documents/f
actsheets/PTR/HeatTransfer.pdf
29
30
Emissivity
Reference International Rectifier, Application
note N-1057, Heatsink Characteristics
31
Emissivity
Reference International Rectifier, Application
note N-1057, Heatsink Characteristics
32
Comments on Radiation
  • In multiple-fin 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)

33
IC Mounted to Heat Sink
  • Interfaces
  • Heat sink-ambient convection (free or forced)
  • Heat sink-case of IC conduction
  • Case junction conduction

34
Multiple Fin Heat Sink
Reference http//www.oldcrows.net/patchell/Audi
oDIY/AudioDIY.html
34
35
IC Mounted to Heat Sink

Reference International Rectifier, Application
Note AN-997
36
IC Mounted to Heat Sink --- Close-up
  • Thermal compound is often used to fill in the
    airgap voids

Reference International Rectifier, Application
Note AN-997
37
IC Mounted to Heat Sink --- Contact Resistance
vs. Torque (TO-247)

Reference International Rectifier, Application
Note AN-997
38
IC Mounted to Heat Sink --- Contact Resistance
vs. Interface Material (TO-247)

Reference International Rectifier, Application
Note AN-997
39
IC Mounted to Heat Sink --- Contact Resistance
vs. Interface Material (TO-247)
  • Dry vs. thermal compound vs. electrically-insulati
    ng pad

Reference International Rectifier, Application
Note AN-997
40
Thermal Grease

40
41
Heat Sink Pad

41
42
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)
Transient thermal impedance Z?(t) Tj(t) -
Ta/P(t)
??? p R? Cs /4 thermal time
constant Tj(t ??) 0.833 Po R?
42
43
Use 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
44
Multilayer Structures
Multilayer geometry
Transient thermal equivalent circuit
Transient thermal impedance (asymptotic) of
multilayer structure assuming widely separated
thermal time constants.
44
45
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, 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
junction-to-case 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
46
Heat 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
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
47
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 -
Ta5.7x10-8EA ( 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
48
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 - Ta1.25
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
dvert0.251.34 A (Ts - Ta )1.25-1 R?,conv
dvert0.25 1.34 A Ts - Ta0.25-1
Example - black anodized cube of aluminum 10 cm
on a side. Ts 120??C and Ta 20
?C. R?,conv 10-10.25(1.34 6x10-2
120 - 200.25)-1 R?,conv 2.2 ?C/W
48
49
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
49
50
Cost for Various Heat Sink Systems
  • Note heat pipe and liquid systems require
    eventual heat sink

Reference http//www.electronics-cooling.com/Res
ources/EC_Articles/JUN95/jun95_01.htm
51
Comparison of Heat Sinks

STAMPED
EXTRUDED
CONVOLUTED
FAN
Reference http//www.ednmag.com/reg/1995/101295/
21df3.htm
52
2N3904 Static Thermal Model

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

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

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

56
Thermoelectric (TE) Cooler

56
57
Fan

57
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

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

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

61
Example 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 ?

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

63
Example 3 Magnetic Brake Temperature Profile
  • PSPICE simulation

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

64
65
Example 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
66
Example 4 Pipe in the Hot Sun
For radiation

with ? 0.9, ? 5.68?10-8 W/(m2K4) and surface
area A 1.0 m2 . For free convection
with free convection heat transfer coefficient
estimated as h ? 8 W/(m2-K).
  • Given these assumptions, temperature rise above
    ambient (Ts TA) ? 7 degrees C with Qconv 195
    W and Qrad 158 W

66
67
Example 5 What Happens if Pipe is Black?

Qrefl goes way down (solar energy absorption goes
up, as ?solar 0.9)
67
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 ?)

69
Some Heat Sinks
  • TO-92 (small transistor package)

Reference Aavid-Thermalloy
70
Some Heat Sinks
  • TO-220

Reference Aavid-Thermalloy
71
Some Heat Sinks
  • TO-247

Reference Aavid-Thermalloy
72
Some Heat Sinks
  • Vicor power brick

Reference Aavid-Thermalloy
73
Some Heat Sinks
  • Liquid cooled plate

Reference Aavid-Thermalloy
74
Extrusions
Reference Aavid-Thermalloy
75
Cooling Fins
References J H. Lienhard IV and J H. Lienhard
V, A Heat Transfer Textbook, 3rd edition,
Phlogiston Press, Cambridge, MA 2008
75
76
Improving Conductive Heat Transfer
References International Rectifier, Application
note N-1057, Heatsink Characteristics
77
Improving Forced Convection Heat Transfer
References International Rectifier, Application
note N-1057, Heatsink Characteristics
78
Improving Forced Convection Heat Transfer
References International Rectifier, Application
note N-1057, Heatsink Characteristics
79
Improving Radiation Heat Transfer
References International Rectifier, Application
note N-1057, Heatsink Characteristics
80
Conversion Factors
References J H. Lienhard IV and J H. Lienhard
V, A Heat Transfer Textbook, 3rd edition,
Phlogiston Press, Cambridge, MA 2008
80
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