Thermal Design and Optimization of Heat Sinks · 80386 80486 Pentium Pentium III Micro 2000 each...
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Thermal Design and Optimization of Heat Sinks J. Richard Culham
Transcript of Thermal Design and Optimization of Heat Sinks · 80386 80486 Pentium Pentium III Micro 2000 each...
Thermal Design andOptimization of Heat Sinks
J. Richard Culham
Outline
Background Modelling Approach Validation Optimization Future Work Summary
40 Watts! What’s the big deal?
Light Bulb ➢ Power: 40 W ➢ Area: 120 cm ➢ Flux: 0.33 W/cm
Pentium III
Silicon Package ➢ Power: 40 W ➢ Area: 1.5 cm ➢ Flux: 26.7 W/cm
➢ Rj-c: 0.94 C/W ➢ Rj-a: 6.8 C/W
(no heat sink)➢ Rj-a: 2.5 C/W
(heat sink)
2 2
❋ 0.25 micron CMOS technology❋ 9.5 million transistors ❋ 450 - 550 MHz
2 2
80 x
75 100 125 15010
0
101
102
103
Component Failure Rate
Junction Temperature ( C)
Nor
mal
ized
Fai
lure
Rat
e
o
FC: 58.2 C
NC: 96.1 C
(2m/s)
o
o
o
Pentium 233 MHz@ 7.9 W
no heat sinkFC: 99.5 C
NC: 136.4 Co
Pentium 233 MHz@ 7.9 W
with heat sink
(2m/s)
Intel Design Specification:
T = 75 Cjo
GaN - SiC
Si - SiO2
Moore’s Law (1965)
1975 1980 1985 1990 1995 2000
10M
1M
100K
10K
(transistors)500
25
1.0
0.1
0.01
(mips)
40048080
8086
8028680386
80486
Pentium
Pentium III
Micro 2000
➣ each new chip contains roughly twice as muchcapacity as its predecessor
➣ a new generation of chips is released every18 - 24 months
From: www.intel.com➥ in 26 years, the
population of transistors per
chip has increasedby 3,200 times
IC Trends: Past, Present & Future
1980 1999 2003 2006 2012
Comp. Per Chip 0.2 M 6.2 M 18 M 39 M 100 M
Frequency (MHz) 5 1250 1500 3500 10000
Chip Area (sq. cm) 0.4 4.45 5.60 7.90 15.80
Max. Power (W) 5 90 130 160 175
Junction Temp. (C) 125 125 125 125 125
From: David L. Blackburn, NIST
Why Use Natural Convection?
simplicity: ➥ low maintenance ➥ lower power consumption ➥ less space (notebook computers)
less noise fail safe heat transfer condition
Thermal Resistance
Heat source (junction)
Heat sink (air)
contactresistance
materialresistance
spreadingresistance
filmresistance
• increased heat transfer coefficient immersion cooling (boiling) impingement cooling forced air natural convection
• increased surface area spreaders heat sinks
Plate Fin H.S. Pin Fin H.S.
Radial Fin H.S. Specialty H.S.
Plate Fin Pin Fin
Turned Fin Spiral Fin
Plate Fin Pin Fin
Turned Fin Spiral Fin
Plate Fin Pin Fin
Turned Fin Spiral Fin
Plate Fin Pin Fin
Turned Fin Spiral Fin
Heat Sink Model
Plate fin heat sink Natural convection Isothermal Steady state Working fluid is air i.e. Pr = 0.71
Modelling Procedure
Exterior surfaces
Interior surfaces
● fins : top, bottom, ends & tip● base plate: top, bottom, ends and back
● fins : side walls● channel base
g
LL
H t
b
bpt
fN
Given:Find
:
dimensions & temperature
Nu vs. Rab b
=g! "T b 3
#$•b
L=hb
k f
Exterior Surfaces
Boundary layer
Diffusion
● lower Rayleigh numbers● thick boundary layers
● higher Rayleigh numbers● thin boundary layers
Diffusion Model
L
L L
D
12
3
GM
Exterior Boundary Layer Model
(in terms of the surface area)
Where:
W
L
H
g
Interior Surfaces
Control surfaces
Channel flow
● Elenbaas model with adjustment for end wall● combined flow : developing + fully developed
● open surfaces with energy migration
Parallel Plates Model
Elenbaas, 1941
Churchill, 1977
fd - fullydevelopeddev - developing
flow
b
L
g
- body gravity function
- Prandtl number function
Comprehensive Model
diffusion channel flow
externalboundarylayer flow
Model Validation
cuboids ➊ plate - Karagiozis (1991), Saunders (1936) ➋ cube - Chamberlain (1983), Stretton (1988) ➌ rectangular prism - Clemes (1990)
parallel plates ➊ Elenbaas (1942), Aihara (1973), Kennard (1941)
Karagiozis (1991) Van de Pol & Tierny (1978)
Limiting Cases
Heat Sinks
Modelling Domain
10-4
10-2
100
102
104
106
108
1010
10-3
10-2
10-1
100
101
102
103
Plate spacing
Aspect ratio
fully-developedlimit
Boundary layer limit
b
Rab
Nu b
CUBE PRISM FLAT PLATE PLATES HEAT SINK
+Nu = Nu0 +Nu12Nu + 43Nu Nu+-2 -2 -1/2
10-2
10-1
100
101
102
103
104
105
10-1
100
101
L x W x H (mm)Chamberlain (1983) 43.2 x 43.2 x 43.2 Stretton (1984) 38.1 x 38.1 38.1 Model
43.2
W
L
H
g
Rab
Nu
b
CUBE PRISM FLAT PLATE PLATES HEAT SINK
+Nu = Nu0 +Nu12Nu + 43Nu Nu+-2 -2 -1/2
10-2
10-1
100
101
102
103
104
105
10-1
100
101
Clemes (1990) Model
g
units inmm
50.43 x 50.43 X 510.6
Rab
Nu
b
CUBE PRISM FLAT PLATE PLATES HEAT SINK
+Nu = Nu0 +Nu12Nu + 43Nu Nu+-2 -2 -1/2
10-310
-210
-110
010
110
210
310
410
510
610
-1
100
101
102
43.2
W
L
H
g
Rab
Nu
b
L x W x H (mm) Karagiozis (1991) 150x170x9.54
Model Saunders (1936) 76x230x.00254
Model
CUBE PRISM FLAT PLATE PLATES HEAT SINK
+Nu = Nu0 +Nu12Nu + 43Nu Nu+-2 -2 -1/2
10-1
100
101
102
103
104
105
10-2
10-1
100
101
Ra b
Nu
b
g
b
Elenbaas (1942) Aihara (1973) Kennard (1941) Model
CUBE PRISM FLAT PLATE PLATES HEAT SINK
+Nu = Nu0 +Nu12Nu + 43Nu Nu+-2 -2 -1/2
10-310
-210
-110
010
110
210
310
410
510
610
-2
10-1
100
101
102
H/b Karagiozis Model Van de Pol & Tierney0.75 1.19 2.98
Nu
b
Rab
H
b
L
t tbp
Which is the Right Tool?
➥ design is known apriori
➥ used to calculate the performance of a given design, i.e. Nu vs. Ra ➥ cannot guarantee an optimized design
Analysis Tool Design Tool vs.
➥ used to obtain an optimized design for a set of known constraintsi.e. given: • heat input • max. temp. • max. outside dimensions find: the most efficient design
Optimization Using EGM
➥ entropy production ∝ amount of energy degraded to a form unavailable for work
➥ lost work is an additional amount of heat that could have been extracted
➥ degradation process is a function of thermodynamic irreversibilities e.g. friction, heat transfer etc.
➥ minimizing the production of entropy, provides a concurrent optimization of all design variables
Why use Entropy Generation Minimization?
Entropy Balance (local)
1st law ofthermodynamics
Gibb’sEquation
heat transfer viscous dissipation
conservation of mass + +
Qx , s x , mx
Qz , sz ,mz
Qy , sy ,my
•
•
•
Entropy Balance (external & internal)
Extended surface
Passage geometry
dx
mℑ
A
T w irreversibilities due to: wall-fluid ∆T fluid friction
AQ B
T B T w Q
irreversibilities due to base-wall ∆T
Total Entropy Generation
differential level
elemental level
component level
dxdy
dz
differentialcontrolvolume
Extended surface• fin • channel flow
System• fins • base plate
where:
base heat flow rate
base - stream temp. difference
ambient temperature
drag forcetotal fin resistance
- specified
- fan curve
- buoyancy induced
Example: Heat Sink Optimization
Board spacing ≡ H
L
W
Step 1: Determine problem constraintsi) power input, Q
ii) maximum chip temperature, Tmax iii) geometry , H, L, W
Example: Heat Sink Optimization
Board spacing ≡ H
L W
H
Step 2: Set maximum heat sink volume i) package foot print = L x W
ii) maximum height - board spacing minus package height
Example: Heat Sink Optimization
Board spacing ≡ H
L W
H
Step 3: Optimize heat sink i) number of fins
ii) fin thickness iii) fin spacing iv) base plate thickness
Single Parameter EGM
0 10 200
0.05
0.1
0.15
0.2
0.25
Number of Fins
Entr
opy
Gen
erat
ion
(W/K
)
14
H = L = W = 50 mm Fin thickness = 1 mm Base plate thickness = 1.25 mmQ = 50 W Find: number of fins
Multi-Parameter Minimization Procedure
where:➥
iterate until
Newton-Raphson Method with Multiple Equations and Unknowns
Future Work
Goal: Develop a comprehensive model to find the best heat sink design givena limited set of design constraints
Physical Design Thermal Cost
Standards
• heat sink type• material • weight • dimensions • surface finish
• maximum volume • boundary conditions• max. allowable temp.• orientation • flow mechanism
• labour • manufacturing• material
• noise • exposure to
touch
Summary
Heat sink design requires both a selection tool & an analysis tool
Selection is based on: ➥ physical constraints - geometry, material, etc. ➥ thermal-fluid conditions - bc’s, properties, etc. ➥ miscellaneous conditions - cost, standards etc.
Analysis is based on simulating a prescribed design
The End
Karagiozis Heat Sink Model
where:
Modified flat plate model ➛ correction term at low Ra
