Direct Liquid Cooling of Microelectronic Compo-nents, in Advances in Thermal Modeling of Electronic Components and Systems, Vol... The Effect of Geometry on Heat Transfer by Free Convect
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whereθ is a configuration factor which must be determined empirically However,
to obtain engineering estimates of the thermal performance, Bar-Cohen et al (1987) have proposed a value of 31.5 forθ The upper bound on the performance maps is
therefore marked with both the CHF limit and the condensation limit
13.8 THERMOELECTRIC COOLERS
The Peltiereffect is the basis forthe thermal electric cooler(TEC), which is a solid-state heat pump If a potential is placed across two junctions, heat will be absorbed into one junction and expelled from the other in proportion to the current Most material combinations exhibit the Peltier effect to some degree However, it is most
obvious across a p-n junction as shown in Fig 13.34 As electrons are transported from the p-side of a junction to the n-side, they are elevated to a higher-energy
state and thus absorb heat, resulting in cooling the surrounding area When they are
transported from the p-side to the n-side, they release heat.
The materials that have been used to make TEC include bismuth telluride (Bi2Te3), lead telluride (PbTe), and silicon germanium (SiGe) To obtain optimum parameters, these semiconductors are doped during fabrication Bi2Te3has the best performance
at temperatures of interest for electronic components and is most commonly used A TEC device is constructed by placing from one to several hundred thermocouples electrically in series and thermally in parallel between two pieces of metallized, thermally conductive ceramic acting as an electrical insulator For continuous cooling
at the low-temperature side of the TEC, the heat absorbed at the cold side, as well as the heat generated by the flow of electricity, must be removed from the hot side by one
of the thermal transport mechanisms described previously Solution of the governing equations for a thermoelectric couple yields a relation for the maximum temperature differential obtainable with such a device, as
∆Tmax= α2T c2
K = k a A a
L a +k b A b
R = ρA a L a
a +ρA b A b
It may thus be observed that the maximum temperature differential can be enhanced
by minimizing the product of the thermal conductanceK and electrical, resistance R.
A TEC device is frequently rated by a figure of merit, as given by
FOM=ρ α2s
TEkTE
(13.96)
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Figure 13.34 Thermoelectric cooler
whereα2
s is the Seebeck coefficient andρTE is the resistivity of the TEC element
Values of this figure of merit are typically in the range 0.002 to 0.005 K−1, but extensive research is under way to improve this FOM by as much as an order of magnitude in the next few years The coefficient of performance of a TEC is defined
as the ratio of heat pumped to the input power:
COP= heat pumped
input power = q c
Pin
(13.97) The optimum COP is given by
COPopt= Tavg
∆T
B − 1
where
B =1+ (FOM · Tavg) (13.99)
A TEC may be selected from the performance and COP curves for a given set of design criteria It is essential that the TEC and heat sink, as well as the power supply used to operate the TEC, be selected together For increased cooling capacity, TECs may be operated in parallel However, for lower chip temperatures it may be necessary
to cascade several TEC devices or to operate them in series
The biggest limitation in the use of a TEC for commercial electronics is the very low FOM Recent years have witnessed extensive research in the area of TECs from a material point of view to increase the FOM Thin-film supperlatice and quantum-well structures have shown evidence of providing high FOM compared to the state-of-the-art TEC
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13.9 CHIP TEMPERATURE MEASUREMENT
As mentioned previously, the total thermal resistance of a package is usually the sum
ofθjc(junction to case) andθca(case to ambient) The object of most experimental programs is to determine these resistances This knowledge then allows the junction temperature to be predicted as a function of power and cooling medium temperature and flow rate.θjcandθcaare typically measured in a lab environment with the help
of test chips popularly known as test vehicles There are basically two measurement methods commonly used to determine the temperature of a test vehicle die The first makes use of a temperature-sensitive parameter on the test vehicle to determine the die temperature, such as one or more dedicated diodes of resistors Calibration of these temperature sensors can be very time consuming Furthermore, as a test vehicle can have more than one temperature sensor and there could also be part-to-part variability
in the test vehicle coming out of the factory, time to calibrate each temperature sensor could be enormous Solbrekken and Chiu (1998) introduced a simplified calibration procedure that utilizes single-resistance measurements either at room temperature or
at the anticipated test temperature In their proposed method 30 temperature sensors are selected randomly and are calibrated at three set-point temperatures Then the average intercept of resistance versus temperature for the 30 temperature sensors is calculated Later, forthe calibration of othertest vehicles forthe same generation
of products, the die is calibrated at a single temperature and the average intercept calculated forthe 30 samples is used in conjunction with the single-point calibration for determining the temperature of the test vehicle A second category of chip tem-perature measurement techniques includes liquid crystals, thermographic phosphors, laser scanners, infrared camera, and so on Each of these methods presents a unique set of concerns, ranging from temperature resolution to cost of implementation
13.10 SUMMARY
The fundamental principles and concepts for thermal management of electronics were presented in this chapter Simplified equations for first-order analysis of the temperature on electronic components were also introduced A variety of cooling techniques, including heat sinks, jet impingement cooling, liquid immersion cooling, and thermoelectric cooling, were also discussed
NOMENCLATURE
Roman Letter Symbols
a heat source area, m2
B constant, dimensionless
b heat source size, m
PCB spacing, m
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Bi Biot number, dimensionless [= hL/k]
C constant in heat transfer coefficient correlations, dimensionless
C p specific heat, J/hg · K CHF critical heat flux, dimensionless COP coefficient of performance, dimensionless
c speed of sound, m/s
El Elenbaas number, dimensionless
El modified Elenbaas number, dimensionless
F ij radiation view factor fromi to j, dimensionless
FOM figure of merit, dimensionless
f impingement area ratio, dimensionless
g gravitational acceleration, m/s2
Kennedy (1959) spreading resistance factor, dimensionless hardness, N/m2
h heat transfer coefficient, W/m2· K
h f v latent heat of vaporization, J/kg · K
¯
h Planck’s constant, dimensionless
k thermal conductivity, W/m · K
k b Boltzmann constant, dimensionless
L length, width, orthickness, m
l mean free path, m
˙m mass flow rate, kg/s
N numberof atomic layers, dimensionless
n number, dimensionless
Nu Nusselt number, dimensionless [= hL/k]
P pressure, N/m2
plate to airparameter, dimensionless perimeter, m
p volume fraction, dimensionless
p c threshold volume fraction, dimensionless PrPrandtl number, dimensionless
= µC p /k
Q total heat flow, W
q heat flux, W/m2
R thermal resistance, °C/W or K/W
asymmetry parameter, dimensionless
r T asymmetry parameter, dimensionless
Ra Rayleigh number, dimensionless
= (gβ∆T L3/ν2)Pr
Re Reynolds number, dimensionless [= ρV L/µ]
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S shape factor, m2
shape parameter, dimensionless
T temperature, °C or K
volume, m3
W characteristic length (length or width), m
x length ordistance, m
Y area-weighted interfacial gap, m
z clearspace between fins, m
∆k change in thermal conductivity, W/m · K
∆T temperature difference, °C or K
∆x distance between two points, m
Greek Letter Symbols
α thermal diffusivity, m2/s
Seebeck coefficient, dimensionless
β volumetric expansion coefficient, K−1
δ thickness orgap width, m
penetration depth, m heaterthickness, m
ε emissivity, dimensionless
ζ ratio of heat source area to substrate area, dimensionless
η fin efficiency, dimensionless
θ thermal resistance, °C/W
asperity angle, deg
conduction factor, dimensionless
µ dynamic viscosity, N· s/m2
ν kinematic viscosity, m2/s
π pi, dimensionless
ρ density, kg/m3
σ Stefan–Boltzmann constant, W/m2· K4
surface tension, N/m surface roughness, m
τ time constant, s
φ Debye temperature, K
ϕ particle volume fraction, dimensionless
maximum packing fraction, dimensionless
ϕm maximum packing fraction, dimensionless
χ ratio of logarithmic conductances, dimensionless
Subscripts
0 initial (at time= 0) orbased on channel inlet
1 item orentity 1
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1D one-dimensional
2 item orentity 2
a ambient orentity a
b boundary orbase orentityb
bj bare junction base heat sink base area
ca case to ambient
cm control material
en equivalent normal
eq equivalent in-plane
ex external or excursion
f g between saturated liquid and saturated vapor fillerfiller
g interstitial fluid or gas (vapor)
ICP integrated circuit package
j junction a counter
jc junction to case
m continuous phase or matrix and maximum packing fraction
mc between interface and matrix
plane
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filler at constant pressure
r radiation or radial direction
mean condition
source source
ss steady state
T total oroverall
TE thermoelectric device TIM thermal interface material
z position along thez-coordinate direction
Superscripts
n normal direction
p in-plane direction
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