Page 396 - Mechanical Engineers' Handbook (Volume 4)

2 Heat-Transfer Correlations for Electronic Equipment Cooling 385

Total Resistance—Single-Chip Packages
To the accuracy of the assumptions employed in the preceding development, the overall
single-chip package resistance, relating the chip temperature to the inlet temperature of the
coolant, can be found by summing the internal, external, and flow resistances to yield
R x R R
Q
1
R R R R (K/W) (30)
T jc ex fl int sp sk
kA q 2 Qc p
In evaluating the thermal resistance by this relationship, care must be taken to determine the
effective cross-sectional area for heat flow at each layer in the module and to consider
possible voidage in any solder and adhesive layers.
As previously noted in the development of the relationships for the external and internal
resistances, Eq. (30) shows R to be a strong function of the convective heat-transfer coef-
T
ficient, the flowing heat capacity of the coolant, and geometric parameters (thickness and
cross-sectional area of each layer). Thus, the introduction of a superior coolant, use of
thermal enhancement techniques that increase the local heat transfer coefficient, or selection
of a heat-transfer mode with inherently high heat-transfer coefficients (boiling, for example)
will all be reflected in appropriately lower external and total thermal resistances. Similarly,
improvements in the thermal conductivity and reduction in the thickness of the relatively
low-conductivity bonding materials (such as soft solder, epoxy or silicone) would act to
reduce the internal and total thermal resistances.
Frequently, however, even more dramatic reductions in the total resistance can be
achieved simply by increasing the cross-sectional area for heat flow within the chip module
(such as chip, substrate, and heat spreader) as well as along the wetted, exterior surface. The
implementation of this approach to reducing the internal resistance generally results in a
larger package footprint or volume but is rewarded with a lower thermal resistance. The use
of heat sinks is, of course, the embodiment of this approach to the reduction of the external
resistance.

2 HEAT-TRANSFER CORRELATIONS FOR ELECTRONIC EQUIPMENT COOLING
The reader should use the material in this section that pertains to heat-transfer correlations
in geometries peculiar to electronic equipment.

2.1 Natural Convection in Confined Spaces

For natural convection in confined horizontal spaces the recommended correlations for air
are 12
4
Nu 0.195(Gr) 1/4 , 10 Gr 4 10 5 (31)
Nu 0.068(Gr) 1/3 , Gr 10 5

where Gr is the Grashof number,
2
g L
T
2
Gr (32)
2
and where, in this case, the significant dimension L is the gap spacing in both the Nusselt
and Grashof numbers.
For liquids 13