Page 404 - Mechanical Engineers' Handbook (Volume 4)

2 Heat-Transfer Correlations for Electronic Equipment Cooling 393

In the pursuit of a more rigorous determination of the contact resistance, Yovanovich
and Antonetti 59 found it possible to predict the area-weighted interfacial gap, Y, in the fol-
lowing form:
Y 1.185 ln 3.132P 0.547
H (48)

where is the effective root mean square (rms) as given by Eq. (46), P is the contact pressure
(Pa), and H is the surface microhardness (Pa) of the softer material, to a depth of the order
of the penetration of the harder material. Using Y as the characteristic gap dimension and
incorporating the solid–solid and fluid gap parallel heat flow paths, they derived the following
equation for the total interfacial thermal resistance.
R 0.95 1

tan
k
P
g
1.25k
co
s
H Y (49)
is the interstitial fluid thermal conductivity. In the absence of detailed information,
where k g
/
tan
can be expected to range from 5 to 9 m for relatively smooth surfaces.
In describing heat flow across an interface, Eq. (49) assumed the existence of a fluid
gap, which provides a parallel heat flow path to that of the solid–solid contact. Because the
noncontact area may occupy in excess of 90% of the projected area, heat flow through the
interstitial spaces can be of great importance. Consequently, the use of high thermal con-
ductivity interstitial materials, such as soft metallic foils and fiber disks, conductive epoxies,
thermal greases, and polymeric ‘‘phase-change’’ materials, can substantially reduce the con-
tact resistance. The enhanced thermal capability of many of the high-performance epoxies,
thermal greases, and ‘‘phase-change’’ materials, commonly in use in the electronic industry,
is achieved through the use of large concentrations of thermally conductive particles. Suc-
cessful design and development of thermal packaging strategies, thus, requires the determi-
nation of the effective thermal conductivity of such particle-laden interstitial materials and
their effect on the overall interfacial thermal resistance.
Comprehensive reviews of the general role of interstitial materials in controlling contact
resistance have been published by several authors including Sauer. 60 When interstitial ma-
terials are used for control of the contact resistance, it is desirable to have some means of
61
comparing their effectiveness. Fletcher proposed two parameters for this purpose. The first
of these parameters is simply the ratio of the logarithms of the conductances, which is the
inverse of the contact resistance, with and without the filler:
ln( )
cm (50)
ln( )
bj
in which is the contact conductance, cm and bj refer to control material and bare junctions,
respectively. The second parameter takes the thickness of the filler material into account and
is defined as
( filler cm
)

(51)
( )
gap bj
in which is the equivalent thickness and
is the effectiveness of the interstitial material.
The performance of an interstitial interface material as decided by the parameter defined
by Fletcher, 61 in Eqs. (50) and (51) includes the bulk as well as the contact resistance
contribution. It is because of this reason that in certain cases that the thermal resistance of
these thermal interface materials is higher than that for a bare metallic contact because the
bulk resistance is the dominant factor in the thermal resistance. To make a clear comparison
of only the contact resistance arising from the interface of the substrate and various thermal