Page 403 - Mechanical Engineers' Handbook (Volume 4)

392 Cooling Electronic Equipment

2.3 Thermal Interface Resistance
Heat transfer across a solid interface is accompanied by a temperature difference, caused by
imperfect contact between the two solids. Even when perfect adhesion is achieved between
the solids, the transfer of heat is impeded by the acoustic mismatch in the properties of the
phonons on either side of the interface. Traditionally the thermal resistance arising due to
imperfect contact has been called the ‘‘thermal contact’’ resistance. The resistance due to the
mismatch in the acoustic properties is usually termed the ‘‘thermal boundary’’ resistance.
The thermal contact resistance is a macroscopic phenomenon, whereas thermal boundary
resistance is a microscopic phenomenon. This section primarily focuses on thermal contact
resistance and methods to reduce the contact resistance.
When two surfaces are joined, as shown in Figure 10, asperities on each of the surfaces
limit the actual contact between the two solids to a very small fraction, perhaps just 1–2%
for lightly loaded interfaces, of the apparent area. As a consequence, the flow of heat across
such an interface involves solid-to-solid conduction in the area of actual contact, A , and
co
conduction through the fluid occupying the noncontact area, A , of the interface. At elevated
nc
temperatures or in vacuum, radiation heat transfer across the open spaces may also play an
important role.
The pressure imposed across the interface, along with the microhardness of the softer
surface and the surface roughness characteristics of both solids, determines the interfacial
gap, , and the contact area, A . Assuming plastic deformation of the asperities and a
co
Gaussian distribution of the asperities over the apparent area, Cooper et al. 58 proposed the
following relation for the contact resistance R :
co
R k (P/H) 0.985
tan
1
s
1.45
co
(45)
where k is the harmonic mean thermal conductivity defined as k 2k k /(k k ), P is
2
1
1 2
s
s
the apparent contact pressure, H is the hardness of the softer material, and is the rms
roughness given by
2 2 (46)
2
1
1
where and are the roughness of surfaces 1 and 2, respectively. The term
tan
in Eq.
1 2
(45) is the average asperity angle:

tan

tan

tan
2 (47)
2
2
1
2
This relation neglects the heat-transfer contribution of any trapped fluid in the interfacial
gap.

T 1
δ Solid 1 Air Gap

Solid 2
Contact
T 2
points
Figure 10 Contact and heat flow at a solid/solid inter-
face.