Page 385 - Mechanical Engineers' Handbook (Volume 4)

374 Cooling Electronic Equipment

Figure 2 Physical contact between two nonideal
surfaces.

2
h h h (W/m K) (7a)
co c g
the contact resistance based on the apparent contact area, A , may be defined as
a
1
R co (K/W) (7b)
hA a
co
In Eq. (7a), h is given by
c
h 54.25k 0.95
P
m
c
s
H (8a)
where k is the harmonic mean thermal conductivity for the two solids with thermal con-
s
ductivities, k and k ,
2
1
2kk
k 12 (W/m K)
s
k k 2
1
is the effective rms surface roughness developed from the surface roughnesses of the two
materials, and ,
1 2
2
2 2 ( m)
1
and m is the effective absolute surface slope composed of the individual slopes of the two
materials, m and m ,
1 2
2
m m m 2 2
1
where P is the contact pressure and H is the microhardness of the softer material, both in
2
N/m . In the absence of detailed information, the /m ratio can be taken equal to 5–9 m
for relatively smooth surfaces. 1,2
In Eq. (7a), h is given by
g
k g
h (8b)
g
Y M
where k is the thermal conductivity of the gap fluid, Y is the distance between the mean
g
planes (Fig. 2) given by