Page 395 - Mechanical Engineers' Handbook (Volume 4)

384 Cooling Electronic Equipment

When a heat sink or compact heat exchanger is attached to the package, the external
resistance accounting for the bond-layer conduction and the total resistance of the heat sink,
R , can be expressed as
sk
x
T T
R c fl R (K/W) (29)
ex sk
q c kA b
where R sk
R 1 1
1
sk
nhS hS
b b
ƒ
is the the parallel combination of the resistance of the n fins
1
R
ƒ
nhS
ƒ
and the bare or base surface not occupied by the fins
1
R
b
hS
bb
Here, the base surface is S S S and the heat-transfer coefficient, h , is used because
ƒ
b
b
the heat transfer coefficient that is applied to the base surfaces is not necessarily equal to
that applied to the fins.
An alternative expression for R involves and overall surface efficiency, , defined by
sk o
nS ƒ
1 (1 )
o
S
where S is the total surface composed of the base surface and the finned surfaces of n
fins
S S nS ƒ
b
In this case, it is presumed that h h so that
b
1
R
sk
h S
o
In an optimally designed fin structure, can be expected to fall in the range of 0.50 to
0.70. 11 Relatively thick fins in a low-velocity flow of gas are likely to yield fin efficiencies
approaching unity. This same unity value would be appropriate, as well, for an unfinned
surface and, thus, serve to generalize the use of Eq. (29) to all package configurations.
Flow Resistance
In convectively cooled systems, determination of the component temperature requires knowl-
edge of the fluid temperature adjacent to the component. The rise in fluid temperature relative
to the inlet value can be expressed in a flow thermal resistance, as done in Eq. (19). When
the coolant flow path traverses many individual components, care must be taken to use R fl
with the total heat absorbed by the coolant along its path, rather than the heat dissipated by
an individual component. For system-level calculations, aimed at determining the average
component temperature, it is common to base the flow resistance on the average rise in fluid
temperature, that is, one-half the value indicated by Eq. (19).