Page 389 - Mechanical Engineers' Handbook (Volume 4)

378 Cooling Electronic Equipment

Flow Resistance
The transfer of heat to a flowing gas or liquid that is not undergoing a phase change results
in an increase in the coolant temperature from an inlet temperature of T to an outlet tem-
in
perature of T , according to
out
q ˙mc (T out T ) (W) (18)
p
in
Based on this relation, it is possible to define an effective flow resistance, R ,as
fl
1
R (K/W) (19)
fl
mc p
˙
where m is in kg/s.
˙
1.4 Radiative Heat Transfer
Unlike conduction and convection, radiative heat transfer between two surfaces or between
a surface and its surroundings is not linearly dependent on the temperature difference and
is expressed instead as
4
4
q SF(T T ) (W) (20)
1 2
where F includes the effects of surface properties and geometry and is the Stefan–Boltzman
4
2
constant, 5.67 10 8 W/m K . For modest temperature differences, this equation can
be linearized to the form
q hS(T T ) (W) (21)
r
1
2
where h is the effective ‘‘radiation’’ heat-transfer coefficient
r
2
2
2
h F(T T )(T T ) (W/m K) (22a)
1
r
2
1
2
and, for small
T T T , h is approximately equal to
1 2 r
h 4 F(TT ) 3/2 (W/m K) (22b)
2
1
2
r
It is of interest to note that for temperature differences of the order of 10 K, the radiative
heat-transfer coefficient, h , for an ideal (or ‘‘black’’) surface in an absorbing environment
r
is approximately equal to the heat-transfer coefficient in natural convection of air.
Noting the form of Eq. (21), the radiation thermal resistance, analogous to the convective
resistance, is seen to equal
1
R (K/W) (23)
r
hS
r
1.5 Chip Module Thermal Resistances
Thermal Resistance Network
The expression of the governing heat-transfer relations in the form of thermal resistances
greatly simplifies the first-order thermal analysis of electronic systems. Following the estab-
lished rules for resistance networks, thermal resistances that occur sequentially along a ther-
mal path can be simply summed to establish the overall thermal resistance for that path. In
similar fashion, the reciprocal of the effective overall resistance of several parallel heat-
transfer paths can be found by summing the reciprocals of the individual resistances. In
refining the thermal design of an electronic system, prime attention should be devoted to