Page 398 - Mechanical Engineers' Handbook (Volume 4)

2 Heat-Transfer Correlations for Electronic Equipment Cooling 387

Table 1 Natural Convection Heat-Transfer Correlations for an Array of Heated Vertical Channels
Condition Fully Developed Limit Composite Correlation
2.873
Symmetric isothermal plates El Nu 576 ( 1/2)
Nu
0 0 2
24 El El
2.873
Asymmetric isothermal plates El Nu 144 ( 1/2)
Nu
0 0 2
12 El El
Symmetric isoflux plates El
Nu
0
48
Asymmetric isoflux plates El
Nu 24
0
Symmetric isoflux plates based on El
Nu 12 1.88 ( 1/2)
0
mid-height temperature Nu 12 0 El
(El
) 2/5
Asymmetric isoflux plates based El
Nu 6 1.88 ( 1/2)
on mid-height temperature Nu 6 0 El
(El
) 2/5
0
C g q b 5
2
El
p (36)
2
kL
ƒ
where q is the heat flux leaving the channel wall(s).
Asymmetry can also occur if adjacent channel walls are isothermal but at different
temperatures or isoflux but dissipating different heat fluxes. Aung 21 defined an asymmetry
parameter for the case where the walls are isothermal but at different wall temperatures T w1
and T w2 as
T T
r w1 0 (37)
T
T w2 T 0
in which T is the air temperature at the channel inlet. Then the heat transfer could be
0
calculated using the parameters listed in Table 2.
In the case of symmetric isoflux plates, if the heat flux on the adjacent walls is not
identical, the equations in Table 1 can be used with an average value of the heat flux on the
two walls. The composite relations listed in Table 1 can be used to optimize the spacing
between PCBs in a PCB card array. For isothermal arrays, the optimum spacing maximizes
the total heat transfer from a given base area or the volume assigned to an array of PCBs.

Table 2 Nusselt Number for Symmetric Isothermal Walls at
Different Temperatures 21

Nu /El
0
r T
1.0 1/24
0.5 17/405
0.1 79/1815
0.0 2/45