A 0.15-m-square circuit board is to be cooled in a vertical position, as shown in the sketch. The board is insulated on one side while on the other, 100 closely spaced square chips are mounted, each of which dissipated 0.06 W of heat. The board is exposed to air at 25°C and the maximum allowable chip temperature is 60°C. Investigate the following cooling options
(a) Natural convection
(b) Air cooling with upward flow at a velocity of 0.5 m/s
(c) Air cooling with downward flow at the velocity of 0.5 m/s
GIVEN
? Square vertical circuit board insulated on one side, chips on the other side
? Length of each side (L) = 0.15 m
? Heat dissipation per chip (q) = 0.06 W
? Number of chips (N) = 100
? Ambient air temperature (T?) = 25°C
? Maximum allowable chip temperature (Ts) = 60°C
FIND
Investigate the following cooling options
(a) Natural convection
(b) Forced air cooling with an upward air velocity (U?) = 0.5 m/s
(c) Forced air cooling with a downward air velocity (U?) = 0.5 m/s
ASSUMPTIONS
? Steady state
? Uniform surface temperature
? Radiative heat transfer is negligible
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 28, for dry air at the mean temperature of 42.5°C
The rate of heat generation per unit area is
(a) The Grashof number is
The Nusselt number for natural convection is given by Equation (8.12b)
Since this is lower than the heat generation rate, the actual surface temperature will be higher than the maximum of 60°C.
Therefore, natural convection alone will not keep the chips cool enough.
(b) The Reynolds number for U? = 0.5 m/s is
From Equation (8.45) the relative importance of natural and forced convection is indicated by the following ratio
Since (GrL/ReL2) ? 1, natural and forced convection are of the same order of magnitude. The average Nusselt number can be estimated from Equation (8.57)
In this case, the natural convective flow is in the same direction as the forced convection flow; therefore, the plus sign is appropriate.
The forced convection Nusselt number is given by Equation (4.38)
Therefore, this configuration is adequate to keep the chip surface temperature below 60°C.
(c) In this configuration, the free convective flow opposes the forced convection
Therefore, this configuration will not keep the chips cool enough.
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