A square silicone chip 7 mm by 7 mm in size and 0.5 mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 watts that must be transferred through the chip. Estimate the steady state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicone is 150 W/(m K).
GIVEN
A 0.007 m by 0.007 m silicone chip
Thickness of the chip (L) = 0.5 mm = 0.0005 m
Heat generated at the back of the chip (Gq) = 5 W
The thermal conductivity of silicon (k) = 150 W/(m K)
FIND
The steady state temperature difference (?T)
ASSUMPTIONS
One dimensional conduction (edge effects are negligible)
The thermal conductivity is constant
The heat lost through the plastic substrate is negligible
SKETCH
For steady state the rate of heat loss through the chip,must equal the rate of
heat generation
Solving this for the temperature difference
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