Solve the following problem:
Q: A square silicone chip 7 mm by 7 mm in size and 0.5 mm thick is mounted on a plastic substrate with its front surface cooled by a synthetic liquid flowing over it. Electronic circuits in the back of the chip generate heat at a rate of 5 watts that have to 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 ( qG ) = 5 W
The thermal conductivity of silicon (k) = 150 W/(m K)
ASSUMPTIONS
One dimensional conduction (edge effects are negligible)
The thermal conductivity is constant
The heat lost through the plastic substrate isnegligible
