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

Physics & Space Science

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