A computer IC chip consumes 10 W of power, which is dissipated as heat. The chip measures 4 cm by 4 cm on a side and is 0.5-cm thick. Currently, the IC chip is packaged into an electronic device as shown. The IC chip is mounted within a thermally insulating ceramic material, which may be assumed to act as a perfect thermal insulator. The top surface of the IC chip is exposed to air flowing over the chip to provide a convective heat transfer coefficient of 100 W/m²· K. The ambient air temperature (T_ˆž) is maintained at 30°C. The chip is operated for a sufficient time that steady-state operation can be assumed. Within the process temperature range of interest, the thermal conductivity of the IC chip material is 1 W/m · K.

a. What is the surface temperature, T₁, of the IC chip exposed to the air?
b. What is the temperature, T₂, of the IC chip package at the base of the IC chip (x = L₁)?
c. What is the failure rate of the chip, based on the average temperature of the chip?
d. What can be done to bring the chip failure rate down to 4%?

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air flow h = 100 W/m2-K T = 30°C x = 0, T = T, 10 W IC Chip, kıc = 1.0 W/m-K x = L, = 0.5 cm, T=T2 insulated boundary 4.0 cm IC chip imbedded in insulated boundary. 80 70 60 50 40 30 20 10 50 150 100 Average chip temperature (°C) Chip failure rate (%)