A computer graphics chip measures 5cm on a side and is 3-mm thick. The chip consumes 15 W of power, which is dissipated as heat from the top side of the chip. A fan blows air over the surface of the chip to promote convective heat transfer. Unfortunately, the chip fails to operate after a certain time, and the temperature of the chip is suspected to be the culprit. A plot of chip failure rate vs. surface temp. is presented in the figure below. An electrical engineer suggests that an aluminum extended heat-transfer surface could be mounted to the top surface of the chip to promote heat transfer, but does not know how to design it. The electrical engineer asks for your help.

A) If the heat-transfer coefficient in air is 50W/m^2-K, what is the surface temperature of the chip at steady state if the bulk air temp. is maintained at 20'C (293 K)? What is the failure rate of the chip?

B) An aluminum extended surface heat-transfer device is next mounted on the top of the chip. It consists of a parallel array of five rectangular fins 1 cm by 5 cm wide by 0.3 mm thick. The new convective heat-transfer coefficient over the fin surfaces is 20 W/m^2-K. Is this configuration suitable? What is the new failure rate of the chip?