A simplified representation for cooling in very

Chapter 4, Problem 4.80

(choose chapter or problem)

A simplified representation for cooling in very large-scaleintegration (VLSI) of microelectronics is shown in thesketch. A silicon chip is mounted in a dielectric substrate,and one surface of the system is convectively cooled,while the remaining surfaces are well insulated from thesurroundings. The problem is rendered two-dimensional by assuming the system to be very long in the directionperpendicular to the paper. Under steady-state operation,electric power dissipation in the chip provides for uni-form volumetric heating at a rate of q.. However, theheating rate is limited by restrictions on the maximumtemperature that the chip is allowed to achieve.For the conditions shown on the sketch, will the maxi-mum temperature in the chip exceed 85C, the maximumallowable operating temperature set by industry stan-dards? A grid spacing of 3 mm is suggested.