Approximately 106 discrete electrical components can be

Chapter , Problem 3.27

(choose chapter or problem)

Approximately 106 discrete electrical components can be placed on a single integrated circuit (chip), with electrical heat dissipation as high as 30,000 W/m2 . The chip, which is very thin, is exposed to a dielectric liquid at its outer surface, with ho 1000 W/m2 K and T,o 20 C, and is joined to a circuit board at its inner surface. The thermal contact resistance between the chip and the board is 104 m2 K/W, and the board thickness and thermal conductivity are Lb 5 mm and kb 1 W/m K, respectively. The other surface of the board is exposed to ambient air for which hi 40 W/m2 K and T,i 20 C. (a) Sketch the equivalent thermal circuit corresponding to steady-state conditions. In variable form, label appropriate resistances, temperatures, and heat fluxes. (b) Under steady-state conditions for which the chip heat dissipation is q c 30,000 W/m2 , what is the chip temperature? (c) The maximum allowable heat flux, q c,m, is determined by the constraint that the chip temperature must not exceed 85 C. Determine q c,m for the foregoing conditions. If air is used in lieu of the dielectric liquid, the convection coefficient is reduced by approximately an order of magnitude. What is the value of q c,m for ho 100 W/m2 K? With air cooling, can significant improvements be realized by using an aluminum oxide circuit board and/or by using a conductive paste at the chip/board interface for which Rt, c 105 m2 K/W?