As more and more components are placed on a single integrated circuit (chip), the amount of heat that is dissipated continues to increase. However, this increase is limited by the maximum allowable chip operating temperature, which is approximately 75°C. To maximize heat dissipation, it is proposed that a 4 × 4 array of copper pin fins be metallurgically joined to the outer surface of a square chip that is 12.7 mm on a side.
(a) Sketch the equivalent thermal circuit for the pin– chip–board assembly, assuming one-dimensional, steady-state conditions and negligible contact resistance between the pins and the chip. In variable form, label appropriate resistances, temperatures, and heat rates.
(b) For the conditions prescribed in Problem 3.27, what is the maximum rate at which heat can be dissipated in the chip when the pins are in place? That is, what is the value of qc for Tc = 75°C? The pin diameter and length are Dp = 1.5 mm and Lp = 15 mm.
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 10-4 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 what is the chip temperature?
(c) The maximum allowable heat flux, is determined by the constraint that the chip temperature must not exceed 85°C. Determinefor 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 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
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