Approximately 10 6 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 L_b = 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 qⁿ_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_cm for the fore-going 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_cm for h_o = 1 00 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 chipboard interface for which R_i,c = 10^-5 m² ∙ K/W?

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Coolant Chip 4. Te -Thermal contact resistance, R. Board, k, Air Tph