A disk-shaped electronic device of thickness Ld, diameter D, and thermal conductivity kd dissipates electrical power at a steady rate Pe along one of its surfaces. The device is bonded to a cooled base at Tv using a thermal pad of thickness Lp and thermal conductivity kp. A long fin of diameter D and thermal conductivity k, is bonded to the heat-generating surface of the device using an identical thermal pad. The fin is cooled by an air stream, which is at a temperature Tx and provides a convection coefficient h.

(a) Construct a thermal circuit of the system.

(b) Derive an expression for the temperature Td of the heat-generating surface of the device in terms of the circuit thermal resistances, To and T∞. Express the thermal resistances in terms of appropriate parameters.

(c) Calculate Td for the prescribed conditions.

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T-15°C Air h- 250 Wim-K Device: L= 3 mm k= 25 W/m-K Heat generating surface, P,- 15 W. T, Pads: 4=1.5 mm - 50 W/m-K T,- 20°C Device, k Long fin, Fin: D.k Thermal pads, k D=6 mem ky 230 W/m-K