2. An electronic device with a diameter of D = 30 mm is soldered on a large metal substrate, as shown in Fig. (A). The substrate has a thermal conductivity of k = 180 W/m.K and is kept at a constant temperature of T2 = 25.C. 50 pin fins Df = 1.5 mm L = 15 mm Copper base t = 5 mm thick D = 30 mm Device T1 T 2 T 2 Metal substrate Metal substrate (A) (B) a) (10 points) Assuming the device has a uniform temperature 71 and it dissipates 100 W into the substrate by conduction, calculate the device temperature 71 at steady state. (Hint: use the conduction shape factor - see the table on the next page) b) (5 points) To increase the power dissipation, a finned heat sink with a circular base and 50 pin fins is attached to the device, as depicted in Fig. (B). The fins and the base are made of copper (k = 400 W/m.K). The base has a diameter of 30 mm and a thickness of 5 mm. Each fin measures 1.5 mm in diameter and 15 mm in length. Air blows past the fins at 25 C and h = 1000 W/m-K. Calculate the efficiency for a single fin. c) (10 points) Sketch the thermal resistance network for heat removal from the device with the finned heat sink and mark each thermal resistance. d) (10 points) For conditions given in part (b), calculate the total resistance of the fin array. e) (15 points) In the new configuration, if the device is maintained at the same temperature T, as what you find in part (a), what is the power dissipation from the device