Square silicon chip (10 mm square, 2.0 mm thick), dissipating 1.5 Watts at steady state. The 2.5 mm thick glass/epoxy boards (have thermal conductivity of 5 W/m. K and contact resistance of 6.5x104 m-K/W) on which the chip is mounted is situated horizontally in a card cage with a nominal board spacing of 20 mm. The boards are cooled by air at 25°C flowing parallel to the boards. Chips are located on one side only of the boards. Design a "heat sink" (finned attachment) to maintain the chip temperature at a maximum 65°C, assuming the convective heat transfer coefficient is uniform 30 W/m².K on all surfaces subjected to the convective boundary condition. Use reasonable assumptions as needed and document them. Your goal is to meet the requirements at minimum cost. You are constrained to choose one of the following materials and the fin profile should be rectangular. Material A: p=2700 kg/m'; Cp=0.95 kJ/kg. K; k = 230 W/m. K; a = 97x10 m/s material cost - $6/kg Manufacturing cost = $[0.15 +0.0016222] (straight or annular fins) Material B: p=8800 kg/m: Cp -0.387 kJ/kg. K; k = 400 W/m. K: a = 120x10 m/s Manufacturing cost = $[0.18 +0.0014a1.) (straight or annular fins) The manufacturing cost equations were obtained from a curve fit of the company's empirical data and "a" is the aspect ratio of the fin, defined as Lt (See Figs. 3.19 and 3.20 in the text). For structural reasons, t2 0.5 mm.