A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.04 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 30 W/m·K. All the heat generated in the chips is conducted across the circuit board and is dissipated from the back side of the board to a medium at 40°C, with a heat transfer coefficient of 40 W/m²·K.

(a) Determine the temperatures on the two sides of the circuit board.

(b) Now a 0.2-cm-thick, 12-cmhigh, and 18-cm-long aluminum plate (k = 237 W/m·K) with 864 2-cm-long aluminum pin fins of diameter 0.25 cm is attached to the back side of the circuit board with a 0.02-cmthick epoxy adhesive (k = 1.8 W/m·K). Determine the new temperatures on the two sides of the circuit board.