Solve the following problem:
Q: As more and more components are placed on a single integrated circuit (chip), the amount of heat that is dissipated continues to increase. However, this increase is limited by the maximum allowable chip operating temperature, which is approximately 75°C. To maximize heat dissipation, it is proposed that a 4 X 4 array of copper pin fins be metallurgically joined to the outer surface of a square chip that is 12.7 mm on a side.
(a) Sketch the equivalent thermal circuit for the pin-chip-board assembly, assuming one-dimensional, steady-state conditions and negligible contact resistance between the pins and the chip. In variable form, label appropriate resistances, temperatures, and heat rates.
(b) For the conditions prescribed in Problem 3.27, what is the maximum rate at which heat can be dissipated in the chip when the pins are in place? That is, what is the value of qc for Tc = 75°C? The pin diameter and length are Dp = 1.5 mm and Lp = 15 mm.
