Chapter 5, Problem 5.28P

Consider the conditions of Problem 5.27. In addition to treating heat transfer by convection directly from the chip to the coolant, a more realistic analysis would account for indirect transfer from the chip to the substrate and then from the substrate to the coolant. The total thermal resistance associated with this indirect route includes contributions due to the chip-substrate interface (a contact resistance), multidimensional conduction in the substrate, and convection from the surface of the substrate to the coolant. If this total thermal resistance is $R_t=200\text{K/W,}$ what is the steady-state chip temperature $T_f?$ Following activation of the chip, how long does it take to come within $1°\text{C}$ of this temperature?