Circuit boards are treated by heating a stack of them under high pressure as illustrated in Problem 5.45. The platens at the top and bottom of the stack are maintained at a uniform temperature by a circulating fluid. The purpose of the pressing-heating operation is to cure the epoxy, which bonds the fiberglass sheets, and impart stiffness to the boards. The cure condition is achieved when the epoxy has been maintained at or above 170°C for at least 5 min. The effective thermo- physical properties of the stack or book (boards and metal pressing plates) are k = 0.613 W/m ∙ K and pc_p = 2.73 X 10⁶ J/m³ ∙ K.

(a) If the book is initially at 15°C and, following application of pressure, the platens are suddenly brought to a uniform temperature of 190°C, calculate the elapsed time 1f! required for the mid plane of the book to reach the cure temperature of 170°C.

(b) If, at this instant of time, t = t_e, the platen temperature were reduced suddenly to 15°C, how much energy would have to be removed from the book by the coolant circulating in the platen, in order to return the stack to its initial uniform temperature?