Question

Reserve Problem 5.003 Circuit boards are treated by heating a stack of them under high pressure, as illustrated in the figure below. 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 thermophysical properties of the stack or book (boards and metal pressing plates) are k = 0.613 W/m-K and pcp = 2.73 X 10° J/mº.K. Assume L = 29 mm. Applied force -Platens with circulating fluid Metal pressing plate Circuit board . Platen (a) If the book is initially at 17°C and, following application of pressure, the platens are suddenly brought to a uniform temperature of 190°C, calculate the elapsed time required for the midplane of the book to reach the cure temperature of 170°C. The elapsed time te is min. (b) If, at this instant of time, t = te, the platen temperature were reduced suddenly to 17°C, how much energy per unit area of platen 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? J/m2 The energy is Physical Properties Mathematical Functions

Answer 1

- Ts=190°c 0 0 Oot =-=t O O O 22 tk Stack, T(1,0)=1; - LO O = 11c, L= 29 mm proberties of the stack!. K = 0.613 W/m-k of Pcp = 2.73 X106 J/m3.k Q = klece = 2.245 xjö? m2/s Foor sudden application Surface temperature - hyo hence, Bison A* Do .: - = Tlo,+) - Ts 170-19 - 17 - 190 = 0.1156 Ti-Ts From table! Foor Bi > 0, the correa bonding constanti!- x = 1-5707 49, = 1.2733 .: From the relation : 0.* , exp(-6? Fol con, Fo= In (05/ca)

Fo= I (1.5707) 2 ln (o. 1156 | 1.2733) Fo - 0.9725 also, Fo= Lt/ [² t = Fol% = 0.9725 Ⓡ (29x173)? 2 2.24 5 X107 = 3643 S it = * = 60-718 min Amir 60-718 min For the interval o te - 0.4 = Pc (2c) (Ti - Too) = 2.73x 106 x (2x29x163) (17-190) 2.* - - 2.739 x 107 J/m2 .: Q* - L - Sin tu o* t- Sin (1-570751ęd) 1-5707 4. - * 0-1156 70-8264 = 0.9264 Q* = 0.9264 x 0* = 0.9264 (2.739x107) Ta* s 2.537x10' 3/m2 A. m2) Amy