Solved: Circuit boards are treated by heating a stack of

Chapter 5, Problem 5.136

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Circuit boards are treated by heating a stack of themunder high pressure as illustrated in 5.45 anddescribed further in 5.46. A finite-differencemethod of solution is sought with two additional con-siderations. First, the book is to be treated as havingdistributed, rather than lumped, characteristics, byusing a grid spacing of ?x?2.36 mm with nodes atthe center of the individual circuit board or plate. Sec-ond, rather than bringing the platens to 190C in onesudden change, the heating schedule Tp(t) shown inthe sketch is to be used to minimize excessive thermalstresses induced by rapidly changing thermal gradientsin the vicinity of the platens.(a) Using a time increment of ?t?60 s and theimplicit method, find the temperature history ofthe midplane of the book and determine whethercuring will occur (170C for 5 min).(b) Following the reduction of the platen temperaturesto 15C (t?50 min), how long will it take for themidplane of the book to reach 37C, a safe temper-ature at which the operator can begin unloadingthe press?(c) Validate your program code by using the heatingschedule of a sudden change of platen tempera-ture from 15 to 190C and compare results withthose from an appropriate analytical solution(see 5.46).