ABSTRACT
A closed-form solution ofEq. (9.128) cannot be obtained. To overcome this difficulty, an approximate method can be introduced by linearizing the around the initial temperature Ti:
and
Using (9. the exponential integral in Eq. 128) becomes
by which the integration of Eq. (9 .128) becomes
0 - RT? CPeE/RT,
E ApcA(-ll.H)
(9.131)
The denominator of the right-hand side of Eq. (9.132) is the charackristic time for the ignition delay:
- RT? ( C"eE/RT, )· td-' E ApcA(-ll.H) 133)
In fact, using td defined by Eq. 133), (9. 32) can be rearranged as
or
(9.135)
which predicts that as t --+ td the critical temperature of the reacting system Tcr goes to infinity, which justifies the definition of fJ by Eq. (9.133).
