——_ Ss me ody ie) 2? Ij @e) 
PaO) ars F Jy (ud) H 15 (p8) 
[73] 
S Ko 
aioe 4 aeING) Poy Yo) = 1 Dae enlogere) 
and 
S 
= 74 
oP) s A (s) [74] 
In these expressions 
bT, (pb) 
Fy eset a a Nae (75] 
I, (p 6) 
A(s)=qa [Po (qb, qa) mi a qoD,, (98,90) ] 
[76] 
P 
+ — [Poo a> 9a) ae oD, (gb,90)| 
Ko oO 
and u2 p? 
GO ff 
=o = a [77] 
po +p 
The temperature change as a function of the time is given by the inverse of the Laplace 
transform which is defined in Equation [27]. As in the former problem the inverse is equal to 
the sum of the residues at the poles of the integrand. Again the integrand has simple poles 
at the origin and at an infinite number of points on the negative real axis. 
When A} =0; p=ip,q=0,and H=Q. Then it may be shown that 
ee al (Se es [78] 
% Q 2Q 2k, 
P 
A) =~ (1+ — tog 2+ = [79] 
Ko % 
1 w? Io(ur) — p? Ip (pr) 
p? + 2 E ROD) a a al 
B o oP [80] 
Clee (ee : Tour)! eee ier 
S95 S| = Il) a Ns 
Q 2Q Jo (ub) 25, (ud) 
