where (C, 7p (x, y) are the cylinder functions which Jaeger‘ defines as 
gitk 
Ci, (@, y) = [dy (a) ¥ (y) - Yo (w) I, (y) | [35] 
dai ay* 
Some of the properties of these functions are listed in the Appendix. The determinant A (A _) 
may be written in terms of N, (8, a) and N, (8,@) as 
A(,)=-B,2N,(6,2)+— (Ba) =0 [36] 
29) 
Equations [31], [82], and [36] are sufficient to determine the three parameters a,>B,> and 
G,. Finally 
. dA 1 pe BN n2Maea) 
— = = ————_ —> a a 
dr}, MILO) Wee 8 0 Bn 
nh 
G 2 Pan Bs ne AL 
= no Bes PON\\ os Sak Sato a n a,” p2 
eae Ky an Kn 
If substitutions are made in Equation [28] the temperature increments in the two 
J (ur) = J (at) =nla? — pt 
(r,t) = b*(b 0 a OSE 1 
$1 (nt) orn] Bee Dees. Tey [38] 
n=1 
[37] 
regions are 
r Q r oo -yB,t 
by ,t)=¢ mp - oes DAM (6,7) e | [39] 
where the steady-state temperature increment at r = 6, }*(6) is written for 
S PIN = Us @)) Sa PAV 
HO) = —— = [40] 
KA) p_@g ie: Po (1+ 2 toe) 
The coefficients A, are given by 
P 
2 (8, |B - = 1 +E toe $)| 
I SS SS SSS SSS SSS SSS SSS [4 
n 2 PS, 2 
1 OPN MOG. pao oie a pO alt EE (Se, 252 
2 n 0 n n n 
Ky KS Ko a2 Kee 
The wire response is obtained from the average temperature change in the wire. Using 
Equation [17] 
10 
