0 0 
a,b (2) = «15 ( a fb (b,¢) = b, (0,¢) [18] 
or or 
f,(0,t) 4 & 
(7,0) = 0 
The solutions for the temperature increments as functions of the radius and time are given 
later in Equations [38] and [39]. The wire response to a step-like change in convective cool- 
ing is given in &quation [42]. 
Laplace transforms?'* have been used in obtaining the solutions to the above set of 
equations. The Laplace transform of ¢(r,¢) is defined by the integral 
¢ (7, S) -{ (r,t) eS? dt [19] 
0 
The transformed set of equations is obtained by multiplying each term in Equation [18] by 
eS‘ and integrating over ¢. Then the problem to be solved becomes 
Od pase 
acl (: cy - p? $, (r,8) = 0 
r 
lo a Dama aa Te 
rae a q py (7,8) = 0 
kya (; 2) + Pg, (a,8) -< [20] 
where 
Pp =5 - ,?, q = [21] 
uf) Y 
The solutions to the differential equations are the modified Bessel functions J, and 
Ko: Then 
b, (rs s)=C I, (pr) 
(22] 
bo (7r,s)=A ly (qr) + BK, (q7) 
