Iba) _ (9% 
iDEN Papa), bh Nota g) Pate) mabe!) 
b,(0,t) # © 
(7,0) = 0 
6 
{ fp, 7,t) rdr = 0 
0 
In this set of equations A/(¢) is contained in y (¢) which is defined as 
2A1(¢) 7 
POs = (710) - ip =z) 
[69] 
[70] 
{71] 
The final solutions for the temperature increments as functions of r and ¢ and for y(¢) are 
given in Equations [88], [89], and [90]. 
Again the solutions of the above set of equations have been obtained by the use of 
Laplace transforms. The transformed problem becomes 
LEG 
r or 
fo) 
281) 92 ,(, hb, (r,s) + p u(s) = Ty Spe 
Jo (ud) 
1a¢ ef) bolts 8) = 0 
Oe A ESE ES 
m0 (2) +P b,(a,8) = 
ag, ad eae hereto 
m0 (St) = nr(S), by (0,8) = 6, (3,8) 
$6, (0,8) # = 
b 
| Gar, s)inar = 0 
where D 
woe Ty 
The solutions to this set of equations for the two regions are 
16 
[72] 
