[7] 
T,*(b) = T,*(b) = T*(b) 
The solutions to the differential equations which satisfy the boundary and compatibility 
equations are 
* es ilies * 1 Jy (ur) 
T*(r)- 1, +4 = E (8) - Ty 3 en 
[8] 
peers) eels (0) Bye bye Rh ee hoe <= 
2 Ky 0 a B 
where 
Plp*(a)—T1=@ [rec =e 1] [9] 
and J, (u7) is the zeroth order Bessel function of the first kind. The constant Q is defined 
by the relation 
k, #5 J, (ub) = Q Jy (ud) [10] 
If at some time ¢ = 0, an arbitrary time-varying disturbance upsets one or more of the 
parameters U, T., or /, the steady-state conditions will be upset and the temperature will be- 
come a function of the time. The differential equations, boundary and compatibility conditions 
for the unsteady heat flow become 
OT OT 
Le peal: +p? T, (r,t) - 7, + a a eet 
ror or @ n Ot 
Ky @ I + P(t) IT, (a,¢) - T, (¢)] = 0 
i f11] 
OT, 0 T. 
kK, 6 (52) =K,6 ( 1) 9 Wao) 10 (6,2) 
0 ) 
b b 
, 
T,(0,t) 4 = 
T (r,0) = T*(r) 
