In most cases the last term is negligibly small. 
The frequency response of the wire may be obtained by writing the initiating disturb- 
ance of Equation [42] as $* cos @t’and by making use of Duhamel’s integral. If the tran- 
sient term is neglected the frequency response becomes 
by, ¢)= 6,7 Alo) cos (wt - 8) [108] 
where a G2 
2, A, Oe 7 Sin, cos 6, 
any S) Sp ae [109] 
n=1 
[110] 
2 
co G, yu 
+ A, 7 sin 6, cos 6, 
iS Qa, 
tan 6, = A JOE ae {111} 
The time constant and frequency response of a constant-current coated wire for a 
change in current input are given by similar expressions in which 4, Gu? /Qe,2 is replaced 
by DG, u?/Qe,? (1+ F). The time constant M, is obtained from the expression 
DC. fe DG een am me 
yByM,=1+ log ed log Lo. So ttl Se eo [112] 
Qe (lua) = DG ice 
Calculations of the time constants and frequency responses for the two initiating con- 
ditions will show how well the response of a constant-current hot wire to a change in current 
approximates the response to a change in convective cooling. In order to make the calcula- 
tions it is necessary to prepare tables of the cylinder functions Cp, (x,y), Co, (4,4), Cy (@¥); 
and C,,(z,y) where y = az/b. These functions are tabulated in Tables 1, 2, and 3 for three 
coating thicknesses: a/b = 1.5, 2, and 3. The functions N, (8, 2), N, (8,7), 4,,D,,M,, and 
M,as functions of P/x, and B, 6 are presented in Tables 4 through 7. For most of these 
calculations the wire parameters chosen were p, Go, DAO ots = 100 x,, and u2b2 = 0.01 
and 0.002. One set of calculations was made for x, = 10 Ko: 
In order to make the set of calculations complete, Table 8 contains similar calculations 
22 
