b2 454 
Sear Va + i 5 
a3 2, 128 nn x 
w(t)=w* {14+ {131] 
If P/«, is small compared with unity, the values of H,,/x, are only slightly less than P/x, 
and the roots €, 6 of Equation [97] are very nearly the zeroes of J, (€, 5). Therefore 
Ky ge b2/2 H,, even for n = 1, is very large compared with the other terms of the denominator 
and Equation [131] is given approximately as 
OP — ome, -H7)t 
p(t)=w*l1 ne aa Y CL SD ERE [132] 
Ky = Be b2 
Initially 
0) =-S ay fi+ 
WO ex ( + ne) [133] 
Therefore a constant-temperature bare hot wire responds to a step-like change in convective 
cooling with a step-like response which has a small overshoot of magnitude P/4«,, which 
decays rapidly. The time constant for the decay of the overshoot is obtained from the 
equation 
wo —n(€7—"2)M 
S eat Ga (134] 
2 72 
n=1 or b 
and Fi 
1M ~ 0.0834 
The response of a constant-temperature hot wire is proportional to the heat flux at the 
wire surface 7 = 5. If the wire has no coating there is no time lag in the response (except for 
the small overshoot) and the frequency response is flat. If the wire has a coating, a step- 
like change in the heat flux at the outer surface is no longer a step function when the flux 
reaches the inner surface and there is an attenuation and a phase distortion inthe wire re- 
sponse. This becomes apparent if the step and frequency responses of a coated wire are 
examined for particular values of the wire parameters. Such responses are shown in Figures 
10 and 11. As the infinite sums converge rather slowly for small values of ¢ and for large 
values of w, there is an uncertainty of a few percent inthe step response for small values of 
t and in the frequency response for aM, >1. As the coating becomes thinner and P/x, 
becomes larger the step response becomes steeper, less like an exponential function and 
more like a stepfunction. As long as there is a thin coating there will be some delay in the 
34 
