response and a meaningful time constant. When a = 5 there is no longer a time delay and the 
response becomes a step. 
This interpretation is borne out by the frequency response which is more characteristic 
of a step response than of an exponential response to a step-like initiating function. Unlike 
the frequency response of a constant-current coated wire which approaches the dotted line 
on Figure 11 from below, the frequency response of a constant-temperature coated wire is al- 
ways above this line and approaches the line A (w) = 1 as the coating shrinks to zero. 
These results show that the type of electronic circuit used to correct the response of 
a constant-current hot wire would not be effective in the case of a constant temperature coated 
wire. Although it might be possible to design a circuit for particular values of the wire param- 
eters, it would be difficult to adjust the components of the circuit for different flow conditions. 
SUMMARY AND CONCLUDING REMARKS 
In setting up the problem for the unsteady heat flow in coated hot wires the assumption 
was made that the initiating disturbance as well as changes in the wire parameters were small 
compared with their steady-state values. Second order small quantities were neglected and 
the differential equations were then linear inthe temperature change and other incremental 
quantities. Solutions were obtained for step-like changes in the initiating conditions and 
equivalent time constants were determined for the wire response. From the step responses 
of the wire the frequency responses were found by applying Duhamel’s theorem. 
Although the time constants for the step response of a constant-current bare wire for 
a change in convective cooling and for a change in current input are nearly identical, they 
become different when the wire has a coating. Whereas a single exponential function is a 
good approximation for the step response of a coated wire to a change in current input, it 
becomes a poor approximation for the step response to a change in convective cooling, par- 
ticularly for a large coating thickness. This is seen in Figure 6 where the two responses 
are compared. The time constant for the change in convective cooling M, is larger than that 
for a change in current M;. The wire also has a better frequency response for changes in 
current input than for changes in convective cooling, as shown in Figure 7. 
When the coating is thin and the two time constants are nearly equal the wire response 
may be corrected by a simple differentiating electronic circuit. The compensation becomes 
less effective as the coating thickness increases, particularly if the elements are adjusted 
by correcting the response to a current input. Therefore, another method of setting the ele- 
ments in the compensation circuit should be found. For perfect compensation a more compli- 
cated electronic circuit must be used. 
The response of a constant-temperature hot wire is quite different from that of a 
constant-current wire. The constant-temperature bare wire responds with a step to a step-like 
change in convective cooling and it has a flat frequency response. When the wire has a coat- 
ing there is a delay in the response and the step function is replaced by a more gradual rise, 
36 
