If the wire is used in a constant-temperature circuit which keeps the average temperature 
constant, there is the additional condition 
b 
i p, (r,t) rdr=0 {16] 
0 
This set of equations is very general and contains all the incremental changes which 
may occur in the operation of a hot wire. The response of a constant-current wire is given by 
@,, (¢), the average temperature change in the wire 
2 b 
be al Br, (Gee) neh 17] 
0 
When the wire responds to a change in convective cooling, A/(¢)=0 and AP and AT. are 
the initiating disturbances. When the wire responds to a change in current input, AP = AT, =0 
and A/ becomes the initiating disturbance. The response of aconstant-temperature hot wire 
to a change in convective cooling is given by the current change A/(¢) and the initiating dis- 
turbances are AP and AT.. For this case Equation [16] applies, as the average temperature 
in the wire does not change. 
In the following sections of this report the problem set up in Equation [15] will be 
solved for three cases in which the initiating disturbances are step functions: (1) a constant- 
current coated wire in which the rate of convective cooling changes, (2) a constant-current 
coated wire in which the current input changes, and (3) a constant-temperature wire in which 
the rate of convective cooling changes. An equivalent time constant and the frequency re- 
sponse will be determined for each case. 
RESPONSE OF A CONSTANT-CURRENT COATED HOT WIRE TO A 
STEP-LIKE CHANGE IN CONVECTIVE COOLING 
When a constant-current coated hot wire is subjected to a step-like change in the rate 
of convective cooling, the wire response is given by the average temperature change in the 
wire. The problem to be solved to obtain the temperature increments ¢, (7,¢) and @, (7,¢) in 
the wire and coating is given by Equation [15] by setting A/ = 0. 
[18] 
