The present study was undertaken to determine how the presence of a coating affects 
the wire response and to investigate methods for correcting the response by suitable electronic 
circuits. The responses of a constant-current coated wire are obtained for achange in convec- 
tive cooling and for a change in current input and the results are compared. The response of 
a constant-temperature coated wire is obtained for a change in convective cooling. The corre- 
sponding responses of bare wires are found by letting the coating thickness shrink to zero. 
In all cases the initiating disturbance is a step function and time constants for the step re- 
sponses are obtained. Finally the frequency responses for the three cases are derived from 
the step responses by applying Duhamel’s theorem. 
GENERAL CONSIDERATIONS OF UNSTEADY HEAT FLOW 
IN A COATED HOT WIRE 
In making this investigation, it is necessary to analyze the unsteady heat flow through 
a cylindrical coating and a solid cylinder. The distribution of temperature in the wire and 
coating will depend upon the relative heat capacities of the two media and upon the rate at 
which heat is generated in the wire and dissipated into the flow medium. If the heat conductiv- 
ity of the coating is much smaller than that of the wire there will be an appreciable temperature 
gradient in the coating but only a small temperature gradient in the wire. Furthermore, since 
the rate of cooling depends upon the flow velocity in the immediate vicinity of its surface, an 
angular variation in temperature may also be expected. In the present analysis, however, this 
angular temperature variation has been neglected as well as temperature gradients along the 
wire length. Thus the wire and its coating are assumed to possess cylindrical symmetry and 
the temperature at any point is a function of the radius only. 
Figure 1 shows a sketch of the wire 
and its coating, where a and 6 are, respectively, 
the outer and inner radii of the coating and 6 
is also the wire radius. Let the wire have an 
average resistivity &,, an average temperature 
T,,, and a heating current /. If the wire is 
placed in a uniform flow of velocity U and con- 
stant ambient temperature 7,, a certain steady- 
state temperature distribution will be set up 
within the wire and its coating which will be 
designated as T*(r). It will be assumed that 
the average resistivity in the wire is a linear 
Flow Medium 
function of the wire temperature 
Figure 1 - Sketch of the Wire and Its Coating RE, =R l+e(T, -T,)] J 
