which is the average resistivity of the unheated wire. If use is made of the relations given 
in Equations [8] and [9] and if the approximation is made that the average temperature of the 
wire is the same as its surface temperature and Q = 4% Ky 2 b?, then a,, is the following 
function of P and Q. 
Q E A Le leet) 
kK b 
— [122] 
IPa=@ (is Eh log 2) 
Ky b 
Values of a,, are included in Tables 4 through 8. 
Although the overheating ratio of a coated wire may be reasonably high, the tempera- 
ture at the outer surface of the coating may not be very much above the ambient temperature 
of the flow. In this case the wire will be more sensitive to temperature fluctuations than to 
velocity fluctuations. If an effective overheating ratio a, is defined in terms of the surface 
temperature of the coating rather than the wire, it may be shown that 
Ee EO es ee ea [123] 
Pomp. fe LE a 
1 Uy ee OE 
2 
Although a, cannot be measured directly it is a more significant parameter than a, for a 
coated wire. 
CONSTANT-TEMPERATURE COATED WIRE 
In a similar manner the step and frequency responses of ‘a constant-temperature coated 
wire may be found. From Equation [90] the wire response to a step-like change in convective 
cooling may be written as 
oo we 2 
BOD TS he yBn "| [124] 
n=1 
where yw* contains the initiating function and other constants. The equivalent time constant 
M, is defined by the equation 
= B, -y(82-B,2)M 
FORE SR osetia BS ni a eM [125] 
The corresponding frequency response is 
u(t) = p* A(@) cos iwt — $) [126] 
30 
