handbook of modern sensors

11.3 Thermal Transport Sensors 365
(A)
(B)
Fig. 11.5. Transfer function of a thermoanemometer (A) and calibration curves for a selfheating
sensor in a thermoanemometer for three different levels of heat (B).
tube is negligibly small, the law of conservation of energy demands that electric power
W be equal to thermal loss to flowing medium:
W = dQ
dt . (11.14)
On the other hand, the electric power through a heating resistance is in a square
relationship with the voltage e across the heating element:
W = e2
R s
. (11.15)
Equations (11.13)–(11.15) yield a relationship between the voltage across the selfheating
detector and the velocity of flow:
v 2a = K ρ
( e
2
R s
1
T s − T 0
) 1.87
. (11.16)
Figure 11.5B shows an example of a calibrating curve for a flow sensor using a selfheating
thermistor (T s = 75 ◦ C) operating in air whose temperature varies from 20 ◦ C
to 45 ◦ C. The thermistor temperature was maintained constant over an entire range of
T 0 temperatures. 2 It should be emphasized, that T s must always be selected higher
than the highest temperature of the flowing medium.
Formula (11.13) suggests that two methods of measurement are possible. In the
first method, the voltage and resistance of a heating element is maintained constant,
2 This can be accomplished by using a self-balancing resistive bridge. See, for example,
Ref. [4].