Consider a wire that's immersed in a fluid flow. Assume that the wire, heated by an electrical current input, is in thermal equilibrium with its environment. The electrical power input is equal to the power lost to convective heat transfer,
where I is the input current, R_{w} is the resistance of the wire, T_{w} and T_{f} are the temperatures of the wire and fluid respectively, A_{w} is the projected wire surface area, and h is the heat transfer coefficient of the wire.
The wire resistance R_{w} is also a function of temperature according to,
where a is the thermal coefficient of resistance and R_{Ref} is the resistance at the reference temperature T_{Ref}.
The heat transfer coefficient h is a function of fluid velocity v_{f} according to King's law,
where a, b, and c are coefficients obtained from calibration (c ~ 0.5).
Combining the above three equations allows us to eliminate the heat transfer coefficient h,
Continuing, we can solve for the fluid velocity,
Two types of thermal (hotwire) anemometers are commonly used: constanttemperature and constantcurrent.
The constanttemperature anemometers are more widely used than constantcurrent anemometers due to their reduced sensitivity to flow variations. Noting that the wire must be heated up high enough (above the fluid temperature) to be effective, if the flow were to suddenly slow down, the wire might burn out in a constantcurrent anemometer. Conversely, if the flow were to suddenly speed up, the wire may be cooled completely resulting in a constantcurrent unit being unable to register quality data.
