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, Rw is the resistance of the wire, Tw and Tf are the temperatures of the wire and fluid respectively, Aw is the projected wire surface area, and h is the heat transfer coefficient of the wire.
The wire resistance Rw is also a function of temperature according to,
where a is the thermal coefficient of resistance and RRef is the resistance at the reference temperature TRef.
The heat transfer coefficient h is a function of fluid velocity vf 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 (hot-wire) anemometers are commonly used: constant-temperature and constant-current.
The constant-temperature anemometers are more widely used than constant-current 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 constant-current anemometer. Conversely, if the flow were to suddenly speed up, the wire may be cooled completely resulting in a constant-current unit being unable to register quality data.