Example: First consider a hot-wire working in constant current mode (Figure 2.25). The wire whose resistance equals is a part of a Wheatstone bridge with a control resistance and a battery voltage . The Joule heating of the wire is and the energy lost to the flow is where is the heat transfer coefficient, the surface area of the wire and its temperature. is the local fluid temperature. The difference between the two energy terms will change the wire temperature at a rate and subsequently the wire resistance. We assume the wire resistance to change as

and so