Analytic model of a two-wire thermal sensor for flow and sound measurements

The Microflown is an acoustic sensor that measures particle velocity instead of pressure, as conventional microphones do. This paper presents an analytical model describing the physical processes that govern the behaviour of the sensor and determine its sensitivity. Forced convection by an acoustic wave causes a small, asymmetrical, perturbation to the temperature profile around the two heated wires of the sensor, so that a temperature difference between these wires occurs. This temperature difference, to which the sensitivity is proportional, is calculated with a perturbation theory. Subsequently the frequency-dependent behaviour of the sensitivity can be analysed; it is found that there are two important corner frequencies, the first related to the time constant of heat diffusion, and the second related to the heat capacity of the heaters. A thorough description has already been given for the realization of the Microflown in a channel, i.e. with fixed walls acting as heat sinks near both heaters. Here, an analytic and two-dimensional model is presented that describes the situation of the present sensor without walls above and under it. Contrary to the previous model, this analytic model allows easy understanding of the sensor and is especially useful for engineering purposes due to its relative simplicity. Especially for small wire separations, the developed analysis appears to be in good agreement with experimental results and the model therefore offers the possibility of optimizing the sensor.