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

Abstract

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.

Modeling of Multifunctional Thermoresistive Transduser Used Heat Exchange Technology

“…The sensor operates on a heat transfer theory for gas flowing over a micromachined overheated bridge or membrane, producing a change in the temperature profile of the membrane [15][16][17][18]. Dual sensing elements positioned at both sides of a central heating element allow for bidirectional flow measurement.…”

An integrated 3D sound intensity sensor using four-wire particle velocity sensors: II. Modelling

“…At first, the static temperature distribution in the device is calculated, when no air flow is present. An acoustic wave gives only a small perturbation to this temperature profile and the output signal of the sensor is linearly proportional to the local temperature gradient at the position of the sensor wires [12,13,26]. Therefore, the…”

“…In general, the heating power is not distributed uniformly over the wire because the local resistance is temperature dependent; however, the variation along the wire is only a few per cent and can therefore be neglected. The coordinate dependence of the heat sources is described by Dirac delta functions since the heater thickness h and width w (400 nm and 5 μm, respectively) are small with respect to the other dimensions of the device and can thus be neglected in calculating the temperature distribution [12,13].…”

“…Similar expressions are found for the other wires at the places (±ξ 0 , ±ζ 0 ). The ratio between ∂ ξ T and ∂ ζ T at the wire location determines α and with this value one obtains the angular shift (equation (13)) of the sensitivity. The result is shown in figure 7, where is shown for varying gap distance l x .…”

“…Changing the wire spacing therefore influences the temperature difference between the wires. To take this effect into account, one should use the full expression for the temperature difference between two wires, T, as a function of wire spacing a, frequency f and velocity v. The explicit function T(f, a, v) was deduced before [12,13,26]; here in this paper we have only made use of the fact that it is linear in v.…”