## 1 Introduction  
Based on different measurement methods, micro-machined flow sensors can be divided into two groups, namely 'direct' measurement or 'indirect' measurement [1]. For direct measurement of wall shear stress, sensors usually use a floating element that is displaced laterally by the tangential viscous forces in the flow. This displacement implies a variation of an electrical parameter. For example, in [2] the authors developed a capacitive wall shear stress sensor with the floating element displacement implying a capacitive variation, reflected in an electric potential variation. A cantilever-based flow sensor using the piezoresistance effect is simulated in [3]. It has a low bandwidth. A capacitive airflow sensor based on out-of-plane cantilevers is designed and manufactured in [4]. These sensors present the clear advantage of a direct wall shear stress measurement. However, the necessary floating element implies an electro-mechanical coupling which is sensitive to vibrations. Moreover, all these calorimetric sensors suffer from their low bandwidth and low sensitivity. With miniaturization, the mechanical resonance frequency comes close to the vibrations of the measured system structure. In the case of moving structures like vehicles vibrations affect at least the measure but can also affect the sensor integrity. For avoiding these drawbacks, indirect wall shear stress measurements were developed with various methods. For example, micro-fences using a cantilever structure and piezoresistors are presented in [5]. The exploitation of optical resonances such as whispering gallery modes of dielectric microspheres is proposed in [6]. The deflection of micro-pillars is presented in [7]. The physical principle used in thermal sensors consists of taking advantage of the convective heat transfer between an electrically heated resistor and a surrounding cooler fluid [1]. As they do not involve a mechanical moving part, thermal flow sensors are widely adopted when dealing with fluid dynamics including laminar or turbulent flows. Two main kinds of thermal sensors for velocity and wall shear stress have been developed: hot-wire and hot-film sensors. The difference between them_lies in the designed structure: in hot-wire sensors the wire resistor is free from the substrate, fixed by two prongs and placed within the flow; on the other hand, the wire of hot-film sensors is deposited on a substrate and placed on a surface adjacent to the flow. Hot-wire sensors therefore enable heating uniformity and high sensitivity [8; 9; 10], but they are fragile and 3D thermal effects occur at the ends of the wire. They have also a low bandwidth because their cutoff frequency is very low. On the contrary, hot-film sensors are very robust despite their operational constraints. In particular, they suffer from heat losses through the substrate on which the wire is deposited. Various materials have thus been used to increase thermal insulation, such as silicon nitride [11], glass [12], or a flexible polymer [13; 14; 15]. These sensors, which are easy to flush-mount to the wall, are often used for detecting flow separation and for wall shear stress measurement. To improve the performance of hot-film sensors, the heat losses need to be reduced and bulk-machining techniques enable the deposition of the wire on a cavity-backed membrane [16]. In fluid mechanics, the flow rate is an intrinsic parameter of which derive several phenomena and principles. Therefore, measuring this quantity accurately and with high frequency is a challenge for researchers in this field [17; 18; 19]. To measure the flow velocity, a constant temperature anemometer is widely used. Indeed, it detects heat transfer between the hot element and the fluid. Convective heat transfer measurement is done by applying the closed loop and open loop method [20; 21]. Turbulent flows are characterized by disordered movements of the particle fluid, with a fluctuation in speed and temperature.