1 Wall Shear Stress Measurements Based on the Thermal Wave Method

A thermal wave based method for wall shear stress measurement is described in this paper. A heat convection problem, with a periodic heating boundary condition and a linear velocity flow field, is discussed to introduce the basic mathematical background of the wall shear stress measurement principle. A shear stress sensor design with a heater and two temperature sensors on a silicon dioxide substrate is proposed. The heater with a periodic source generates a temperature oscillation field which interacts with the flow field. The temperature sensors pick up the temperature response that contains information on the velocity gradient at the wall. Based on the above sensor design, a two-dimensional conjugate heat transfer model is developed and solved numerically with a finite difference method. Two designs, with and without a heat sink under the silicon dioxide substrate, are studied. The simulation results show that the temperature signal, especially the phase information, can be a strong function of the velocity gradient at the wall. The effects of the two main design parameters, the operating frequency and the distance between the heater and the temperature sensor, are discussed. Due to linearity and locality of this heat transfer phenomenon, this type of sensor design could be a good candidate for reliable and accurat