Numerical and analytic study on the time-of-flight thermal flow sensor

In this study, a numerical study on the time shift of time-of-flight (TOF) thermal flow sensor is performed based on Finite Volume Method (FVM). The TOF is modeled as parallel cylinders, and the governing equations for transient fluid flow and heat transfer, as well as boundary conditions, are established. In order to provide a physical understanding, a simple analytic model is also developed, and an excellent agreement is shown between numerical and analytic results. Based on the validated simulation results, the effects of wire diameter, flow velocity, and fluid Prandtl number on the time shift is investigated. The results show that the convection time shift becomes negligible as either the wire diameter or the flow velocity decreases. The effect of the wire diameter on the time shift becomes insignificant as the wire diameter decreases beyond several tens of micrometers. The time shift is shown to increase as the Prandtl number of fluid increases. The suggested computational scheme, together with the simple analytic model, can be effectively utilized for calibrating and designing the TOF sensors.