Unsteady two-dimensional analytical model for a thermal time-of-flight flow sensor

A thermal time-of-flight sensor consists of a resistive element that periodically delivers heat to a flow and two downstream thermocouples that detect the temperature change due to this heat addition. This study presents an analytical solution to the two-dimensional advection diffusion equation in cylindrical coordinates for an axially semi-infinite domain subjected to a time-dependent Neumann boundary condition. The results describe the propagation of heat in the thermal time-of-flight sensor. The finite Hankel transformation and the generalized integral technique are used to solve the governing equation. The analytical temperature profile shows dependence on the Peclet number and on the tube diameter. The derived temperature distribution is compared with measured data from an experimental setup using R134a as the working fluid. The model demonstrates good agreement with the experimental data, with an average relative error of <9%. (C) 2019 Elsevier Ltd. All rights reserved.