Theoretical derivation and analysis of the transfer function for a heat flux sensor based on one-dimensional heat conduction

Abstract

The dynamic response characteristics of sensors in heat flux measurement, such as rising time and frequency band width, determine the capture ability and measurement error of transient thermal load. In order to quantitatively evaluate the dynamic response characteristics of the heat flux sensor, including rise time and frequency band width, based on the differential equation constructed by one-dimensional heat conduction, an analytical expression of the temperature difference between the front and rear surfaces of the sensor sensitive element is derived. Furthermore, the heat flux-temperature transfer function model is established by differential operation and the Laplace transform, and the amplitude-frequency response characteristics of the system are analysed accordingly. The results of theoretical analysis are verified by finite element simulation, and the dynamic analysis characteristics of two types of heat flux sensors are analysed. Finally, the dynamic performance index of a plug calorimeter with an adiabatic rear wall is defined. The modelling method and quantitative conclusion put forward in this study provide a theoretical basis for the dynamic characteristic optimisation and system design of high-precision heat flux sensors.