Conduction and Inertia Correction for Transient Thermocouple Measurements. Part I: Analytical and Numerical Modelling

Abstract

Two-wire thermocouples are often used for temperature measurements. Under transient conditions, measurement errors can occur due to capacitive inertia and heat conduction along the stem of the thermocouples. The present study presents a correction of these thermocouple measurement errors caused by transient inertia and conductive effects using a simplified analytical approach and its numerical solution. Based on an energy balance the mathematical modelling is derived and analytically solved for specific boundary conditions. Further, numerical solutions have been implemented with different model complexities. Thereby the models show the significance of the necessary correction as well as the good agreement with theoretical considerations. A corresponding experimental validation is given in Part II.