Determination of thermal properties of materials by Monte Carlo inversion of pulsed needle probe data

Abstract

Needle probe measurements are used in a wide variety of fields for measuring the thermal conductivity of materials. It is most common to extract the thermal conductivity from the temperature rise data using the asymptotic solution to the heat equation. With special reference to, but not limited to Earth materials, this study presents an inversion procedure using pulsed needle probe data to determine both thermal conductivity and thermal diffusivity. The measured temperature response data are interpreted using a finite element forward model and a Markov Chain Monte Carlo inversion algorithm. The thermal properties of the needle probe are part of the forward model and determined by measurements on calibration standards. We examine several factors by synthetic modelling and quantify their effects by Monte Carlo inversions. This include (1) the heat production rate of the probe in order to produce similar temperature increases in materials of different thermal properties, (2) the contact resistance between needle probe and sample, (3) the limitations imposed by sample diameter and the thermal properties of the surrounding medium, and (4) the duration of heating period required to obtain good results. Laboratory test measurements on selected materials (water, glycerol, ceramic standard, clay) demonstrate good agreement with expected values obtained from literature. We demonstrate that the combination of numerical forward modelling and Monte Carlo inversion, applied to the pulsed needle, is a flexible and powerful methodology for accurate laboratory measurements of material thermal properties and with well-defined estimates of uncertainty. With the given equipment and laboratory setup, thermal conductivity is measured to within few percent, while thermal diffusivity generally has a somewhat higher degree of uncertainty, up to about five percent.