A New Thermophysical Property Estimation Approach Based on Calibration Equations and Rescaling Principle

Abstract

A novel thermophysical property estimation method is proposed, which incorporates both calibration and rescaling principles for estimating both unknown thermal diffusivity and thermal conductivity of materials. In this process, temperature and heat flux calibration equations are developed, which account for temperature-dependent thermophysical property combinations. This approach utilizes a single in-depth temperature measurement and a known set of boundary conditions. To acquire both thermal diffusivity and thermal conductivity, two distinct stages are proposed for extracting these properties. The first stage uses a temperature calibration equation for estimating the unknown thermal diffusivity. This process determines the thermal diffusivity by minimizing the residual of the temperature calibration equation with respect to the thermal diffusivity. The second stage uses the estimated thermal diffusivity and a heat flux calibration equation for estimating the unknown thermal conductivity. This stage produces the desired thermal conductivity by minimizing the residual of the heat flux calibration equation with respect to the thermal conductivity. Results verify that the proposed estimation process works well even in the presence of significant measurement noise for the chosen two representative materials. The relative error between the exact properties and the estimated values is shown to be small. For both test materials (stainless steel 304 and a representative carbon composite), the maximum relative prediction error is approximately 2–3%. Finally, as an added benefit, this method does not require explicit knowledge of the slab thickness or sensor position which further reduces systematic errors.