Simultaneous Estimation of Thermal Conductivity and Volumetric Heat Capacity of a Solid Plate Using the Levenberg-Marquardt Method

Abstract

The aim of this study is to implement inverse techniques for the estimation of thermophysical properties that are otherwise difficult to measure directly. The Levenberg–Marquardt method is applied for parameter identification, focusing on properties such as density, specific heat, thermal conductivity, and thermal diffusivity. A numerical simulation is carried out on a solid plate of given thickness and known properties to validate the approach. The transient temperature fields within the plate are computed from the direct problem and used as virtual measurements at optimally selected sensor locations and experiment durations, determined through a sensitivity analysis. These temperature fields serve as input for the inverse procedure, allowing the estimation of the thermophysical properties. To enhance the realism of the study, simulated measurements are further perturbed with random errors to mimic experimental uncertainties. The results show that the method accurately recovers the exact properties, with estimation errors less than 0.5% for thermal conductivity and below 1% for specific heat under noise-free conditions. When perturbed data with ±2% random error are introduced, deviations remain limited, with errors below 3%, confirming the robustness of the approach. Furthermore, the identification of optimal wall characteristics provides a practical contribution to building energy management, as selecting materials with favourable thermophysical properties reduces heat transfer from the external environment, thereby lowering the load on air-conditioning systems and improving overall cooling efficiency in hot climates.