Estimation of Thermal Conductivity and Volumetric Heat Capacity in a Solid Plate using the Levenberg-Marquardt Method.

Abstract

The city of Ouargla is characterized by extremely high summer temperatures, which pose substantial challenges to achieving indoor thermal comfort, as conventional cooling systems often prove insufficient. This study seeks to mitigate this issue by investigating the thermal behavior of building materials and optimizing their properties to reduce cooling energy demand. An inverse analysis based on the Levenberg-Marquardt technique is employed to estimate key thermal properties-namely density, specific heat capacity, thermal conductivity, and thermal diffusivity-which are generally difficult to determine through direct measurement. To validate the proposed algorithm, a numerical simulation is performed on a solid plate with known thermophysical properties, enabling the computation of transient temperature fields. Sensitivity analysis is used to assess the influence of sensor placement and experiment duration on parameter estimation accuracy. To better represent real experimental conditions, the simulated temperature data are deliberately perturbed with random noise of amplitude 0.01, simulating measurement uncertainties. The results indicate excellent accuracy when using exact temperature data and only minor deviations in the presence of noise, highlighting the robustness and efficiency of the proposed inverse approach. These outcomes offer valuable insights for enhancing building design in Ouargla, improving thermal performance, and alleviating the load on cooling systems during extreme summer periods.