Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Given Boundary Data

This work aims to estimate temperature-dependent thermal conductivity and heat capacity given measurements of temperature and heat flux at the boundaries. This estimation problem has many engineering and industrial applications, such as those for the building sector and chemical reactors. Two approaches are proposed to address this problem. The first method uses an integral approach and a polynomial approximation of the temperature profile. The second method uses a numerical solver for the nonlinear heat equation and an optimization algorithm. The performance of the two methods is compared using synthetic data generated with different boundary conditions and configurations. The results demonstrate that the integral approach works in limited scenarios, whereas the numerical approach is effective in estimating temperature-dependent thermal properties. The second method is also extended to account for noisy measurements and a comprehensive uncertainty quantification framework is developed.