###### Abstract
[PERSON] in [21] reported on the basis of the conducted experiment that, e.g., the relaxation times are equal to about 20 s for sand and 29 s for sodium bicarbonate in the Cattaneo model. However, e.g., in two later independent works [22; 23], the authors tried to reproduce the experiment conducted by [PERSON], but finally they stated in the conclusion that there are doubts about the application of the Cattaneo model to describe heat conduction in materials with the non-homogeneous inner structure in the considered parameter ranges. These above-mentioned remarks motivated us to conduct similar experimental studies and make measurements to confirm the observations in the work [23], where the authors have used a cylindrically symmetric system filled with granular material heated by an electrical heat source along the axis. Our experiment differs in that the system is heated by the outer surface; details are presented in the next Section. Each mathematical model of heat conduction can be described by the appropriate partial differential equation (or system of such equations) along with geometric, physical, boundary and initial conditions [14; 15; 19; 24]. Solutions to such direct heat conduction problems require determining appropriate boundary conditions at the boundaries of the considered domain, as well as knowledge of the initial condition and the assumption of all thermophysical parameters occurring in the model. These parameters include the specific heat capacity (that determines the quantity of heat that must be added to one unit of mass of the material in order to raise its temperature by one unit), the thermal conductivity (that indicates the ability of the material to conduct heat, so-called an intensive property) and density. All these quantities can be constants or determined by functional relationships. A solution to the direct heat conduction problem is the spatiotemporal temperature field in the considered domain. The inverse heat conduction problems [2; 24; 25] concern, among others, temperature measurements in order to estimate unknown parameter values appearing in the mathematical formulation of problems. In the inverse problems, the unknown parameters of the adopted mathematical model are determined on the basis of discrete-in-time temperature measurements (both on the surface and inside the considered domain) using sensors. This approach also allows the validation of experimental results with theoretical ones. Due to the fact that inverse problems are treated as ill-posed problems [26], the solutions may be unstable. It should also be taken into account here that the measured temperature data used in the analysis of the inverse problems includes measurement errors. The estimated parameter values in the inverse analysis are not exact and should be treated with the associated uncertainties. In this research, in order to find the solution to the inverse problem, we use minimization algorithms that are also used in many optimization problems [27; 28; 29; 30]; the details are presented in Section 3. The problem of identification of unknown thermophysical parameters of materials can also be solved, e.g., using the sensitivity analysis methods [31], the evolutionary algorithm [32] or the Monte Carlo simulation [33]. The essence of sensitivity analysis is to show the impact of different values of an independent variable on the dependent variable taking into account a given set of assumptions. Often, the inverse heat conduction problem is solved using the criterion of the least squares by applying the sensitivity coefficients. In recent times, artificial intelligence (AI) algorithms have been increasingly used. [PERSON] et al. [34], have considered various mathematical models (including AI algorithms) to predict the thermal conductivity of the quartz sand, while, in the [35], AI is used to reconstruct the heat transfer coefficient during the heat conduction in the solidification process.