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In our recent work [Gusev and Lurie, Int. J. Mod. Phys. B26 (2012) 125003], we have presented the theory of spacetime elasticity. The theory advocates its own law of heat conduction in solids, involving both wave and relaxation (diffusion) modes of heat propagation. Here we use that heat conduction law — together with the classical Fourier's and Maxwell–Cattaneo laws — to analyze the temperature dynamics occurring in Fermi–Pasta–Ulam (FPU-β) chains. We focus on the acoustic limit and use a combination of the Langevin and molecular dynamics to study the corresponding temperature decay functions. We have found that all the three laws suit well for describing the high-temperature, exponential-form temperature decay functions. However, at low temperatures the wave dynamics becomes prevailing and it is only the spacetime-elasticity heat conduction law that provides the appropriate functional forms. At all the temperatures and wavelengths studied, the observed temperature dynamics is anomalous, and we discuss both theoretical and practical implications of such anomalous behavior

Frequency-resolved thermal lensing (FRTL) is an approach used to measure thermal diffusivity coefficients of liquid samples. The theoretical model of this approach is based on thermal waves and the Fresnel diffraction approximation. This model predicts that only two experimental parameters are needed to estimate the thermal diffusivity of the sample. Experiments performed on pure solvents validate the theoretical predictions and confirm the feasibility of using this approach to thermally characterize liquid samples. The results show that the method is a simple and sensitive approach to determine thermal diffusivity coefficients in liquid samples.

This paper describes experimental results of thermal diffusivity measurements performed on different concentrations of aqueous Tartrazine solutions. The measurements are performed using the frequency-resolved thermal lensing technique and the results are compared with the thermal diffusivity value of pure water used as a solvent or host liquid. The results show that at low concentrations, the thermal properties of the solution are roughly equal to those of the water. However, when the concentration is increased, the thermal properties of the solutions diverge from that of the host liquid.

A model for predicting thermal waves within a surface-heated porous structure has been developed. The relevant phenomena for the moisture, pressure and temperature fields are coupled. Considering mass and energy transfer processes, a set of governing differential equations is presented. The solution of the problem has been obtained with a finite difference scheme.