Interpretation of Second Law of Thermodynamics in Extended Procedures for the Exploitation of the Entropy Inequality: Korteweg Fluids and Strain-Gradient Elasticity as Examples.

In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the assumption that, at an arbitrary instant, t0, in an arbitrary point, P0, of a continuous system, the entropy production is zero if, and only if, P0 is in thermodynamic equilibrium. In 2022, Cimmelli and Rogolino incorporated such an assumption in a more general formulation of the second law of thermodynamics. In this paper, we prove that the same conclusions hold if both the fundamental balance laws and their gradients are substituted into the entropy inequality. Such a methodology is applied to analyze the strain-gradient elasticity.

Thermodynamics of Composition Graded Thermoelastic Solids.

We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman-Noll procedure. For the material at hand, the specific entropy and the stress tensor may depend on the gradient of the unknown fields, resulting in a very general theory. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or equilibrium states. We characterize several different types of perturbations depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well.

Tunable Heat-Flux Rectification in Graded Nanowires in Non-Linear Guyer-Krumhansl Regime.

We study heat rectification in composition-graded nanowires, with nonlocal and nonlinear effects taken into account in a generalized Guyer-Krumhansl equation. Using a thermal conductivity dependent on composition and temperature, the heat equation is solved. Introducing a non-vanishing heat supply (as for instance, a lateral radiative heat supply), we explore the conditions under which either nonlocal or nonlinear effects or both contribute to heat rectification and how they may be controlled by means of the external radiative flux. The corresponding rectification coefficients are calculated as well, and the physical conditions under which the system becomes a thermal diode are pointed out.

New and Recent Results for Thermoelectric Energy Conversion in Graded Alloys at Nanoscale.

In this article, we review the main features of nonlocal and nonlinear heat transport in nanosystems and analyze some celebrated differential equations which describe this phenomenon. Then, we present a new heat-transport equation arising within the so-called thermomass theory of heat conduction. We illustrate how such a theory can be applied to the analysis of the efficiency of a thermoelectric energy generator constituted by a Silicon-Germanium alloy, as the application and new results for a nanowire of length L=100 nm, are presented as well. The thermal conductivity of the nanowire as a function of composition and temperature is determined in light of the experimental data. Additionally, the best-fit curve is obtained. The dependency of the thermoelectric efficiency of the system on both the composition and the difference of temperature applied to its ends is investigated. For the temperatures T=300 K, T=400 K, and T=500 K, we calculate the values of the composition corresponding to the optimal efficiency, as well as the optimal values of the thermal conductivity. Finally, these new results are compared with recent ones obtained for a system of length L=3 mm, in order to point out the benefits due to the miniaturization in thermoelectric energy conversion.

Approximation of Composition and Temperature Dependent Heat Conductivity and Optimization of Thermoelectric Energy Conversion in Silicon-Germanium Alloys.

We analyze the efficiency as thermoelectric energy converter of a silicon-germanium alloy with composition and temperature dependent heat conductivity. The dependency on composition is determined by a non-linear regression method (NLRM), while the dependency on temperature is approximated by a first-order expansion in the neighborhood of three reference temperatures. The differences with respect to the case of thermal conductivity depending on composition only are pointed out. The efficiency of the system is analyzed under the assumption that the optimal energy conversion corresponds to the minimum rate of energy dissipated. The values of composition and temperature which minimize such a rate are calculated as well.

Thermoelectric Efficiency of Silicon-Germanium Alloys in Finite-Time Thermodynamics.

We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon-Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (T=300 K, T=400 K, T=500 K), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out.