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A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.
Ruth Estephania Gonzalez-Narvaez; Mariano López de Haro; Federico Vázquez. Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach. Journal of Non-Equilibrium Thermodynamics 2021, 1 .
AMA StyleRuth Estephania Gonzalez-Narvaez, Mariano López de Haro, Federico Vázquez. Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach. Journal of Non-Equilibrium Thermodynamics. 2021; ():1.
Chicago/Turabian StyleRuth Estephania Gonzalez-Narvaez; Mariano López de Haro; Federico Vázquez. 2021. "Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach." Journal of Non-Equilibrium Thermodynamics , no. : 1.
There has been much interest in semiconductor superlattices because of their low thermal conductivities. This makes them especially suitable for applications in a variety of devices for the thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometric 1D multilayer systems by considering the separation of ballistic and diffusive heat fluxes, which are both described by Guyer-Krumhansl constitutive equations. The dispersion relations, as derived from the ballistic and diffusive heat transport equations, are used to derive an effective heat conductivity of the superlattice and to explain the minimum of the effective thermal conductivity.
Federico Vázquez; Péter Ván; Róbert Kovács. Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity. Entropy 2020, 22, 167 .
AMA StyleFederico Vázquez, Péter Ván, Róbert Kovács. Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity. Entropy. 2020; 22 (2):167.
Chicago/Turabian StyleFederico Vázquez; Péter Ván; Róbert Kovács. 2020. "Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity." Entropy 22, no. 2: 167.
This paper presents a numerical analysis of the transient heat transfer problem arising when a functionally graded material is subjected to a fixed temperature difference. Varying the gradation of the system, the thermal performance of the material is assessed both in time-dependent and steady-state conditions by means of temperature profiles and entropy production. One of the main contributions of this paper is the analysis of the system in the transient, from which it is found that the entropy production has a non-monotonic behaviour since maximum and minimum values of this physical quantity could be identified by varying the grading profile of the material. The latter allows to propose an optimization criterion for functionally graded materials which consists of the identification of spatial regions where temperature gradients are large and find thermal conductivity profiles that attenuate those gradients, thus reducing the thermal stresses present inside the material.
James Pérez-Barrera; Aldo Figueroa; Federico Vázquez. Controlling and Optimizing Entropy Production in Transient Heat Transfer in Graded Materials. Entropy 2019, 21, 463 .
AMA StyleJames Pérez-Barrera, Aldo Figueroa, Federico Vázquez. Controlling and Optimizing Entropy Production in Transient Heat Transfer in Graded Materials. Entropy. 2019; 21 (5):463.
Chicago/Turabian StyleJames Pérez-Barrera; Aldo Figueroa; Federico Vázquez. 2019. "Controlling and Optimizing Entropy Production in Transient Heat Transfer in Graded Materials." Entropy 21, no. 5: 463.
In this paper, we address theoretically and experimentally the optimization problem of the heat transfer occurring in two coupled thermoelectric devices. A simple experimental set up is used. The optimization parameters are the applied electric currents. When one thermoelectric is analysed, the temperature difference ΔT between the thermoelectric boundaries shows a parabolic profile with respect to the applied electric current. This behaviour agrees qualitatively with the corresponding experimental measurement. The global entropy generation shows a monotonous increase with the electric current. In the case of two coupled thermoelectric devices, elliptic isocontours for ΔT are obtained in applying an electric current through each of the thermoelectrics. The isocontours also fit well with measurements. Optimal figure of merit is found for a specific set of values of the applied electric currents. The entropy generation-thermal figure of merit relationship is studied. It is shown that, given a value of the thermal figure of merit, the device can be operated in a state of minimum entropy production.
Jaziel A. Rojas; Iván Rivera; Aldo Figueroa; Federico Vázquez. Coupled Thermoelectric Devices: Theory and Experiment. Entropy 2016, 18, 255 .
AMA StyleJaziel A. Rojas, Iván Rivera, Aldo Figueroa, Federico Vázquez. Coupled Thermoelectric Devices: Theory and Experiment. Entropy. 2016; 18 (7):255.
Chicago/Turabian StyleJaziel A. Rojas; Iván Rivera; Aldo Figueroa; Federico Vázquez. 2016. "Coupled Thermoelectric Devices: Theory and Experiment." Entropy 18, no. 7: 255.
In this paper we address the problem of optimization of the so called supercooling effect in thermoelectric nanoscaled layers. The effect arises when a short term electric pulse is applied to the layer. The analysis is based on constitutive equations of the Maxwell-Cattaneo type describing the time evolution of dissipative flows with the thermal and electric conductivities depending on the width of the layer. This introduces memory and nonlocal effects and consequently a wave-like behaviour of system’s temperature. We study the effects of the shape of the electric pulse on the maximum diminishing of temperature by applying pulses of the form ta with a a power going from 0 to 10. Pulses with a a fractionary number perform better for nanoscaled devices whereas those with a bigger than unity do it for microscaled ones. We also find that the supercooling effect is improved by a factor of 6.6 over long length scale devices in the best performances and that the elapsed supercooling time for the nanoscaled devices equals the best of the microscaled ones. We use the spectral methods of solution which assure a well representation of wave behaviour of heat and electric charge in short time scales given their spectral convergence.
Iván Rivera; Aldo Figueroa; Federico Vázquez. Optimization of supercooling effect in nanoscaled thermoelectric layers. Communications in Applied and Industrial Mathematics 2016, 7, 98 -110.
AMA StyleIván Rivera, Aldo Figueroa, Federico Vázquez. Optimization of supercooling effect in nanoscaled thermoelectric layers. Communications in Applied and Industrial Mathematics. 2016; 7 (2):98-110.
Chicago/Turabian StyleIván Rivera; Aldo Figueroa; Federico Vázquez. 2016. "Optimization of supercooling effect in nanoscaled thermoelectric layers." Communications in Applied and Industrial Mathematics 7, no. 2: 98-110.
In this work, the irreversible processes in light heating of Silicon (Si) and Germanium (Ge) thin films are examined. Each film is exposed to light irradiation with radiative and convective boundary conditions. Heat, electron and hole transport and generation-recombination processes of electron-hole pairs are studied in terms of a phenomenological model obtained from basic principles of irreversible thermodynamics. We present an analysis of the contributions to the entropy production in the stationary state due to the dissipative effects associated with electron and hole transport, generation-recombination of electron-hole pairs as well as heat transport. The most significant contribution to the entropy production comes from the interaction of light with the medium in both Si and Ge. This interaction includes two processes, namely, the generation of electron-hole pairs and the transferring of energy from the absorbed light to the lattice. In Si the following contribution in magnitude comes from the heat transport. In Ge all the remaining contributions to entropy production have nearly the same order of magnitude. The results are compared and explained addressing the differences in the magnitude of the thermodynamic forces, Onsager’s coefficients and transport properties of Si and Ge.
José Ernesto Nájera-Carpio; Federico Vazquez; Aldo Figueroa. Modeling and Analysis of Entropy Generation in Light Heating of Nanoscaled Silicon and Germanium Thin Films. Entropy 2015, 17, 4786 -4808.
AMA StyleJosé Ernesto Nájera-Carpio, Federico Vazquez, Aldo Figueroa. Modeling and Analysis of Entropy Generation in Light Heating of Nanoscaled Silicon and Germanium Thin Films. Entropy. 2015; 17 (12):4786-4808.
Chicago/Turabian StyleJosé Ernesto Nájera-Carpio; Federico Vazquez; Aldo Figueroa. 2015. "Modeling and Analysis of Entropy Generation in Light Heating of Nanoscaled Silicon and Germanium Thin Films." Entropy 17, no. 12: 4786-4808.
In this paper we undertake the theoretical analysis of a two-stage semiconductor thermoelectric module (TEM) which contains an arbitrary and different number of thermocouples, n1 and n2, in each stage (pyramid-styled TEM). The analysis is based on a dimensionless entropy balance set of equations. We study the effects of n1 and n2, the flowing electric currents through each stage, the applied temperatures and the thermoelectric properties of the semiconductor materials on the exergetic efficiency. Our main result implies that the electric currents flowing in each stage must necessarily be different with a ratio about 4.3 if the best thermal performance and the highest temperature difference possible between the cold and hot side of the device are pursued. This fact had not been pointed out before for pyramid-styled two stage TEM. The ratio n1/n2should be about 8.
Miguel Angel Olivares-Robles; Federico Vázquez; Cesar Ramirez-Lopez. Optimization of Two-Stage Peltier Modules: Structure and Exergetic Efficiency. Entropy 2012, 14, 1539 -1552.
AMA StyleMiguel Angel Olivares-Robles, Federico Vázquez, Cesar Ramirez-Lopez. Optimization of Two-Stage Peltier Modules: Structure and Exergetic Efficiency. Entropy. 2012; 14 (8):1539-1552.
Chicago/Turabian StyleMiguel Angel Olivares-Robles; Federico Vázquez; Cesar Ramirez-Lopez. 2012. "Optimization of Two-Stage Peltier Modules: Structure and Exergetic Efficiency." Entropy 14, no. 8: 1539-1552.
The heat transfer problem of a zero-mean oscillatory flow of a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. The local and global time-averaged entropy production are computed, and the consequences of convective cooling of the plates are also assessed. It is found that the global entropy production is a minimum for certain suitable combination of the physical parameters and a discrete set of values of the separation between the parallel plates. The transferred heat at the plates also shows minima in the same discrete set of values of the plates separation.
Federico Vazquez; Miguel Ángel Olivares-Robles; Sac Medina. Size Effects on the Entropy Production in Oscillatory Flow between Parallel Plates. Entropy 2011, 13, 542 -553.
AMA StyleFederico Vazquez, Miguel Ángel Olivares-Robles, Sac Medina. Size Effects on the Entropy Production in Oscillatory Flow between Parallel Plates. Entropy. 2011; 13 (2):542-553.
Chicago/Turabian StyleFederico Vazquez; Miguel Ángel Olivares-Robles; Sac Medina. 2011. "Size Effects on the Entropy Production in Oscillatory Flow between Parallel Plates." Entropy 13, no. 2: 542-553.