The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Dimitrios Tsagkarogiannis - One of the best experts on this subject based on the ideXlab platform.
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Fourier Law phase transitions and the stationary stefan problem
Archive for Rational Mechanics and Analysis, 2011Co-Authors: Anna De Masi, Errico Presutti, Dimitrios TsagkarogiannisAbstract:We study the one-dimensional stationary solutions of the integro-differential equation which, as proved in Giacomin and Lebowitz (J Stat Phys 87:37–61, 1997; SIAM J Appl Math 58:1707–1729, 1998), describes the limit behavior of the Kawasaki dynamics in Ising systems with Kac potentials. We construct stationary solutions with non-zero current and prove the validity of the Fourier Law in the thermodynamic limit showing that below the critical temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied: we show that if metastable values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier Law is not satisfied. It regains its validity however in the thermodynamic limit where the limit profile is again monotone away from the interface.
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Fourier Law phase transitions and the stationary stefan problem
arXiv: Mathematical Physics, 2010Co-Authors: Anna De Masi, Errico Presutti, Dimitrios TsagkarogiannisAbstract:We study the one-dimensional stationary solutions of an integro-differential equation derived by Giacomin and Lebowitz from Kawasaki dynamics in Ising systems with Kac potentials, \cite{GiacominLebowitz}. We construct stationary solutions with non zero current and prove the validity of the Fourier Law in the thermodynamic limit showing that below the critical temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied. We show that if metastable values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier Law is not satisfied. It regains however its validity in the thermodynamic limit where the limit profile is again monotone away from the interface.
J J Alvaradogil - One of the best experts on this subject based on the ideXlab platform.
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steady state and modulated heat conduction in layered systems predicted by the phonon boltzmann transport equation
arXiv: Mesoscale and Nanoscale Physics, 2015Co-Authors: Jose Ordonezmiranda, Ronggui Yang, Sebastian Volz, J J AlvaradogilAbstract:Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that both steady state and modulated components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path, and they exhibit the diffusive behavior as predicted by the Fourier Law of heat conduction when this ratio is much larger than the unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than the unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fourier Law. Furthermore, we derived an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gerko work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fourier Law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laser-based transient heating techniques.
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a model for the effective thermal conductivity of metal nonmetal particulate composites
Journal of Applied Physics, 2012Co-Authors: Jose Ordonezmiranda, Ronggui Yang, J J AlvaradogilAbstract:The effective thermal conductivity of particulate composites with oriented spheroidal metallic particles embedded in a dielectric matrix is analyzed under the framework of the two-temperature model of heat conduction. The obtained analytical results show that the effective thermal conductivity depends strongly on (1) the relative size of the particle inclusions with respect to the electron-phonon coupling length and (2) the ratio between the electron and phonon thermal conductivities. The effect of the electron-phonon coupling inside metallic particles is expressed by the reduction of the composite thermal conductivity with respect to its corresponding values obtained for an infinite electron-phonon coupling factor, where the analysis could be established based on the Fourier Law of heat conduction. It is shown that the composite thermal conductivity has upper and lower bounds, which are determined by the particle size in comparison with the electron-phonon coupling length. The generalized model for spher...
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a constitutive equation for nano to macro scale heat conduction based on the boltzmann transport equation
Journal of Applied Physics, 2011Co-Authors: Jose Ordonezmiranda, Ronggui Yang, J J AlvaradogilAbstract:A constitutive equation for heat conduction is derived from the exact solution of the Boltzmann transport equation under the relaxation time approximation. This is achieved by a series expansion on multiple space derivatives of the temperature and introducing the concept of thermal multipoles, where the thermal conductivity defined under the framework of the Fourier Law of heat conduction is just the first thermal pole. It is shown that this equation generalizes the Fourier Law and Cattaneo equation of heat conduction, and it depends strongly on the relative values of the length and time scales compared with the mean-free path and mean-free time of the energy carriers, respectively. In the limiting case of steady-state heat conduction, it is shown that the heat flux vector depends on a spatial scale ratio whose effects are remarkable in the micro-scale spatial domains. By applying a first-order approximation of the obtained thermal multipole expansion to the problem of transient heat conduction across a t...
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a constitutive equation for nano to macro scale heat conduction based on the boltzmann transport equation
Journal of Applied Physics, 2011Co-Authors: Jose Ordonezmiranda, Ronggui Yang, J J AlvaradogilAbstract:A constitutive equation for heat conduction is derived from the exact solution of the Boltzmann transport equation under the relaxation time approximation. This is achieved by a series expansion on multiple space derivatives of the temperature and introducing the concept of thermal multipoles, where the thermal conductivity defined under the framework of the Fourier Law of heat conduction is just the first thermal pole. It is shown that this equation generalizes the Fourier Law and Cattaneo equation of heat conduction, and it depends strongly on the relative values of the length and time scales compared with the mean-free path and mean-free time of the energy carriers, respectively. In the limiting case of steady-state heat conduction, it is shown that the heat flux vector depends on a spatial scale ratio whose effects are remarkable in the micro-scale spatial domains. By applying a first-order approximation of the obtained thermal multipole expansion to the problem of transient heat conduction across a thin film and comparing the results with the predictions for the same problem using the Fourier, Cattaneo and Boltzmann transport equations, it is shown that our results could be useful in the study of the heat transport in short as well as in long scales of space and time. The common and different features of the multipole expansion compared with the Ballistic-diffusive model of heat conduction are also discussed. Special emphasis is put to the cases where the physical scales of space and time are comparable to the mean-free path and mean-free time of the energy carriers.
Ashok T Ramu - One of the best experts on this subject based on the ideXlab platform.
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a compact heat transfer model based on an enhanced Fourier Law for analysis of frequency domain thermoreflectance experiments
Applied Physics Letters, 2015Co-Authors: Ashok T Ramu, John E BowersAbstract:A recently developed enhanced Fourier Law is applied to the problem of extracting thermal properties of materials from frequency-domain thermoreflectance (FDTR) experiments. The heat transfer model comprises contributions from two phonon channels: one a high-heat-capacity diffuse channel consisting of phonons of mean free path (MFP) less than a threshold value, and the other a low-heat-capacity channel consisting of phonons with MFP higher than this value that travel quasi-ballistically over length scales of interest. The diffuse channel is treated using the Fourier Law, while the quasi-ballistic channel is analyzed using a second-order spherical harmonic expansion of the phonon distribution function. A recent analysis of FDTR experimental data suggested the use of FDTR in deriving large portions of the MFP accumulation function; however, it is shown here that the data can adequately be explained using our minimum-parameter model, thus highlighting an important limitation of FDTR experiments in exploring ...
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a generalized enhanced Fourier Law and underlying connections to major frameworks for quasi ballistic phonon transport
arXiv: Mesoscale and Nanoscale Physics, 2015Co-Authors: Ashok T Ramu, John E BowersAbstract:An enhanced Fourier Law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables, is derived from the Boltzmann transport equation, assuming a gray population of quasi-ballistic phonon modes. This equation is generalized to an arbitrary phonon population. Other phonon transport models are analyzed in the context of the generalized EFL and connections are made between the generalized EFL and other models, revealing the essential unity of seemingly disparate models reported in the literature.
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a compact heat transfer model based on an enhanced Fourier Law for analysis of frequency domain thermoreflectance experiments
arXiv: Mesoscale and Nanoscale Physics, 2015Co-Authors: Ashok T Ramu, John E BowersAbstract:A recently developed enhanced Fourier Law is applied to the problem of extracting thermal properties of materials from frequency-domain thermoreflectance (FDTR) experiments. The heat transfer model comprises contributions from two phonon channels; one a high-heat-capacity diffuse channel consisting of phonons of mean free path (MFP) less than a threshold value, and the other a low-heat-capacity channel consisting of phonons with MFP higher than this value that travel quasi-ballistically over length scales of interest. The diffuse channel is treated using the Fourier Law, while the quasi-ballistic channel is analyzed using a second-order spherical harmonic expansion of the phonon distribution function. A recent analysis of FDTR experimental data suggested the use of FDTR in deriving large portions of the MFP accumulation function; however, it is shown here that the data can adequately be explained using our minimum-parameter model, thus highlighting an important limitation of FDTR experiments in exploring the accumulation function of bulk matter.
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quasi ballistic phonon transport effects on the determination of the mean free path accumulation function for the effective thermal conductivity
arXiv: Mesoscale and Nanoscale Physics, 2015Co-Authors: Ashok T Ramu, John E BowersAbstract:The mean-free path (MFP) accumulation function for the effective thermal conductivity, introduced by Dames and Chen is a compact, universal and highly useful summary of the effect of ballistic thermal transport on the effective thermal conductivity measured by various experiments. The frequency domain thermoreflectance (FDTR) experiment is especially well suited to its determination. Extraction of the accumulation function from this experiment uses the thermal penetration depth (TPD) of phonons at each frequency as a cut-off for classifying phonons as ballistic or diffusive at that frequency. In this paper, we show that using the TPD as a cut-off is arbitrary and prone to serious error. We report on a new technique to deduce the MFP accumulation function from the FDTR experiment by numerical solution of an enhanced Fourier Law.
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an enhanced Fourier Law derivable from the boltzmann transport equation and a sample application in determining the mean free path of nondiffusive phonon modes
Journal of Applied Physics, 2014Co-Authors: Ashok T RamuAbstract:An enhanced Fourier Law that we term the unified nondiffusive-diffusive (UND) phonon transport model is proposed in order to account for the effect of low-frequency phonon modes of long mean-free path that propagate concomitantly to the dominant high-frequency modes. The theory is based on spherical harmonic expansions of the phonon distribution functions, wherein the high-frequency mode distribution function is truncated at the first order in the expansion, while the low-frequency mode distribution function, which is farther out of thermal equilibrium, is truncated at the second order. As an illustrative application, the predictions of the proposed model are compared with data from a recent experiment that utilized the transient gratings method to investigate the deviation of thermal transport in a silicon membrane from the predictions of the Fourier Law. The good fit of the experimental effective thermal conductivity (ETC) with the analytical solution derived in this work yields quantitative information about the mean-free path of the dominant low-frequency heat-transfer mode in silicon.
Reinhard Racke - One of the best experts on this subject based on the ideXlab platform.
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on the stability of damped timoshenko systems cattaneo versus Fourier Law
Archive for Rational Mechanics and Analysis, 2009Co-Authors: Hugo Fernandez D Sare, Reinhard RackeAbstract:We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While exponential stability under the Fourier Law of heat conduction holds, it turns out that the coupling via the Cattaneo Law does not yield an exponentially stable system. This seems to be the first example that a removal of the paradox of infinite propagation speed inherent in Fourier’s Law by changing to the Cattaneo Law causes a loss of the exponential stability property. Actually, for systems with history, the Fourier Law keeps the exponential stability known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property.
Anna De Masi - One of the best experts on this subject based on the ideXlab platform.
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Fourier Law phase transitions and the stationary stefan problem
Archive for Rational Mechanics and Analysis, 2011Co-Authors: Anna De Masi, Errico Presutti, Dimitrios TsagkarogiannisAbstract:We study the one-dimensional stationary solutions of the integro-differential equation which, as proved in Giacomin and Lebowitz (J Stat Phys 87:37–61, 1997; SIAM J Appl Math 58:1707–1729, 1998), describes the limit behavior of the Kawasaki dynamics in Ising systems with Kac potentials. We construct stationary solutions with non-zero current and prove the validity of the Fourier Law in the thermodynamic limit showing that below the critical temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied: we show that if metastable values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier Law is not satisfied. It regains its validity however in the thermodynamic limit where the limit profile is again monotone away from the interface.
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Fourier Law phase transitions and the stationary stefan problem
arXiv: Mathematical Physics, 2010Co-Authors: Anna De Masi, Errico Presutti, Dimitrios TsagkarogiannisAbstract:We study the one-dimensional stationary solutions of an integro-differential equation derived by Giacomin and Lebowitz from Kawasaki dynamics in Ising systems with Kac potentials, \cite{GiacominLebowitz}. We construct stationary solutions with non zero current and prove the validity of the Fourier Law in the thermodynamic limit showing that below the critical temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied. We show that if metastable values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier Law is not satisfied. It regains however its validity in the thermodynamic limit where the limit profile is again monotone away from the interface.