On the Rarefied Gas Experiments

Kovács, Róbert

doi:10.3390/e21070718

Cited by 11 publications

(7 citation statements)

References 84 publications

(179 reference statements)

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“…Staying in the linear and quasi-linear regime, the compatibility between RET and NET-IV (consequently, with EIT, too) is proved in [13]. However, the situation could be different in the nonlinear case, which becomes apparent regarding the rarefied gas experiments [68]. The importance of these experiments lies in the mass density dependence of the coefficients (58).…”

Section: Coupled Heat and Mass Transportmentioning

confidence: 93%

“…However, when the ω and T are constants, the density remains a mere variable to change in order to reveal the change in the speed of sound. That is, decreasing the density of gas from its normal state down to the low-pressure region (e.g., 10 Pa [68]), continuously enhance the role of the coupling between the fluid and thermal equations together with their hyperbolic character (i.e., the relaxation times become higher and higher). Therefore, these coefficients must be mass density-dependent.…”

Section: Coupled Heat and Mass Transportmentioning

confidence: 99%

“…are equilibrium distribution and auxiliary function, respectively. Densities (68) are recovered as moments of f 14 through (72), as well as entropy and entropy flux (70) while using the relation α = (D − 5)/3. However, the main advantage comes from computation of the productions (69) as moments, i.e., weak form of the collision operator:…”

Section: Molecular Extended Thermodynamics-application Of the Maximum...mentioning

confidence: 99%

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Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities

2020

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Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties, and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions that are related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view. In the present work, we restrict ourselves on non-relativistic models.

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Section: Coupled Heat and Mass Transportmentioning

confidence: 93%

Section: Coupled Heat and Mass Transportmentioning

confidence: 99%

Section: Molecular Extended Thermodynamics-application Of the Maximum...mentioning

confidence: 99%

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Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities

2020

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“…The macroscopic models of heat transfer can predict the general form of heat propagation and also can connect the different levels of the hierarchical material behavior [16]. The hyperbolic models with relaxation type dissipation predict a wave behavior of heat but they are not able to incorporate emerging processes related to the coherent behavior of phonons and also the quantitative modelling of ballistic propagation can be problematic [17]. These aspects of the dynamics of non Fourier heat propagation and in particular the form of the evolution equations determines the stationary processes, as well.…”

Section: Introductionmentioning

confidence: 99%

Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity

Vázquez

Ván

Kovács

2020

Entropy

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There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for 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.

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“…The paper written by R. Kovács [ 3 ] deals with the experiments on rarefied gases. The generalized system of Navier-Stokes-Fourier equations is presented, which is required to model the ballistic effects appearing in gases at low pressures.…”

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confidence: 99%