Comparison of kinetic theory analyses of linearized heat transfer between parallel plates

Bassanini, Piero; Cercignani, Carlo; Pagani, Carlo

doi:10.1016/0017-9310(67)90165-2

Cited by 82 publications

(18 citation statements)

References 15 publications

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“…1a and b show that the correction factors for slip-velocity and temperature jump, b u and b T , respectively, are close to unity when Kn > 0.1. These particular factors have been the subject of many previous investigations [1,[28][29][30][31]. In particular, Figs.…”

Section: Resultsmentioning

confidence: 98%

“…To compensate for this necessary simplification, empirical correction factors, b u ðu ¼ u; T ; r 11 ; r 22 ; r 12 ; q 1 ; q 2 Þ have been introduced into the boundary conditions. This type of approach has been used before to correct the slip-velocity and temperature jump for the Navier-Stokes equations [1,[27][28][29][30][31].…”

Section: Calibration Of the Boundary Valuesmentioning

confidence: 99%

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A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions

Emerson

2007

Journal of Computational Physics

108

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Section: Resultsmentioning

confidence: 98%

Section: Calibration Of the Boundary Valuesmentioning

confidence: 99%

A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions

Emerson

2007

Journal of Computational Physics

108

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“…The problem of heat transfer between parallel plates has been studied extensively, both for single gases [171,172,173,174,175] and mixtures [176] in the whole range of the Knudsen number. Even more, it has been used to benchmark the efficiency of several semi-analytical and numerical methods solving kinetic equations [177,99,178]. In the case of heat transfer in a rarefied gas between coaxial cylinders, it is commonly found in various technological applications, such as the Pirani gauge [4] for monitoring pressure in vacuum technology.…”

Section: Non-linear Heat Transfermentioning

confidence: 99%

“…The study of heat transfer phenomena in rarefied gases is important in several practical applications, as seen in Chapter 2, and have therefore been theoretically investigated by many researchers [187,177,179,188,113]. In most cases, only small values of the normalized temperature difference have been considered since the linearization of the distribution function leads to a more tractable mathematical formulation with a robust theoretical background.…”

Section: Introductionmentioning

confidence: 99%

“…A set of nonlinear kinetic equations subject to suitable boundary conditions is solved numerically for the unknown distribution function based on the discrete velocity method. Complete treatment of the heat transfer problems under consideration has been successfully applied in the literature only in the case of small temperature differences based on linearized kinetic theory [177,175,113].…”

Section: Introductionmentioning

confidence: 99%

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Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

Πανταζής¹

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The approval of the current dissertation by the Department of Mechanical Engineering of the University of Thessaly does not imply acceptance of the author's opinions (Law 5343/32 number 202 paragraph 2). Also, the views and opinions expressed herein do not necessarily reflect those of the European Commission. There are several other people who I feel that have contributed in the writing of this dissertation.The most important contributions, along with several helpful conversations, were made by Prof. F.Sharipov, who provided the basic concept of the channel end effect study, and Dr. Chr. Day along with the KIT personnel, who briefly introduced me in the world of experimental rarefied gas dynamics. It was also a priviledge to discuss and work for a brief period of time with Prof. A. Grecos, who tirelessly discussed with me on various subjects of statistical mechanics. Financial support for this Ph.D. has been provided by the Euratom Association -Hellenic Republic, to which I am deeply indepted. Also, partial support for conference mobility expenses has been received from the GASMEMS Marie Curie programme. In this work, non-equilibrium transport phenomena have been examined via the kinetic theory of gases. The behaviour of the gas in low pressure conditions or in low-dimensionality systems can not be captured by the usual Navier-Stokes formulation, in conjunction with the constitutive laws of Newton-Fourier-Fick. The limited number of intermolecular collisions results in departure from equilibrium and the particulate nature of the gas must be taken into account, greatly increasing the computational effort.The problem is described by the integro-differential Boltzmann equation, which is used to determine the distribution of particles in physical and molecular velocity space, as well as in time.There are difficulties associated with the seven-dimensional nature of the distribution function, as well as with the complexity of the collision term, which is usually substituted by an appropriate model.The most widely used and successful numerical methodologies, the Discrete Velocity Method (DVM) and the Direct Simulation Monte Carlo (DSMC), are applied here in the whole range of the Knudsen number. It is important to employ approaches based on kinetic theory, since these are the only ones which are valid for any rarefaction level.In this work, several problems including non-equilibrium phenomena are considered. The interaction of gases with solid surfaces is considered for several problems according to the CercignaniLampis boundary conditions. The non-linear form of this scattering kernel, which had not been pre- viously used in the literature, is applied on the problem of heat transfer between parallel plates and coaxial cylinders. Its linearized form has also been employed for both flow and heat transfer problems and a comparison with relevant experiments has lead to surface characterization with respect to argon and helium flows.Non-linear heat conduction phenomena are also studied for the parallel plates and coaxial c...

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A numerical solution of boltzmann's equation

Sod¹

1977

Comm Pure Appl Math

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We consider the numerical solution of Boltzmann's equation for a gas model consisting of rigid spheres by means of Hilbert's expansion. If we retain only the first two terms of the expansion, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert ex:Pansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solv:ed by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another 6 expansion of the distribution function in terms,o.f Hermite polynomials, the e:x--pansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition.TI1e numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.

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Comparison of kinetic theory analyses of linearized heat transfer between parallel plates

Cited by 82 publications

References 15 publications

A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions

A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

A numerical solution of boltzmann's equation

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