On the Temperature‐Jump Problem in Rarefied Gas Dynamics: The Effect of the Cercignani–Lampis Boundary Condition

Knackfuss, Rosenei Felippe; Barichello, Liliane Basso

doi:10.1137/050643209

Cited by 10 publications

(16 citation statements)

References 32 publications

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“…We note that, results for the Cercignani-Lampis kernel have been also recently obtained [32,35,13], although we are not going to treat this case, in this work.…”

Section: Introductionmentioning

confidence: 93%

An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. I. Flow problems

Scherer

Filho

Barichello

2008

Z. angew. Math. Phys.

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The ADO method, an analytical version of the discrete-ordinates method, is used to solve several classical problems in the rarefied gas dynamics field. The complete development of the solution, which is analytical in terms of the spatial variable, is presented in a way, such that, a wide class of kinetic models are considered, in an unified approach. A series of numerical results are showed and different simulations are used in order to establish a general comparative analysis based on this consistent set of results provided by the same methodology.

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“…We note that, results for the Cercignani-Lampis kernel have been also recently obtained [32,35,13], although we are not going to treat this case, in this work.…”

Section: Introductionmentioning

confidence: 93%

An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. I. Flow problems

Scherer

Filho

Barichello

2008

Z. angew. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…(38) to (40), we write the normalized heat flow in terms of the solution of the problem given by Eq. (30), and the boundary conditions given by Eqs. (32), as…”

Section: Basic Formulationmentioning

confidence: 99%

“…Because of that, we disregard the associated elementary solutions and we add four exact solutions of the problem given by Eq. (30), to the general solution given in Eq. (64), which we rewrite in the form…”

Section: A Discrete Ordinates Solutionmentioning

confidence: 99%

“…(58), which includes the S model case: the derivation here presented, for the ADO method, is simpler than the one described for the temperature-jump problem, for the S model in Ref. [30], which related the one gas and the binary gas mixture cases.…”

Section: A Discrete Ordinates Solutionmentioning

confidence: 99%

“…In recent years, analytical solutions in terms of the spatial variable have been developed, for both of the above mentioned problems [8], [26] - [30], by the ADO method [31], which is an analytical version of the discrete-ordinates method [32]. In these listed works, different procedures were proposed to deal with kinetic equations, as the BGK [33] and the S model [34] equations.…”

Section: Introductionmentioning

confidence: 99%

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An analytical approach to the unified solution of kinetic equations in the rarefied gas dynamics. II. Heat transfer problems

Scherer

Filho

Barichello

2008

Z. Angew. Math. Phys.

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The ADO method, an analytical version of the discrete-ordinates method, is used here to solve a heat-transfer problem in a rarefied gas confined in a channel, as well as to solve a half-space problem in order to evaluate the temperature jump at the wall. This work is an extension of a previous work, devoted to flow problems, where the complete development of the solution, which is analytical in terms of the spatial variable, is presented in a way, such that, a wide class of kinetic models are considered, in an unified approach. A series of numerical results are showed and different simulations are used in order to establish a general comparative analysis based on this consistent set of results provided by the same methodology. In particular, numerical results for heat-flow profile, temperature and density perturbations are obtained for channels (walls), defined by different materials, on which different temperatures are imposed.

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Quasi-random discrete ordinates method for neutron transport problems

Konzen

Guidi

Richter

2019

Annals of Nuclear Energy

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On the Temperature‐Jump Problem in Rarefied Gas Dynamics: The Effect of the Cercignani–Lampis Boundary Condition

Cited by 10 publications

References 32 publications

An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. I. Flow problems

An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. I. Flow problems

An analytical approach to the unified solution of kinetic equations in the rarefied gas dynamics. II. Heat transfer problems

Quasi-random discrete ordinates method for neutron transport problems

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