Heat Transfer Problem in a Van Der Waals Gas

Barbera, Elvira; Brini, Francesca; Sugiyama, Masaru

doi:10.1007/s10440-014-9892-1

Cited by 18 publications

(6 citation statements)

References 22 publications

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“…Equations (32), (34), (35,36,37) give the requested transformation law between the two reference frames, and it is very interesting that it looks like Equation (16). Now, if the Lagrange multipliers are taken as independent variables, Equation (37) is only a change of independent variables from µ a B to µ r C , while (32), (34), (35,36) are conditions, because they involve constitutive functions:…”

Section: The Galilean Relativity Principlementioning

confidence: 99%

“…If we substitute µ a B from Equation (37) in (38,39,40,41) and then substitute the result in (32), (34), (35,36), we obtain:…”

Section: The Galilean Relativity Principlementioning

confidence: 99%

“…Obviously, it is now necessary to speak about the new model [30], which inspired many other subsequent articles, a restricted part of which are [31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions

Carrisi

Pennisi

2015

Entropy

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The 14 moments model for dense gases, introduced in the last few years by Arima, Taniguchi, Ruggeri and Sugiyama, is here extended up to 18 moments. They have found the closure of the balance equations up to a finite order with respect to equilibrium; it is also possible to impose for that model the entropy and Galilean relativity principles up to whatever order with respect to equilibrium, but by using Taylor's expansion. Here, the exact solution is found, without expansions, but a bigger number of moments has to be considered and reasons will be shown suggesting that this number is at least 18.

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Section: The Galilean Relativity Principlementioning

confidence: 99%

“…If we substitute µ a B from Equation (37) in (38,39,40,41) and then substitute the result in (32), (34), (35,36), we obtain:…”

Section: The Galilean Relativity Principlementioning

confidence: 99%

See 1 more Smart Citation

An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions

Carrisi

Pennisi

2015

Entropy

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“…They started a new framework of research where many and many other articles followed them. Some of them have been published in the last years and are [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Relativistic extended thermodynamics from the Lagrangian view-point

et al. 2015

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The salient points of Relativistic Extended Thermodynamics (R.E.T.) are here revised according to the Lagrangian view-point: Attention is focused to each material particle and to its physical properties, during all the motion of the same particle. The results for the non relativistic case are already present in literature. Here a similar procedure is followed for R.E.T. with an arbitrary number of moments. It is also shown how the Einstenian Relativity Principle and some symmetry condition, which are present in the Eulerian view-point, can be "translated" in the Lagrangian view-point, where they are no more so self-evident

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“…A new approach has been proposed in [24] and other articles, such as [25][26][27][28][29][30][31][32][33][34][35][36][37][38], which overcomes this problem by considering two blocks of balance equations. In this framework, we have recently studied two different cases: one deals with rarefied polyatomic gases [37], even if the reduced set of applicability is not indicated in the title of that paper.…”

Section: Introductionmentioning

confidence: 99%

Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries

Carrisi

Tchame

Obounou

et al. 2015

Entropy

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Extended Thermodynamics of dense gases is characterized by two hierarchies of field equations, which allow one to overcome some restrictions on the generality of the previous models. This idea has been introduced by Arima, Taniguchi, Ruggeri and Sugiyama. In the case of a 14-moment model, they have found the closure of the balance equations up to second order with respect to equilibrium. Here, the closure is obtained up to whatever order and imposing only the necessary symmetry conditions. It comes out that the first non-symmetric parts of the higher order fluxes appear only at third order with respect to equilibrium, even if Arima, Taniguchi, Ruggeri and Sugiyama found a non-symmetric part proportional to an arbitrary constant also at first order with respect to equilibrium. Consequently, this constant must be zero, as Arima, Taniguchi, Ruggeri and Sugiyama assumed in the applications and on an intuitive ground.

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Heat Transfer Problem in a Van Der Waals Gas

Cited by 18 publications

References 22 publications

An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions

An 18 Moments Model for Dense Gases: Entropy and Galilean Relativity Principles without Expansions

Relativistic extended thermodynamics from the Lagrangian view-point

Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries

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