Internal constraint theories for the thermal expansion of viscous fluids

Bechtel, Stephen E.; Rooney, Frank; Forest, M. Gregory

doi:10.1016/s0020-7225(03)00242-8

Cited by 11 publications

(2 citation statements)

References 25 publications

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“…Thus, the class of flows encapsulated by Case 2 is characterized by vanishing speed of sound c. Because p = p(S), the isentropic condition (5) immediately implies that, necessarily, pressure is constant along particle lines. Constitutive laws with the property (19) governing so-called "infinitely compressible" fluids have been investigated in [15][16][17] in connection with thermal expansion models of viscous fluids. Their physical relevance has been analyzed therein, in particular, by experiments involving both Couette and Poiseuille flows.…”

Section: Vanishing Speed Of Soundmentioning

confidence: 99%

The Euler Equations of Spatial Gasdynamics and the Integrable Heisenberg Spin Equation

Schief

Rogers

2011

Stud Appl Math

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The Euler equations for an inviscid and thermally nonconducting gas are investigated with a view to isolating particular integrable structure. A natural physical constraint is imposed and it is demonstrated that, in the generic case, the steady Euler equations are equivalent to an integrable Heisenberg spin equation subject to a volume‐preserving constraint. A limiting case in which this constraint is not present is indicated.

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Section: Vanishing Speed Of Soundmentioning

confidence: 99%

The Euler Equations of Spatial Gasdynamics and the Integrable Heisenberg Spin Equation

Schief

Rogers

2011

Stud Appl Math

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“…However to keep the incompressible condition unchanged does not corresponds to the reality. Indeed, heat-conducting viscous flows are thermally compressible (see [2,15,20,21] and the references therein):…”

Section: Introductionmentioning

confidence: 99%

The Non-Incompressibility on Heat-Conducting Fluids. The Stationary Case

Consiglieri

2009

J. Math. Fluid Mech.

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This work deals with generalized viscous flows that can only undergo isochoric motions in isothermal processes, but can sustain motions that are not necessarily isochoric in processes that are not isothermal. The heat-conducting Stokes and Bingham fluids appear as a direct application. The method used here is a combination of a fixed point argument, the Uzawa-type algorithm and the optimization theory. The pressure is found as a limit of a sequence such that satisfies a constraint condition. (2000). Primary 35J25, 35Q35, 80A20; secondary 35R45, 49J40, 49N15. Mathematics Subject Classification

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