Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade

Dunn, James E.; Fosdick, Roger

doi:10.1007/bf00280970

Cited by 570 publications

(325 citation statements)

References 25 publications

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“…We refer to [10] and [7] for further reading on fluid of complexity two and on second grade fluids. These fluids are non-Newtonian and modelling a large class of dilute polymeric solutions, industrial fluids, slurry flows and food rheology.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

Razafimandimby

Sango

2010

Comptes Rendus. Mathématique

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

Razafimandimby

Sango

2010

Comptes Rendus. Mathématique

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“…Numerous papers have applied this idea in developing constitutive relations. See, for example, [2,8,[24][25][26][27]. Equation (8) is appropriate for obtaining restrictions on the constitutive parameters.…”

Section: The Governing Equationsmentioning

confidence: 99%

Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

Yang

Massoudi

Kirwan

2017

Entropy

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Flowing media in both industrial and natural processes are often characterized as assemblages of densely packed granular materials. Typically, the constitutive relations for the stress tensor and heat flux vector are fundamentally nonlinear. Moreover, these equations are coupled through the Clausius-Duhem inequality. However, the consequences of this coupling are rarely studied. Here we address this issue by obtaining constraints imposed by the Clausius-Duhem inequality on the constitutive relations for both the stress tensor and the heat flux vector in which the volume fraction gradient plays an important role. A crucial result of the analysis is the restriction on the dependency of phenomenological coefficients appearing in the constitutive equations on the model objective functions.

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“…It is assumed that the flow meets the Clausius-Duhem inequality and that the specific Helmholtz free energy of the fluid is minimum at equilibrium [29] when…”

Section: Mathematical Formulation Of the Problem And Analytic Solutionmentioning

confidence: 99%

Effects of Hall Current on Flow of Unsteady MHD Axisymmetric Second-Grade Fluid with Suction and Blowing over an Exponentially Stretching Sheet

Zaman¹,

Sohail²,

Ali³

et al. 2014

OJMSi

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This paper investigates effects of Hall current on flow of unsteady magnetohydrodynamic (MHD) axisymmetric second-grade fluid with suction and blowing over a sheet stretching exponentially with radius. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow over an exponentially stretching sheet in cylindrical coordinates. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the radial and axial components of the velocity are illustrated through plots. Also the effects of the pertinent parameters on the shear stress at the wall are presented numerically in tabular form.

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Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade

Cited by 570 publications

References 25 publications

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

Effects of Hall Current on Flow of Unsteady MHD Axisymmetric Second-Grade Fluid with Suction and Blowing over an Exponentially Stretching Sheet

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