New Constitutive Equations for Conducting Magnetic Fluids With Internal Rotation : Thermodynamical Discussions

Shizawa, Kazuyuki; Tanahashi, Takahiko

doi:10.1299/jsme1958.29.2878

Cited by 19 publications

(18 citation statements)

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“…However, in the balance law of the angular momentum the internal rotation because of the magnetization has not been included, since magnetization was considered parallel to the magnetic field. To this end, Shizawa et al [29] obtained a set of equations for micropolar fluids with good thermal and electrical conductivity including internal rotation. In their context, magnetization does not depend only on thermodynamic quantities, but on the state of flow as well because of the anisotropy of magnetic fluids.…”

Section: Introductionmentioning

confidence: 99%

Micromagnetorotation of MHD Micropolar Flows

et al. 2020

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The studies dealing with micropolar magnetohydrodynamic (MHD) flows usually ignore the micromagnetorotation (MMR) effect, by assuming that magnetization and magnetic field vectors are parallel. The main objective of the present investigation is to measure the effect of MMR and the possible differences encountered by ignoring it. The MHD planar Couette micropolar flow is solved analytically considering and by ignoring the MMR effect. Subsequently, the influence of MMR on the velocity and microrotation fields as well as skin friction coefficient, is evaluated for various micropolar size and electric effect parameters and Hartmann numbers. It is concluded that depending on the parameters’ combination, as MMR varies, the fluid flow may accelerate, decelerate, or even excite a mixed pattern along the channel height. Thus, the MMR term is a side mechanism, other than the Lorentz force, that transfers or dissipates magnetic energy in the flow direct through microrotation. Acceleration or deceleration of the velocity from 4% to even up to 45% and almost 15% deviation of the skin friction were measured when MMR was considered. The crucial effect of the micromagnetorotation term, which is usually ignored, should be considered for the future design of industrial and bioengineering applications.

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Section: Introductionmentioning

confidence: 99%

Micromagnetorotation of MHD Micropolar Flows

et al. 2020

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“…We utilize with modifications the formulation of Shizawa and Tanahashi 11 for an electrically conductive magnetic fluid with the methodology based on integral formulation of equations governing the balance of linear momentum, angular momentum, and energy. We utilize with modifications the formulation of Shizawa and Tanahashi 11 for an electrically conductive magnetic fluid with the methodology based on integral formulation of equations governing the balance of linear momentum, angular momentum, and energy.…”

Section: Introductionmentioning

confidence: 99%

Continuum equations for magnetic and dielectric fluids with internal rotations

Rosensweig

2004

The Journal of Chemical Physics

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Several authors have attempted with varying success to derive a complete set of basic equations for the motion of polar fluids having internal rotations and hence in a state of polarization disequilibrium. This work develops a complete set of governing equations derived on the basis of dynamic balance relationships with the dissipation function determined from thermodynamic consideration. The magnetization relaxation equation is thereby determined from requirement of positive entropy production along with a complete set of constitutive laws including antisymmetric terms of the total stress tensor. The analysis employs the Minkowski expression of electromagnetic momentum and assumes that the product of electromagnetic stress and velocity contributes to the energy balance on the same footing as contact stresses of pressure and viscous origin. The work refines the treatment of our earlier effort carrying out the analysis to first order in the ratio of fluid velocity to light speed throughout.

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“…In case of considering internal rotation, Shliomis (5), (6) , Berkovsky, et al (7) , Jansons (8) , Tanahashi, et al (9) , , Shizawa-Tanahashi (11), (12) , the authors (13) - (16) , Liu (17) , Felderhof-Kroh (18) , Felderhof (19) , Müller-Engel (20) and Müller-Liu (21) reported the theoretical discussion on the basic equations of magnetic fluids. Tanahashi-Okanaga (22) and the authors (23), (24) reported the micropolar theory for electrically conducting fluids in which magnetic fluids were included.…”

Section: Introductionmentioning

confidence: 99%

“…When the volume concentration of suspended ferromagnetic particles φ tends to 1 under the assumption that electromagnetic field is steady and uniform, the equation of magnetization should reduce to the relaxation equation for solid ferromagnetic materials. However, the constitutive equations of magnetization proposed by Shizawa-Tanahashi (12) and the authors (14) leads to M → M 0 as φ → 1, where M is the magnetization and M 0 is the equilibrium magnetization. On the other hand, there has been uncertainty concerning whether the Abraham expression of electromagnetic momentum E × H/c 2 (where E is the electric field intensity vector, H is the magnetic field intensity vector and c is the speed of light) or the Minkowski expression D× B (where D is the electric flux density vector and B is the magnetic flux density vector) is appropriate.…”

Section: Introductionmentioning

confidence: 99%

“…However, it has not been cleared which expression is correct in the material control volume of magnetic fluids. In our previous papers (4), (13) - (15) and Shizawa-Tanahashi's theory (3), (11), (12) , D-H analogy and the Minkowski expression of electromagnetic momentum were adopted, thus, it is important to show the difference in the basic equations in cases of the Abraham expression and the Minkowski expression, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Basic Equations and Constitutive Equations of Micropolar Magnetic Fluids with E-B Analogy and the Abraham Expression of Electromagnetic Momentum

Ido

2005

JSME international journal. Ser. B, Fluids and thermal engineer

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A complete set of basic equations for magnetic fluids with internal rotation is proposed in this paper. The basic equations are derived from the conservation laws of mass, linear momentum, angular momentum and energy, while the constitutive equations are obtained by the thermodynamical method that is based on the free energy and the dissipation function. The concrete expression of constitutive equations are determined by the principle of material frame indifference and the principle of maximal dissipation rate. The Abraham expression of the electromagnetic momentum and E-B analogy are adopted in this theory. It is shown that the difference in the basic equations in case of adopting the Abraham expression and the Minkowski expression, respectively. The constitutive equation of magnetization which includes the Shliomis relaxation equation (1972) is proposed.

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New Constitutive Equations for Conducting Magnetic Fluids With Internal Rotation : Thermodynamical Discussions

Cited by 19 publications

References 0 publications

Micromagnetorotation of MHD Micropolar Flows

Micromagnetorotation of MHD Micropolar Flows

Continuum equations for magnetic and dielectric fluids with internal rotations

Basic Equations and Constitutive Equations of Micropolar Magnetic Fluids with E-B Analogy and the Abraham Expression of Electromagnetic Momentum

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