Theories of Fluids with Microstructure

Stokes, Vijay K.

doi:10.1007/978-3-642-82351-0

Cited by 209 publications

(162 citation statements)

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“…The fluid angular velocity in the cylinder axis direction z  on the wall surface should therefore be the wall angular velocity  . The no-slip condition has been recognized as the physically more suitable boundary condition in the literature 22,30 . Next, we physically describe the interaction between a fluid point and a wall surface as well as the interaction between a magnetization (magnetic moment per unit volume of the fluid) and a magnetic field and mathematically state the boundary setting.…”

Section: Boundary Settingmentioning

confidence: 99%

Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation

Weng¹,

Chen²,

Chang³

2013

Smart Science

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Section: Boundary Settingmentioning

confidence: 99%

Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation

Weng¹,

Chen²,

Chang³

2013

Smart Science

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“…The properties, applications and the earlier literature on of micropolar fluid flow can be found in Refs. 16,17. Reiner 18 performed the first investigation into non-Newtonian flow between two cylinders then several micropolar studies were reported much later.…”

Section: Introductionmentioning

confidence: 99%

The effects of Soret and Dufour, chemical reaction, Hall and ion currents on magnetized micropolar flow through co-rotating cylinders

Gajjela

Matta

Kaladhar³

2017

AIP Advances

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The influence of cross diffusions, Hall and Ion slip of a dissipative magnetized micropolar fluid flow through an infinite concentric rotating vertical cylinders were investigated in addition to the first order chemical reaction. Cylinders are taken into account for Isothermal (constant temperature wall condition) and mixed gradient condition at inner cylinder, while convection cooling and constant wall concentration condition is taken at outer cylinder. The governing equations in cylindrical polar coordinates are coupled ordinary differential equations (ODEs) and are solved numerically with help of Shooting method with fourth order Runge Kutta method. A parametric study illustrating the influence of the emerging parameters on flow, heat and mass transfer components as well as on Skin Friction, Nusselt number and Sherwood number through graphical illustrations.

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“…The purpose of the present paper is to investigate the effect of couple stresses on the flow by obtaining the effect of the couple stress parameter besides other parameters entering the problem on the velocity distribution. The field equations are [7]:The continuity equationρ + ρv i,i = 0, Cauchy's first law of motion ρa i = T ji, j + ρ f i , and Cauchy's second law of motion M ji, j + ρ i + e i jk T jk = 0, where ρ is the density of the fluid, v i are the velocity components, a i the components of the acceleration, T i j is the second order stress tensor, M i j the second order couple stress tensor, f i the body force per unit volume, i the body Unauthenticated Download Date | 5/11/18 6:27 AM …”

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Effect of Couple Stresses on the MHD of a Non-Newtonian Unsteady Flow between Two Parallel Porous Plates

Eldabe

Hassan

Mohamed

2003

Zeitschrift Für Naturforschung A

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In this paper the MHD of a Non-Newtonian unsteady flow of an incompressible fluid under the effect of couple stresses and a uniform external magnetic field is analysed by using the Eyring Powell model. In the first approximation the solution is obtained by using the Mathematica computational program with assuming a pulsatile pressure gradient in the direction of the motion. In the second order approximation a numerical solution of the non-linear partial differential equation is obtained by using a finite difference method. The effects of different parameters are discussed with the help of graphs in the two cases. In [4] an unsteady MHD non-Newtonian flow between two parallel fixed porous walls was studied using the Eyring Powell model [5], and in first approximation an exact solution of the velocity distribution was obtained if the pressure gradient in the direction of the motion is an arbitrary function of time. In second approximation a numerical solution was obtained when the pressure gradient is constant. A non-0932-0784 / 03 / 0400-0204 $ 06.00 c 2003 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com Newtonian fluid flow between two parallel walls, one of them moving with a uniform velocity under the action of a transverse magnetic field, was studied in [6].The present paper treats the flow of a pulsatile nonNewtonian incompressible and electrically conducting fluid in a magnetic field. Possible applications of these calculations are the flow of oil under ground, where there is a natural magnetic field and the earth is considered as a porous solid, and the motion of blood through arteries where the boundaries are porous.Couple stresses are the consequence of assuming that the mechanical action of one part of a body on another across a surface is equivalent to a force and moment distribution. In the classical nonpolar theory, moment distributions are not considered and the mechanical action is assumed to be equivalent to a force distribution only. The state of stress is measured by a stress tensor τ i j and a couple stress tensor M i j . The purpose of the present paper is to investigate the effect of couple stresses on the flow by obtaining the effect of the couple stress parameter besides other parameters entering the problem on the velocity distribution. The field equations are [7]:The continuity equationρ + ρv i,i = 0, Cauchy's first law of motion ρa i = T ji, j + ρ f i , and Cauchy's second law of motion M ji, j + ρ i + e i jk T jk = 0, where ρ is the density of the fluid, v i are the velocity components, a i the components of the acceleration, T i j is the second order stress tensor, M i j the second order couple stress tensor, f i the body force per unit volume, i the body Unauthenticated Download Date | 5/11/18 6:27 AM

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Theories of Fluids with Microstructure

Cited by 209 publications

References 1 publication

Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation

Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation

The effects of Soret and Dufour, chemical reaction, Hall and ion currents on magnetized micropolar flow through co-rotating cylinders

Effect of Couple Stresses on the MHD of a Non-Newtonian Unsteady Flow between Two Parallel Porous Plates

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