Showing papers on "Second-order fluid published in 2006"
TL;DR: In this article, an analysis for flow and heat transfer of a steady laminar boundary-layer flow of an electrically conducting fluid of second grade subject to suction and to a transverse uniform magnetic field past a semi-infinite stretching sheet is performed.
128 citations
TL;DR: The well known solutions for a Navier-Stokes fluid in the hydrodynamic case appear as the limiting cases of the solutions of this paper.
76 citations
TL;DR: In this article, the authors derived the relationship between the ensemble average stress in a dilute suspension of spheres and the imposed rate of strain and rotation for a general linear flow of a suspension in a second-order fluid.
Abstract: The relationship between the ensemble average stress in a dilute suspension of spheres and the imposed rate of strain and rotation is derived for a general linear flow of a suspension in a second-order fluid. In a Newtonian fluid, the particulate phase only contributes to the stress via the shear viscosity; the contribution takes the form of a stresslet, the symmetric first moment of the force distribution on the surface of a suspended particle. In a second-order fluid, the interactions of the particles and polymers contribute to the stress in three ways: (1) the particle-induced fluid velocity disturbance alters the polymer stress in the fluid; (2) the polymer stresses exerted on the particle contribute to the particle’s stresslet; (3) the non-Newtonian nature of the fluid changes the pressure and velocity field, thereby modifying the Newtonian contributions to the particle stresslet. The particle contributions Ψ 1 P and Ψ 2 P to the first and second normal stress differences are related to the corresponding stress differences ( Ψ 1 0 and Ψ 2 0 ) for the suspending fluid by Ψ 1 P = ( 5 / 2 ) ϕ Ψ 1 0 and Ψ 2 P = ( 75 / 28 ) ϕ Ψ 2 0 − ( 5 / 28 ) ϕ Ψ 1 0 , where ϕ is the particle volume fraction.
56 citations
TL;DR: In this article, the authors show that in the case of a micro-discharge modelling using the hydrodynamics assumption, the second order fluid model involving the complete electron momentum conservation equation must be used to better quantify the radical formation in a microdischarge applied to air pollution control.
Abstract: The present paper shows that in the case of a micro-discharge modelling using the hydrodynamics assumption, the second order fluid model involving the complete electron momentum conservation equation must be used in order to better quantify the radical formation in a micro-discharge applied to air pollution control. The present results show large differences in the micro-discharge parameters (such as velocity and electron density) between the three tested hydrodynamics models: the classical first order model using the local electric field approximation and two second order models using the local energy approximation with or without the drift–diffusion approximation. The tests have been carried out in the case of a wire-to-plane corona reactor filled with a typical flue gas (76% N2, 12% CO2, 6% O2, 6% H2O) at atmospheric pressure and ambient temperature. The simulation of the micro-discharge dynamics is performed using a 1.5D numerical streamer model coupled with a simple chemical kinetics model involving 31 species (charged and neutral particles in their fundamental or metastable state) reacting following 29 selected chemical reactions.
45 citations
TL;DR: In this article, an exact solution of an incompressible fluid of second-order by causing disturbances in the liquid, which is initially at rest due to bottom oscillating sinusoidally, has been obtained in terms of non-dimensional elasticoviscosity parameter ( ) which depends on the non-Newtonian coefficient and the frequency of excitation of the external disturbance while considering the porosity (K) of the medium.
Abstract: Exact solution of an incompressible fluid of second-order by causing disturbances in the liquid, which is initially at rest due to bottom oscillating sinusoidally, has been obtained in this study. The results presented are in terms of nondimensional elasticoviscosity parameter ( ) which depends on the non-Newtonian coefficient and the frequency of excitation of the external disturbance while considering the porosity (K) of the medium. The flow parameters are found to be identical with that of Newtonian case as 0 and K .
15 citations
TL;DR: In this article, it was shown that the results of Giesekus and Tanner are special cases of a more general theorem in which the velocity field, in any dimension, of the equilibrium Reiner-Rivlin problem also satisfies the corresponding problem for the materially steady stress system (a generalization of the CEF system).
Abstract: In 1963 Giesekus [H. Giesekus, Die simultane Translations- und Rotationsbewegung einer Kugel in einer elastikoviskosen Flussigkeit, Rheol. Acta 3 (1962) 59–71] showed that a Stokes velocity field also satisfies the equilibrium equation for the flow of a restricted form of the second order fluid. The same result was found by Tanner [R.I. Tanner, Plane creeping flows of incompressible second order fluids, Phys. Fluids 9 (1966) 1246–1247] in 1966 in the context of plane flow for which the restrictions on the second order fluid are not relevant. Tanner [R.I. Tanner, Some extended Giesekus-type theorems for non-Newtonian fluids, Rheol. Acta 28 (1989) 449–452] later showed that the velocity field for the inertialess, plane flow of the generalized Newtonian fluid is also the velocity field for the flow of a special form of the Criminale–Ericksen–Filbey (CEF) stress system [W.O. Criminale Jr., J.L. Ericksen, G.L. Filbey Jr., Steady flow of non-Newtonian fluids, Arch. Rat. Mech. 1 (1958) 410–417]. In this paper it will be shown that the results of Giesekus and Tanner are special cases of a more general theorem in which the velocity field, in any dimension, of the equilibrium Reiner–Rivlin problem also satisfies the corresponding problem for the materially steady stress system (a generalization of the CEF system) provided the coefficients of the Reiner–Rivlin stress [M. Reiner, A mathematical theory of dilatancy, Am. J. Math. 67 (1945) 350–362; R.S. Rivlin, The hydrodynamics of non-Newtonian fluids, Proc. R. Soc. Lond. 193 (1948) 260–281] are derivable from a strain-rate potential. As with the Giesekus–Tanner theorems the new theorem holds generally for velocity boundary conditions, but in some cases, such as the free jet, stress boundary conditions can be imposed.
13 citations
TL;DR: In this paper, the axisymmetric unsteady flow of a nonNewtonian incompressible second order fluid in a straight rigid and impermeable tube with circular cross-section of constant radius is analyzed.
Abstract: The aim of this paper is to analyze the axisymmetric unsteady flow of a nonNewtonian incompressible second order fluid in a straight rigid and impermeable tube with circular cross-section of constant radius. To study this problem, we use the one dimensional (1D) nine-directors Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this system we obtain the relationship between mean pressure gradient and volume flow rate over a finite section of the tube. Assuming that the pressure gradient rises and falls exponentially with time, the 3D exact solution for unsteady volume flow rate is compared with the corresponding 1D solution obtained by the Cosserat theory using nine directors.
12 citations
TL;DR: In this article, the velocity and temperature fields of the flow through a porous medium of a generalized second grade fluid with fractional derivative model are described by fractional partial differential equations and exact analytical solutions of these differential equations are obtained in terms of the Fox's H-function by using the discrete Laplace transform of the sequential fractional derivatives and Hankel transform.
11 citations
TL;DR: In this paper, the Lie symmetry analysis and the basic similarity reductions are performed for the rotating flow of a second-order fluid on a porous plate, and two new exact solutions generated from the similarity transformation to these equations, are provided.
9 citations
TL;DR: The introduction of a second-order FSPN in a fixed point iteration scheme has been made possible thanks to the efficiency of the proposed solution technique.
6 citations
01 Jan 2006
TL;DR: In this paper, the lateral migration of a neutrally buoyant rigid sphere suspended in a second-order fluid is studied theoretically for unidirectional two-dimensional flows, and the authors demonstrate the existence of migration induced by normal stresses whenever there is a lateral variation of the shear rate in the undisturbed flow.
Abstract: The lateral migration of a neutrally buoyant rigid sphere suspended in a secondorder fluid is studied theoretically for unidirectional two-dimensional flows. The results demonstrate the existence of migration induced by normal stresses whenever there is a lateral variation of the shear rate in the undisturbed flow. The migration occurs in the direction of decreasing absolute shear rate, which is towards the centre-line for a plane Poiseuille flow and towards the outer cylinder wall for Couette flow. The direction of migration agrees with existing experimental data for a viscoelastic suspending fluid, and qualitative agreement is found between the theoretically predicted and experimentally measured sphere trajectories.
TL;DR: In this article, the slow motion of rigid bodies of arbitrary shape sedimenting in a quiescent viscoelastic liquid under the action of gravity was studied and steady state solutions for small Weissenberg numbers and zero Reynolds numbers were derived.
Abstract: We study the slow motion of rigid bodies of arbitrary shape sedimenting in a quiescent viscoelastic liquid under the action of gravity. The liquid is modeled by the full second order fluid equations with arbitrary material parameters α 1 + α 2 . We show existence of steady state solutions for small Weissenberg numbers and zero Reynolds numbers and apply our equations to study the steady state orientations of symmetric bodies sedimenting in viscoelastic fluids.