Showing papers on "Second-order fluid published in 2012"
TL;DR: In this article, an ensemble averaging technique was used to calculate the average stress for a dilute suspension of liquid drops that are instantaneously spherical, where the solvent and the drops consist of second-order fluids with differing properties.
Abstract: We use an ensemble averaging technique to calculate the average stress for a dilute suspension of liquid drops that are instantaneously spherical. The solvent and the drops consist of second-order fluids with differing properties. The suspension is itself a second-order fluid and its viscosity and normal stress coefficients are determined. For the special case of a rigid sphere suspension the results agree with Koch & Subramanian (J. Non-Newtonian Fluid Mech., vol. 138, 2006, p. 87, and vol. 153, 2008, p. 202). Differences from other results in the literature are discussed.
27 citations
TL;DR: In this article, the influence of heat and mass transfer on the peristaltic flow of magnetohydrodynamic second-order fluid in a channel when the induced magnetic field effects are present is investigated.
Abstract: SUMMARY
In this article, we investigate the influence of heat and mass transfer on the peristaltic flow of magnetohydrodynamic second-order fluid in a channel when the induced magnetic field effects are present. Problem formulation in a wave frame of reference is presented. The governing nonlinear analysis is carried out under the assumption of small wave number. Explicit expressions of the pressure gradient, the stream function, the magnetic force function, the axial induced magnetic field, the current density distribution, the temperature, and the concentration distribution are derived. The effects of embedded parameters are also examined. Copyright © 2011 John Wiley & Sons, Ltd.
25 citations
TL;DR: In this article, the slow sedimentation of a dilute suspension of spherical particles in a second-order fluid is investigated using theory and numerical simulations, where the velocity of the particle is calculated, and the nonlinear coupling of the settling motion with the local flow field is shown to result in a lateral drift in a direction perpendicular to gravity.
Abstract: The slow sedimentation of a dilute suspension of spherical particles in a second-order fluid is investigated using theory and numerical simulations. We first analyze the motion of a single isolated spherical particle sedimenting under gravity when placed in a linear flow field. In the limit of weak viscoelasticity (low Deborah number), the velocity of the particle is calculated, and the nonlinear coupling of the settling motion with the local flow field is shown to result in a lateral drift in a direction perpendicular to gravity. By the same effect, the mean flow driven by weak horizontal density fluctuations in a large-scale suspension of hydrodynamically interacting particles will also result in a horizontal drift, which has the effect of reinforcing the fluctuations as we demonstrate using a linear stability analysis. Based on this mechanism, an initially homogeneous suspension is expected to develop concentration fluctuations, a prediction supported by previous experiments on sedimentation in polymer...
21 citations
TL;DR: In this paper, the authors study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in the gradients of the hydrodynamic variables and show that conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier-Stokes form.
16 citations
TL;DR: In this article, a second-order fluid model was proposed to predict cross-slope height variations in regions with considerable crossslope velocity shear, consistent with the experiments.
Abstract: Laboratory experiments have shown that the steady flow of granular material down a rough inclined plane has a surface that is not parallel to the plane, but has a curvature across the slope with the height increasing toward the middle of the flow. We study this observation by postulating a new granular rheology, similar to that of a second order fluid. This model is applied to the experiments using a shallow water approximation, given that the depth of the flow is much smaller than the width. The model predicts that a second normal stress difference allows cross-slope height variations to develop in regions with considerable cross-slope velocity shear, consistent with the experiments. The model also predicts the development of lateral eddies, which are yet to be observed.
11 citations
TL;DR: In this article, a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor, is considered.
Abstract: We consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a appropriate modified form These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid Generalized thermodynamic constraints on the constitutive equation are presented The required properties of free energy functionals are discussed In particular, it is shown that they differ from the standard Graffi conditions Various free energy functionals, which are well-known in relation to simple materials, are generalized so that they apply to this fluid In particular, expressions for the minimum free energy and a more recently introduced explicit functional of the minimal state are proposed Derivations of various formulae are abbreviated if closely analogous proofs already exist in the literature
8 citations
01 Jan 2012
TL;DR: In this article, the authors considered the unsteady flow of an incompressible electrically conducting second grade fluid in a rigidly rotating parallel plate channel bounded below by a sparsely packed porous bed.
Abstract: In this paper, we consider the unsteady flow of an incompressible electrically conducting second grade fluid in a rigidly rotating parallel plate channel bounded below by a sparsely packed porous bed. The flow in nonporous region is governed by the equation of motion derived using the constitutive equation for the stress in compressible second order fluid, while the Brinkman’s model equation has been used for the momentum equation in the porous bed. In the undisturbed state both the fluid and the plates are in rigid rotation with same angular velocity about the normal to the plates and at t >0 the fluid is driven by the constant pressure gradient-parallel to the channel wall and in addition, the lower plate perform non-torsional oscillation in its own plane. Exact solution of the velocity in the clean fluid and the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated and the ultimate quasi steady state solution has been derived analytically and its behaviour is computationally discussed with reference to the governing parameter. The shear stress on the boundary is obtained analytically and its behaviour is computationally discussed.
5 citations
TL;DR: In this article, the effect of magnetic parameter and permeability on non-Newtonian fluid flow was studied and the results of steady non Newtonian flow with second order flow were derived.
Abstract: The aim of the paper is to study non Newtonian fluid flow of second order flowing through porous medium bounded by an impermeable infinite plate rotating with acceleration. We have studied all the special cases regarding the effect of permeability of the medium and the micro rotation of the fluid above the infinite plate under the influence of magnetic field. Various situations of the flow with Newtonian case are derived as special cases. Several investigations are made at length. The effect of porous medium increase the flow of the fluid with a decrease in permeability K. The presence of magnetic parameter decrease the flow pattern as its values increase. The effects of magnetic parameter and permeability will decrease the boundary layer and the results of steady non Newtonian Fluid flow will also be deduced as k 0.
3 citations
01 Jan 2012
TL;DR: In this article, the diffusion of reactive species undergoing first-order chemical reaction in a boundary layer flow of an incompressible homogeneous second order fluid over a linearly shrinking sheet in the presence of a transverse magnetic field was studied.
Abstract: This paper deals with the study of diffusion of reactive species undergoing first-order chemical reaction in a boundary layer flow of an incompressible homogeneous second order fluid over a linearly shrinking sheet in the presence of a transverse magnetic field. Using similarity variables, the boundary layer equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations. Exact solutions of the reduced equations are obtained for power-law surface concentration (PSC) as well as power-law wall mass flux (PMF) boundary conditions. The study reveals that the velocity is getting more closer towards wall for increasing magnetic parameter whereas it is going away from the wall for increasing viscoelastic parameter. It is also found that the diffusion of reactive species is considerably reduced with increasing values of Schmidt number, magnetic and reaction rate parameter whereas it is increased for enhanced values of viscoelastic parameter for both PSC and PMF cases. For PSC case, the concentration boundary layer thickness is enhanced with the increasing values of power-law index parameter. Negative concentration is observed in some cases which may not have real world applications.
2 citations
TL;DR: In this article, the authors investigated the effect of elastico-viscosity, cross viscosity parameters and ratio of the angular velocity on the temperature profile and Nusselt number for the cases of radial outflow and inflow in the regions of no-recirculation and recirculation.
Abstract: The problem of heat transfer in the steady flow of an incompressible second-order fluid between two enclosed discs rotating with different angular velocities has been discussed. The effect of elastico-viscosity, cross-viscosity parameters and ratio of the angular velocity on the temperature profile and Nusselt number for the cases of radial outflow and inflow have been investigated in the regions of no-recirculation and recirculation.