Mehrdad Massoudi

Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe

Abstract The flow of a fluid-solid mixture is very complicated and may depend on many variables, such as the physical properties of each phase and the size and shape of the solid particles. One approach to the study of these flows is to model the mixture as a non-Newtonian fluid. Much effort has been put into analyzing various transport processes in non-Newtonian fluids, such as coal slurries. Heat transfer plays an important role in the handling and processing of these fluids. In this paper, the fully developed flow of an incompressible, thermodynamically compatible fluid of grade three in a pipe is studied. The temperature of the pipe is assumed to be higher than the temperature of the fluid and the shear viscosity of the fluid is assumed to be a function of the temperature.

Flow of a fluid—solid mixture between flat plates

Abstract A mathematical description for a flowing mixture of solid particulates and a fluid is developed within the context of mixture theory. Specifically, the equations governing the flow of a two-component mixture of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing a steady flow of the mixture between flat plates. The resulting boundary value problem is solved numerically and results are presented for cases in which drag and lift interactions are important.

Flow of a fluid infused with solid particles through a pipe

Abstract Using a mathematical description for a flowing mixture of solid particulates developed previously within the context of Mixture Theory, the equations governing the flow of a two-component mixture of a Newtonian fluid and a granular solid are derived. In the case of steady pressure driven flow through a pipe of circular cross-section, these equations reduce to a system of coupled ordinary differential equations. The resulting boundary value problem is solved numerically and results are presented for cases in which drag and lift interactions are important.

Flow of a generalized second grade fluid between heated plates

SummaryWe examine the fully developed flow of a generalized fluid of second grade between heated parallel plates, due to a pressure gradient along the plate. The constant coefficient of shear viscosity of a fluid of second grade is replaced by a shear dependent viscosity with an exponentm. If the normal stress coefficients are set equal to zero, this model reduces to the standard power-law model. We obtain the solution for the case when the temperature changes only in the direction normal to the plates for the two most commonly used viscosity models, i.e. (i) when the viscosity does not depend on temperature, and (ii) when the viscosity is an exponentially decaying function of temperature.

Constitutive relations for the interaction force in multicomponent particulate flows

Abstract In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.

Pulsatile flow of blood using a modified second-grade fluid model

We study the unsteady pulsatile flow of blood in an artery, where the effects of body acceleration are included. The blood is modeled as a modified second-grade fluid where the viscosity and the normal stress coefficients depend on the shear rate. It is assumed that the blood near the wall behaves as a Newtonian fluid, and in the core as a non-Newtonian fluid. This phenomenon is also known as the Fahraeus-Lindqvist effect. The equations are made dimensionless and solved numerically.

A theory for granular materials exhibiting normal stress effects based on Enskog's dense gas theory

Abstract Granular materials exhibit phenomena such as normal stress differences, which are typical of materials whose response is non-linear. For example, when a non-linearly elastic slab is sheared, its motion is not determined by the shear force but by the normal forces that manifest themselves due to the shearing (Poynting effect). Another example is a non-linear fluid which exhibits normal stress differences that lead to phenomena like “die-swell” or “rod-climbing,” which is again a manifestation of the stresses that develop orthogonal to planes of shear. In this paper, an expression for the stress tensor of a granular material that can exhibit normal-stress effects due to a solids fraction gradient is derived from both continuum and kinetic models. The continuum model motivates and develops the form of the stress tensor, but introduces undetermined coefficients. The kinetic model evaluates those coefficients using Enskogs dense gas theory. The dependence of the granular stress tensor on the solids fraction gradient arises by requiring that the correlating factor that links the two-particle distribution function to the two single-particle distribution functions be the contact value for the radial distribution function of a non-homogeneous, hard-sphere fluid. A representation for that contact value is found by developing the generalized van der Waals theory expression for a stress tensor element of a nonhomogeneous fluid (a fluid that exhibits a density gradient) in equilibrium, and comparing it to the exact expression. That representation of the contact value is introduced into the two-particle distribution function, and its contribution to the stress tensor is found. The resulting stress tensor expression is applied to a simple shear flow problem in which a linear, solids-fraction profile is transverse to the flow. The resulting normal-stress effects increase with the solids-fraction and its gradient.

A continuum model for granular materials: Considering dilatancy and the Mohr-Coulomb criterion

SummaryIn this paper we will explore the consequences of the Mohr-Coulomb criterion on the constitutive equation proposed by Rajagopal and Massoudi [1]. This contunuum model which is based on the earlier works of Cowin [2] has also the ability to predict the dilatancy effect which is related to the normal stress effects. At the same time, if a proper representation is given to some of the material parameters, this model would also comply with the Mohr-Coulomb criterion. We also present, as a special case, an exact solution for the case of simple shear flows.

Effect of injection or suction on the Falkner-Skan flows of second grade fluids

Abstract The boundary layer flow of an incompressible fluid of grade two past a wedge with surface injection or suction placed symmetrically with respect to the flow direction is investigated. The effects of the non-Newtonian nature of fluid on the shear stress at the wall and the velocity profiles for different injection/suction rates and different wedge angle factor β are studied.

Local non-similarity solutions for the flow of a non-Newtonian fluid over a wedge

Abstract The boundary layer and heat transfer equations for a non-Newtonian fluid, represented by a power-law model, over a porous wedge is studied. The free stream velocity, the surface temperature variations, and the injection velocity at the surface are assumed variables. Similar and non-similar solutions are presented and the restrictions for these cases are studied. The results are presented for velocity and temperature profiles for various values of the dimensionless numbers. The effects of the different parameters on the skin friction co-efficient and the local heat transfer co-efficient are also studied.