Mixed convection of non-newtonian fluids from a vertical plate embedded in a porous medium

This paper investigates mixed free and forced convection of non-Newtonian fluids from a vertical isothermal plate embedded in a homogenous porous medium. A mathematical model is developed based on the modified Darcy's law and boundary-layer approximations, and the exact similarity solution is obtained as well as an integral solution. These two solutions agree within 3% for aiding flows and 10% for opposing flows. It is found that, non-Newtonian characteristics of fluids have appreciable influences on velocity profiles, temperature distributions and flow regimes.     

Non-Newtonian effects of second-order fluids on double-layered porous Rayleigh-step bearings

Theoretical study of double-layered porous Rayleigh-step bearings with second-order fluid as lubricant is presented. An approximate method for the solutions of the governing fluid film equations for a porous region is proposed. The expressions for the pressure distribution, load capacity and frictional coefficient are obtained in compact form. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. It is found that the double porous layer yields an increase in the load capacity and ensures decrease in frictional force at the porous lining as compared with the conventional porous Rayleigh-step bearings. The maximum dimensionless load-carrying capacity is found to occur at a slightly larger step ratio as compared with the conventional porous Rayleigh-step bearings.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Internal waves from a body accelerating in a thermocline

Many papers study the steady wave system around bodies moving in thermoclines but little attention has been given to unsteady wave systems. This paper concentrates on the unsteady wave systems around accelerating bodies in thermoclines. The wave shapes are calculated using a theory derived from a dispersion relation based on an exp-tanh density profile. All modes of oscillation can be determined and it is shown that for the lowest mode both oblique and transverse waves occur whereas for the higher modes the presence of transverse waves depends on the background conditions and on the speed of the body. Cauchy-Poisson impulsive start waves are included. The theoretical wave shapes compare quite well with those calculated using finite-difference formulations of the full Navier-Stokes equations when a body accelerates from rest.It is also shown how the dispersion relation =N sin together with the WKB approximation can produce the same plan-view wave forms as those obtained using the thermocline wave dispersion relation given by [17, 30].     

On the existence of self-similar solutions of the equations governing unsteady flow through a porous medium

In this paper the conditions for the existence of self-similar solutions of the equations governing unsteady flows through a porous medium are presented and discussed. The first two sections deal with the case of non-Newtonian fluids of power-law behavior; the third section analyzes the case of non-Darcy gas flows. The boundary and initial conditions occuring currently in a large class of fluid mechanics problems, of practical interest in engineering, are considered.     

Constitutive relations for the interaction force in multicomponent particulate flows

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.     

The solid–fluid transition in a yield stress shear thinning physical gel

We present an experimental investigation of the solid–fluid transition in a yield stress shear thinning physical gel (Carbopol^® 940) under shear. Upon a gradual increase of the external forcing, we observe three distinct deformation regimes: an elastic solid-like regime (characterized by a linear stress–strain dependence), a solid–fluid phase coexistence regime (characterized by a competition between destruction and reformation of the gel), and a purely viscous regime (characterized by a power law stress-rate of strain dependence). The competition between destruction and reformation of the gel is investigated via both systematic measurements of the dynamic elastic moduli (as a function of stress, the amplitude, and temperature) and unsteady flow ramps. The transition from solid behavior to fluid behavior displays a clear hysteresis upon increasing and decreasing values of the external forcing. We find that the deformation power corresponding to the hysteresis region scales linearly with the rate at which the material is being forced (the degree of flow unsteadiness). In the asymptotic limit of small forcing rates, our results agree well with previous steady state investigations of the yielding transition. Based on these experimental findings, we suggest an analogy between the solid–fluid transition and a first-order phase transition, e.g., the magnetization of a ferro-magnet where irreversibility and hysteresis emerge as a consequence of a phase coexistence regime. In order to get further insight into the solid–fluid transition, our experimental findings are complemented by a simple kinetic model that qualitatively describes the structural hysteresis observed in our rheological experiments. The model is fairly well validated against oscillatory flow data by a partial reconstruction of the Pipkin space of the material’s response and its nonlinear spectral behavior.