Abstract:
The second-law analysis of a non-Newtonian fluid flowing through a channel made of two heated parallel plates is investigated. The flow is assumed to be steady, laminar and fully-developed. The effect of heat generation by viscous dissipation is included. Velocity, temperature and entropy generation profiles are presented. The effects of the flow behaviour index, the Brinkman number and the group parameter on velocity, temperature and entropy generation number are discussed. The results show that velocity profile depends largely on the flow behaviour index. They are flat near the centreline of the channel for pseudoplastic fluids and linear for dilatant fluids. Temperature profiles are higher for higher flow behaviour index and Brinkman number. The entropy generation number increases with Brinkman number and the group parameter because of the heat generated by viscous dissipation effect. For pseudoplastic fluids, the irreversibility is dominated by heat transfer, whereas, for dilatant fluids, irreversibility due to fluid friction is more dominant.

Abstract:
In this paper we consider the problem of a steady MHD flow of a non-Newtonian power-law and electrically conducting fluid in presence of an applied magnetic field. The boundary layer equations are solved in similarity form via the Lyapunov energy method, we show that this problem has an infinite number of positive global solutions.

Abstract:
The aim of this work is related to an analysis of journal bearings lubrication using non-Newtonian fluids which are described by a power-law model. The performance characteristics of the journal bearings are determined for various values of the non-Newtonian power-law index “ ” which is equal to: 0.9, 1, and 1.1. Obtained numerical results show that for the dilatant fluids ( ), the load-carrying capacity, the pressure, the temperature, and the frictional force increased while for the pseudo-plastic fluids ( ) they decreased. The influence of the thermal effects on these characteristics is important at higher values of the flow behavior index “ .” Obtained results are compared to those obtained by others. Good agreement is observed between the different results. 1. Introduction The evolution of machines with severe operating conditions, following to the number of revolutions increasingly high and shafts strongly charged, has a consequence on energy dissipation in the lubricating film by shearing. The dissipated energy induces an increase in the fluid film temperature, a reduction of the lubricant fluid viscosity and the bearing pressure of the mechanism, and a premature wear of the material used. The isothermal theory of lubrication is widely used in the performances determination of the butted and hydrodynamic bearings. However, the technological requirements, such as the increase in loads and the number of revolutions per hours, generate important dissipation of energy in the lubricated mechanisms [1]. The classical theory of lubrication developed by O. Reynolds for isothermal cases is improved by Kingsbury [2] by taking into account the heat transfer phenomena and by assuming the fluid used as viscous and Newtonian. However, in most mechanisms encountered in real situations, non-Newtonian fluids are used in order to increase the lubricants viscosity index by adding additives such as polymers [3]. The first approach modelling of the thermal aspect of lubrication was proposed by Kingsbury, in order to take into account the temperature evolution through the thickness of the film. The method of resolution applied to the conical sleeve viscometer case is a graphic method. In his study, Kingsbury has showed that the shearing stress of the bearing surface is about 40% of the constraint value calculated by using the isothermal theory. It can be deduced easily whereas the heating of the film causes a reduction of the load supported by the shaft of 60% compared to the load calculated by the isothermal theory for similar operating conditions. The behaviour’s law

Abstract:
ABSTRACT Non-Newtonian fluids are often used during various drilling, workover and enhanced oil recovery processes. Most of the fracturing fluids injected into reservoir-bearing formations possess non- Newtonian nature and these fluids are often approximated by Newtonian fluid flow models. In the field of well testing, several analytical and numerical models based on Bingham, pseudoplastic and dilatant non-Newtonian behavior, have been introduced in the literature to study their transient nature in porous media for a better reservoir characterization. Most of them deal with fracture wells and homogeneous formations. Well test interpretation is conducted via the straight-line conventional analysis or type-curve matching. Only a few studies consider the pressure derivative analysis. However, there is a need for a more practical and accurate way of characterizing such systems. So far, there is no methodology to characterize heterogeneous formation bearing non-Newtonian fluids through well test analysis. In this study, an interpretation methodology using the pressure and pressure derivative log-log plot is presented for non-Newtonian fluids in naturally fractured formations. The dimensionless fracture storativity ratio, omega, and interporosity flow parameter, lambda, are obtained from characteristics points found on such plot. The developed equations and correlations are successfully verified by their application only to synthetic well test data since no actual field data are available. A good match is found between the results provided by the proposed technique and the values used to generate the simulated data. RESUMEN Los fluidos no Newtonianos se usan a menudo en varios procesos de perforación, trabajo a pozos y actividades de recobro mejorado. La mayoría de los fluidos de fracturamiento inyectados en los yacimientos que contienen hidrocarburos se comportan no Newtoniamente y, sin embargo, estos fluidos comúnmente se representan en los modelos como modelos fluidos Newtonianos. En el campo de pruebas de presión, se han desarrollado varios modelos numéricos y analíticos que tienen en cuenta el comportamiento no Newtoniano Bingham, pseudoplá;stico y dilatante, para estudiar la naturaleza transitoria de estos fluidos en una mejor caracterizacion del yacimiento. Se han propuesto varios modelos numericos y analiticos para estudiar el comportamiento transitorio de los fluidos no Newtonianos en medios porosos. La mayoría de ellos tratan pozos fracturados y formaciones homogeneas y la interpretacion de los datos de presion se conduce mediante el metodo convencio

Abstract:
We carry out an analytical study of laminar circular hydraulic jumps, in generalized-Newtonian fluids obeying the two-parametric power-law model of Ostwald-de Waele. Under the boundary-layer approximation we obtained exact expressions determining the flow, an implicit relation for the jump radius is derived. Corresponding results for Newtonian fluids can be retrieved as a limiting case for the flow behavior index n=1, predictions are made for fluids deviating from Newtonian behavior.

Abstract:
We prove that there exists a class of non-stationary solutions to the Einstein-Euler equations which have a Newtonian limit. The proof of this result is based on a symmetric hyperbolic formulation of the Einstein-Euler equations which contains a singular parameter $\ep = v_T/c$ where $v_T$ is a characteristic velocity scale associated with the fluid and $c$ is the speed of light. The symmetric hyperbolic formulation allows us to derive $\ep$ independent energy estimates on weighted Sobolev spaces. These estimates are the main tool used to analyze the behavior of solutions in the limit $\ep \searrow 0$.

Abstract:
The perturbations of weakly-viscous, barotropic, non-self-gravitating, Newtonian rotating fluids are analyzed via a single partial differential equation. The results are then used to find an expression for the viscosity-induced normal-mode complex eigenfrequency shift, with respect to the case of adiabatic perturbations. However, the effects of viscosity are assumed to have been incorporated in the unperturbed (equilibrium) model. This paper is an extension of the normal-mode formalism developed by Ipser & Lindblom for adiabatic pulsations of purely-rotating perfect fluids. The formulas derived are readily applicable to the perturbations of thin and thick accretion disks. We provide explicit expressions for thin disks, employing results from previous relativistic analyses of adiabatic normal modes of oscillation. In this case, we find that viscosity causes the fundamental p- and g- modes to grow while the fundamental c-mode could have either sign of the damping rate.

Abstract:
We prove some regularity results for a class of two dimensional non-Newtonian fluids. By applying results from [Dashti and Robinson, Nonlinearity, 22 (2009), 735-746] we can then show uniqueness of particle trajectories.

Abstract:
We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier-Stokes equations.

Abstract:
We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad's moment method.