A note on the universal stability of convective flow with variable viscosity

The stability of convective motion of a fluid driven by volumetric heat sources and applied pressure gradient is investigated. The viscosity of the fluid is assumed to depend linearly on temperature. The sufficient conditions for the existence of such a flow are obtained based on the energy inequalities. Copyright © 2007 John Wiley & Sons, Ltd.     

On the flow of a viscous incompressible fluid between two coaxial rotating porous cylinders

Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically.     

The flow of a variable viscosity fluid between parallel plates with shear heating

A model for the flow of a fluid through a channel with parallel plates is investigated. The channel is narrow, so that the lubrication approximation may be applied. The channel walls are maintained at a constant temperature. Shear heating effects are included and the fluid viscosity decreases exponentially with temperature. When the flow is driven solely by shear stress or imposed velocity at the top, analytical progress is possible. When pressure gradient also drives the flow the problem is solved numerically.     

A note on the unsteady flow of dusty viscous fluid between two parallel plates

We study the isothermal flow of a dusty viscous incompressible conducting fluid between two types of boundary motions-oscillatory and non-oscillatory, under the influence of gravitational force. Within the frame work of some physically realistic approximations and suitable boundary conditions, closed form solutions were obtained for the velocity profiles and the skin friction of the particulate flow. These results show that for a constant pressure gradient, only the velocity profile of the fluid and the skin friction are unaffected by gravity, while magnetic field is seen to affect both the fluid, particle velocities and the skin friction. Thus, our results are extension of previous results in literature, and graphical demonstration of some these solutions have been presented.     

Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a generalized Maxwell fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and after some time both cylinders suddenly begin to oscillate around their common axis with different angular frequencies of their velocities. The solutions that have been obtained are presented under integral and series forms in terms of generalized G and R functions. Moreover, these solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary Maxwell fluid are also obtained as limiting cases of our general solutions. At the end, flows corresponding to the ordinary Maxwell and generalized Maxwell fluids are shown and compared graphically by plotting velocity profiles at different values of time and some important results are remarked.     

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.     

Effect of a radial temperature gradient on the stability of the flow of a second-order fluid between two co-axial cylinders

Summary It has been found that the effect of a radial temperature gradient on the Taylor stability problem for a viscoelastic fluid and for a Newtonian fluid is the same.

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Résumé On montre que l'effet d'un gradient de la température radial sur le problème de stabilité de Taylor pour un fluide viscoélastique est semblable à celui d'un fluide Newtonien.

     

Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium

This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.     

Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effect of variable viscosity on the peristaltic flow of a Newtonian fluid in an asymmetric channel has been discussed. Asymmetry in the flow is induced due to travelling waves of different phase and amplitude which propagate along the channel walls. A long wavelength approximation is used in the flow analysis. Closed form analytic solutions for velocity components and longitudinal pressure gradient are obtained. The study also shows that, in addition to the effect of mean flow parameter, the wave amplitude also effect the peristaltic flow. This effect is noticeable in the pressure rise and frictional forces per wavelength through numerical integration.     

Effects of radial temperature gradient on the stability of flow of a viscous incompressible fluid between two rotating cylinders

Stability of the flow of a viscous incompressible fluid in a narrow gap between two concentric cylinders rotating in opposite directions is studied. Exact values of critical Taylor number for the first and second modes are derived by a numerical procedure and these are compared with the known results. It is observed that the value of the critical Taylor number T_crit decreases with increasing the values of a parameter $\text{N (N =}\text{Ra}\text{T}\text{,}\text{Ra = Rayleigh number, T = Taylor number}\text{)}$, and the rate of decrease in the value of T_crit is more when the two cylinders rotate in the opposite directions.     

A note on the regularity of flows with shear-dependent viscosity

We consider a non-Newtonian fluid governed by stationary, incompressible Navier–Stokes equations with shear-dependent viscosity. Using a fixed point argument in an appropriate functional setting, we establish the existence of a strong solution for small and suitably regular data. Uniqueness results are obtained under similar conditions.     

A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid

The velocity field and the adequate tangential stress that is induced by the flow due to a constantly accelerating plate in an Oldroyd-B fluid, are determined by means of Fourier sine transforms. The solutions corresponding to a Maxwell, Second grade and Navier–Stokes fluid appear as limiting cases of the solutions obtained here. However, in marked contrast to the solution for a Navier–Stokes fluid, in the case of an Oldroyd-B fluid oscillations are set up which decay exponentially with time.     

Flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders in the presence of magnetic field

In this paper, the flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders has been investigated in the presence of magnetic field. For this purpose, the constitutive equation of such a fluid flow was simplified, and the existence of the solution to the governing equation was established using Schauder's fixed point theorem. Using the finite difference method, the numerical solution of the non-dimensionalized form of the established governing equation was obtained. The effect of sundry parameters such as the rotating speed of the cylinders, the physical properties of fluid, and magnetic field intensity on the fluid velocity field was studied as well.     

A note on some solutions for the flow of a fourth grade fluid in a porous space

This paper investigates the time independent unidirectional flow of a fourth grade fluid filling the porous half space. Flow modelling is based upon a modified Darcy’s law. Travelling wave and conditional symmetry solutions are developed. The graphs are plotted and discussed for the sundry parameters.     

A note on the proportionate flow shop with a bottleneck machine

Choi, B.-C., Yoon, S.-H., Chung, S.-J., 2007. Minimizing maximum completion time in a proportionate flow shop with one machine of different speed. European Journal of Operational Research 176, 964–974 consider the proportionate flow shop with a slow bottleneck machine and propose the SLDR heuristic for it. Choi et al. (2007) derive a data-dependent worst-case ratio bound for the SLDR heuristic which is then bounded by two. In this note, we show that the tight worst-case ratio bound of the SLDR heuristic is 3/2.     

Effects of variable viscosity on pulsatile flow of blood in a tapered stenotic flexible artery

The objective of the present study is to investigate the effects of variable viscosity on incompressible laminar pulsatile flow of blood through an overlapping doubly constricted tapered artery. To mimic the realistic situation, wall of the artery is taken to be flexible, and physiologically relevant pulsatile flow is introduced. The governing equations of blood flow are made dimensionless. A coordinate transformation is used to make the overlapping doubly constricted wall geometry of tube to a straight tube. Taking advantage of the Stream function–Vorticity formulation, the system of partial differential equations is then solved numerically by finite difference approximations. Effects of Reynolds number, Strouhal number, degree of contraction, tapering angle, and viscosity parameters are presented graphically and analyzed. The results show that formation of stenosis and tapering disturb the flow field significantly, and degree of stenosis is more important in influencing blood flow compared with tapering.     

A note on the cpu usage of a computer system with many I/O channels

A recursive formula, to model CPU performance of a multiprogrammed computer system, is derived using a conventional mathematical model. This new formula computes faster and gives reliable results in cases where the conventional one fails to produce any.     

A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit

We revisit a result by Coron and Guerrero stating that the one-dimensional transport-diffusion equation

     

A remark on the Cauchy problem of 1D compressible Navier-Stokes equations with density-dependent viscosity coefficients

This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefcients.By assumingρ0∈L1（R）,we will prove the existence of weak solutions to the Cauchy problems forθ〉0.This will improve results in Jiu and Xin’s paper（Kinet.Relat.Models,1（2）：313–330（2008））in whichθ〉12is required.In addition,We will study the large time asymptotic behavior of such weak solutions.