The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium

In this article, analysis is presented to study the effect of Hall current on the rotating flow of a non-Newtonian fluid in a porous medium taking into consideration the modified Darcy's law. The Oldroyd-B fluid model is used to characterize the non-Newtonian fluid behavior. The governing equations for unsteady rotating flow have been modeled in a porous medium. The analysis includes the flows induced by general periodic oscillations and elliptic harmonic oscillations of a plate. The effect of the various emerging parameters is discussed on the velocity distribution. The analytical results are confirmed mathematically by giving comparison with previous studies in the literature. It is observed that the velocity distribution increases with an increase of Hall parameter. The behavior of permeability is similar to that of the Hall parameter.     

Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions

The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method (HAM) is discussed graphically and numerically. The graphs are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed.     

On corner flows of Oldroyd-B fluids

Exact series solutions for planar creeping flows of Oldroyd-B fluids in the neighbourhood of sharp corners are presented and discussed. Both reentrant and non-reentrant sectors are considered. For reentrant sectors it is shown that more than one type of series solution can exist formally, one type exhibiting Newtonian-like asymptotic behaviour at the corner, away from walls, and another type exhibiting the same kind of asymptotics as an Upper Convected Maxwell (UCM) fluid. The solutions which are Newtonian-like away from walls are shown to develop non-integrable stress singularities at the walls when the no-slip velocity boundary condition is imposed. These mathematical solutions are therefore inadmissible from the physical viewpoint under no-slip conditions. An inadmissible solution, with stress singularities which are not everywhere integrable, is identified among the solutions of UCM-type. For a 270° reentrant sector the radial behaviour of the normal stress is everywhere r^−0.613. In the viscometric region near a wall, the radial normal stress σ^rr behaves like (rε)^−0.613, where ε is the angle made with the wall. In addition σ^rθ is infinite (not integrable) at the wall even when r is non-zero. Another UCM-type solution has a normal stress behaviour away from walls which is r^−0.985 for 270° sector. Again, this solution has a non-integrable stress singularity and is therefore inadmissible. Finally, for non-reentrant sectors it is shown that the flow is always Newtonian-like away from walls.     

Stagnation point flow of a micropolar fluid towards a stretching sheet

The steady two-dimensional stagnation point flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation point, has been studied in this paper. The resulting equations of non-linear ordinary coupled differential equations are solved numerically using the Keller-box method. The results obtained for velocity, microrotation and skin friction are shown in tables and graphs. Comparison with the recent results of Mahapatra and Gupta {Heat Mass Transfer 38 (2002) 517} for the corresponding problem of a viscous fluid (K=0) has been done and it has been shown that the results are in excellent agreement.     

Squeezing of an Oldroyd-B fluid from a tube: Limiting Weissenberg number

It is shown that the squeezing flow of an Oldroyd-B fluid from a tube with a prescribed time-dependent radius has an exact separable solution. In the special case where the tube radius varies exponentially with time a similarity solution exists. However, in this case there is a critical Weissenberg number above which a component of the stress tensor increases without bound in time.     

非稳态分数阶Oldroyd-B流体绕楔形体流动研究

研究了非稳态分数阶Oldroyd-B流体在多孔介质中通过楔形拉伸板的驻点流动问题。基于分数阶Oldroyd-B流体的本构模型建立了动量方程,并在其中引入了浮升力和驻点流动特征。此外,考虑了具有热松弛延迟时间的修正的分数阶Fourier定律,并将其应用于能量方程和对流换热边界条件。接着,采用与L1算法相结合的有限差分法求解控制偏微分方程。最后,分析了相关物理参数对流动的影响。结果表明,随着楔角参数的增加,流体受到的浮升力增大,导致速度加快;达西数越大,介质的孔隙度变大,流体的流动越快;此外,温度分布先略有上升后明显下降,这表明Oldroyd-B流体具有热延迟特性。     

Flow of Oldroyd-B fluid with nanoparticles and thermal radiation

The two-dimensional boundary layer flow of an Oldroyd-B fluid in the presence of nanoparticles is investigated. Convective heat and mass conditions are considered in the presence of thermal radiation and heat generation. The Brownian motion and thermophoresis effects are retained. The nonlinear partial differential equations are reduced into the ordinary differential equation (ODE) systems. The resulting ODE systems are solved for the series solutions. The results are analyzed for various physical parameters of interest. Numerical values of the local Nusselt and Sherwood numbers are also computed and analyzed.     

Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

The aim of this note is to present the exact solutions corresponding to two types of unsteady flows of an Oldroyd-B fluid in a channel of rectangular cross-section. The solutions that have been obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For λ_r or λ→0 they tend toward similar solutions for a Maxwell or second-grade fluid. If both λ_r and λ→0, the solutions for Navier-Stokes fluids are recovered.     

Rheology of semiconcentrated fibre suspension in the Oldroyd-B fluid

The constitutive equation for a semiconcentrated fibre suspension in the Oldroyd-B fluid has been derived from a statistical model of such a suspension by employing the molecular theory for polymeric liquids. To circumvent theoretical difficulties in viscoelastic fluid mechanics, several simplified models are used to account for the interactions of fibres and polymer molecules. Some of material functions are calculated in terms of the constitutive equation. The project Supported by the University of Melbourne of Australia, the National Natural Science Foundation of China and Zhejiang Province     

Numerical simulation of viscoelastic flows with Oldroyd-B constitutive equations and novel algebraic stress models

The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in the bent channel is used to illustrate the frame-invariant property of the new models in a pure shear flow exhibiting strong streamline curvature. The flow in the 4:1 contraction serves as a benchmark test in a situation where strong elongation occurs. For both geometries, it is found that the predictions of the new AES-models are in good agreement with Oldroyd-B up to Deborah numbers of order 0.5, with a significant reduction in computational effort.