Slow motion of a micropolar fluid through a porous sphere bounded by a solid sphere

The paper examines the slow motion of a micropolar fluid produced by the relative motion of a solid sphere to an inside porous sphere. The result extends the Cunningham’s problem to micropolar fluid when the inner sphere is porous with prescribed radial suction/injection velocity at the surface of the sphere. The result can also be taken as an extension of the work of Ramkissoon and Majumdar when the fluid is bounded at a radiusr=b (b>a) but the solid sphere is replaced by a porous sphere. The force experienced by the inner sphere has been calculated and particular cases of interest have been deduced.     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel’s models of viscosities

In this paper, the steady incompressible flow of a fourth grade fluid down a vertical cylinder with variable viscosity and heat transfer analysis are considered. The governing equations of motion of fourth grade fluid in cylindrical coordinates have been derived. The complete analytic solutions of momentum and energy equations have been obtained by homotopy analysis method (HAM). The entropy generation number for two cases of viscosities namely (i) Reynold’s model and (ii) Vogel’s model have also been computed. The results are compared with the available finite difference and perturbation solutions of third grade fluid. At the end the pressure gradient for the fourth grade fluid has also been calculated.     

Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip

The entrained flow and heat transfer of a non-Newtonian third grade fluid due to a linearly stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that the slip and the third grade fluid parameter have opposite effects on the velocity and the thermal boundary layers.     

Analytical solutions to Stokes-type flows of inhomogeneous fluids

In this paper, we study the unsteady motion of an inhomogeneous incompressible viscous fluid, where the viscosity varies spatially according to various models. We study the Stokes-type flow for these types of fluids where in the first case the flow between two parallel plates is examined with one of the plates oscillating and in the second case when the flow is caused by a pulsatile pressure gradient. A general argument establishes the existence of oscillatory solutions to our problem. Exact solutions are obtained in terms of some special functions and comparisons are made with the cases of constant viscosity and the slow flow regimes.     

Dynamics and self-propulsion of a spherical body shedding coaxial vortex rings in an ideal fluid

We describe a model for the dynamic interaction of a sphere with uniform density and a system of coaxial circular vortex rings in an ideal fluid of equal density. At regular intervals in time, a constraint is imposed that requires the velocity of the fluid relative to the sphere to have no component transverse to a particular circular contour on the sphere. In order to enforce this constraint, new vortex rings are introduced in a manner that conserves the total momentum in the system. This models the shedding of rings from a sharp physical ridge on the sphere coincident with the circular contour. If the position of the contour is fixed on the sphere, vortex shedding is a source of drag. If the position of the contour varies periodically, propulsive rings may be shed in a manner that mimics the locomotion of certain jellyfish. We present simulations representing both cases.     

On the flow of a dusty viscous liquid through a circular pipe

Analytical solution of the flow problem of a dusty viscous liquid through a circular pipe in case of axial symmetry is obtained when pressure gradient varies harmonically with time. It is found that the effect of the fine dust is to make the velocity of sedimentation zero and when dust is sufficiently coarse, the effect of the dust is equivalent to an extra frictional force proportional to the fluid velocity.     

生物磁粘弹性流体的流动:应用动脉电磁过热评估血液的流动,癌症治疗进程

利用生物磁流体动力学(BFD)原理,在生物磁流体经由遭受磁场作用的多孔介质时,研究其流动的基本理论.所研究流体的磁化强度随温度而变化.流体被认为是非Newton流体,其流动由二阶梯度流体方程所控制,并考虑了流体的粘弹性效应.假设管道壁是能够伸展的,管壁表面的速度与到坐标原点的纵向距离成正比.首先将问题简化为包括7个参数的、耦合的非线性微分方程组的求解.将血液看作生物磁流体,并用上述方法分析,目的是计算某些血液的流动参数,并配以适当的数值方法,导数用差分格式近似.计算结果用图形给出,从而在磁场作用下,得到过热状态中关系血液的、血流动力学流动的理论预测.结果清楚地表明,在电磁过热治疗进程期间,磁偶极子对动脉中血液流动特征的影响起着重大作用.该研究引起了临床医学的关注,其结果有益于癌症病人采用电磁过热的治疗.     

On exact solutions of Stokes second problem for a Burgers’ fluid, I. The case γ < λ2/4

In the present work, the exact solutions of Stokes second problem for a Burgers’ fluid are investigated. The expressions for the velocity field and the corresponding tangential stress are obtained when the relaxation times satisfy the condition γ < λ²/4. The solutions have been determined by means of Laplace transform. Only one initial condition is necessary for velocity and these solutions presented in the forms of simple or multiple integrals in terms of Bessel functions. The corresponding solutions for a Newtonian fluid as well as Oldroyd-B fluid appear as the limiting cases of the presented results. The obtained solutions are graphically analyzed for the variations of interesting flow parameters. Moreover, a comparison for velocity is made with Oldroyd-B and Newtonian fluids.     

Analytic solution for MHD Transient rotating flow of a second grade fluid in a porous space

This article looks into the unsteady rotating magnetohydrodynamic (MHD) flow of an incompressible second grade fluid in a porous half space. The flow is induced by a suddenly moved plate in its own plane. Both the fluid and plate rotate in unison with the same angular velocity. Analytic solution of the governing flow problem is obtained by using Fourier sine transform. Based on the modified Darcy's law, expression for velocity is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. Several existing solutions of Newtonian fluid have been also deduced as limiting cases.     

Fully Coupled Thermo-Hydrodynamic Simulation Model for Journal Bearings

The isothermal form of Reynolds fluid film equation is used to predict the pressure generation in hydrodynamic journal bearings if temperature effects are neglected. Often, however, temperature effects may be important and cannot be neglected, because oil viscosity significantly varies with temperature. Also, thermal expansion of journal shaft and bearing housing must be taken into account since the bearing clearance changes with increasing temperature. Hence, the Reynolds pressure field equation, the energy equation for the fluid film and the heat transfer equations for journal and bearing housing have to be solved simultaneously. The coupled thermo-hydrodynamic fluid flow problem is mathematically defined by a system of nonlinear integro-differential equations. The governing equations are discretized and solved by a finite element approach. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

RANS closures for non-neutral microscale CFD simulations sustained with inflow conditions acquired from mesoscale simulations

This study focuses on bridging the gap between the turbulence modelling methodologies of meterological and engineering codes by proposing a novel methodology to define the closure coefficients of Reynolds-Averaged Navier-Stokes turbulence models consistently with the physics of the atmospheric boundary layer. In this framework, different turbulence closures have been developed and tested on different full-scale test cases corresponding to different atmospheric stability conditions by performing microscale simulations with the inflow conditions provided by a numerical weather prediction (NWP) code. Developed turbulence models have been implemented into the open source computational fluid dynamics (CFD) toolbox, OpenFOAM and the inflow conditions have been acquired with another open source code, the Weather Research and Forecasting (WRF) model.     

Second order fluid models with general boundary behaviour

A crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling. This work is partially supported by the Italian-Hungarian bilateral R&D programme, by OTKA grant n. T-34972, by Italian Ministry for University and Research (MIUR) through PRIN project Famous and by EEC project Crutial.     

Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload

We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisfied and penalties are incurred otherwise. Within the context of the corresponding fluid model, we investigate the dynamic scheduling of different classes of service under conditions where the workload of certain classes may be overloaded for a transient period of time. Specifically, we consider the case with two fluid classes and a single server whose capacity can be shared arbitrarily among the two classes. We assume that the class 1 arrival rate varies with time and the class 1 fluid can more efficiently reduce the holding cost. Under these assumptions, we characterize the optimal server allocation policy that minimizes the holding cost in the fluid model when the arrival rate function for class 1 is known. Using the insights gained from this deterministic case, we study the stochastic fluid system when the arrival rate function for class 1 is random and develop various policies that are optimal or near optimal under various conditions. In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.     

Microcomputer-based simulation of heat conduction between solid of tapered shape and the fluid

Simulating the heat conduction in between a solid conducting body immersed in fluid at a given temperature is a difficult task, particularly when the body is tapered in shape and the costs have to be kept low. The body in question is cylindrical, symmetrical about z-axis, tapered in shape and has been heated to a high temperature before being immersed into the fluid. The heat conduction equation in cylindrical polar coordinates with all derivative boundary conditions is attempted to be solved in two ways – first analytically making use of Bessel's function and then by numerical modelling with the help of Finite Difference method, and equations thus formed have been solved through ADI explicit and Implicit (Peaceman Rachford) scheme on microcomputer. The paper is an account of work already done on this and includes further possibilities for general solution with analytical methods and a suitable low-cost numerical solution. Also possible analogy with flow of fluids have been explored. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel

This paper is devoted to the study of peristaltic flow of a fourth grade fluid in a channel under the considerations of long wavelength and low-Reynolds number. The flow is examined in a wave frame of reference moving with velocity of the wave. The analytic solution has been obtained in the form of a stream function from which the axial velocity and axial pressure gradient have been derived. The results for the pressure rise and frictional force per wavelength have also been computed numerically. The computational results indicate that the pressure rise and frictional force per wavelength are increased in case of non-Newtonian fluid when compared with Newtonian fluid. Several graphs of physical interest are displayed and discussed.     

Mathematical modelling of bottom evolution by particle deposition and resuspension

A two-dimensional numerical model for the evolution of a bottom due to particle deposition and resuspension by a fluid flow is here presented. A computational fluid dynamic approach is used to calculate the flow field and a Lagrangian particle tracking technique is applied to solve the dispersed phase. The evolution of the lower boundary is simulated taking into account the mass conservation of the solid phase and the geotechnical properties of the granular material. The model is characterized by two important features. First, fluid dynamics are coupled with the bottom evolution due to particle deposition and resuspension. This permits to use the model to simulate complex flow fields as well as complex time-evolving geometries. Second, the dispersed phase is calculated by a Lagrangian approach, which retains the discrete information of the individual particles of the granular bottom which may be of interest for some industrial processes (coating) and environmental flows (sediment stratification). First consistency checks have been performed for some deposition and resuspension test cases with fluid at rest. The model has also been tested by comparison with a physical experiment of deposition inside a cavity. Finally, as an example of possible applications of industrial and environmental interest, the model has been applied to investigate particle deposition in rectangular cavities and the evolution of a sand heap by a fluid flow.     

Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus

This paper deals with the unsteady axial Couette flow of fractional second grade fluid (FSGF) and fractional Maxwell fluid (FMF) between two infinitely long concentric circular cylinders. With the help of integral transforms (Laplace transform and Weber transform), generalized Mittag–Leffler function and H-Fox function, we get the analytical solutions of the models. Then we discuss the exact solutions and find some results which have been known as special cases of our solutions. Finally, we analyze the effects of the fractional derivative on the models by using the numerical results and find that the oscillation exists in the velocity field of FMF.     

The shape of axisymmetric rotating fluid

The equations for axisymmetric self-gravitating rotating fluid have been studied extensively since Poincaré. The model derives its primary interest from celestial mechanics, where it can be used to study the geometry of stars and planets. Existence of a solution for both the compressible and the incompressible cases is known. The smoothness of the boundary of the fluid is studied, and, in particular, it is proved that the rotating fluid has at most a finite number of rings.     

Unsteady flow of fluids with microstructure between parallel plates—II

Two types of unsteady flow between two parallel plates of a fluid with microstructure have been considered. (i) Initially the fluid is at rest and the motion is caused by a sudden change of pressure gradient from zero to a constant value. It is shown that for a given time asα* decreases from infinity to zero, the velocity in the flow decreases. (ii) One plate is fixed and the other is accelerated with a velocity ν = Ut ⁿ (U andn being positive constants). The flow pattern is discussed in both cases in detail.