Numerical Study of a Magneto-fluid Motion Through a Porous Medium Between Two Wavy Plates with Constant Suction

In this note, the problem of an incompressible viscous fluid moving through a porous medium (Brinkman model) between two wavy plates under the effects of a constant inclined magnetic field that makes an angle with the vertical axis and constant suction, are studied numerically by a method related to the method of Takabatake and Ayukawa in 1982. The present approach is not restricted by any of the parameters appearing in the problem such as Reynolds number, magnetic parameter, suction parameter, the wave number and amplitude ratio. The variations in velocity, flow rate and pressure gradient with the above governing parameters are presented. Moreover, the effect of varying the porous medium and the inclined angle is also studied.     

High-order shear theory for static analysis of functionally graded plates with porosities

The bending responses of porous functionally graded (FG) thick rectangular plates are investigated according to a high-order shear deformation theory. Both the effect of shear strain and normal deformation are included in the present theory and so it does not need any shear correction factor. The equilibrium equations according to the porous FG plates are derived. The solution to the problem is derived by using Navier's technique. Numerical results have been reported and compared with those available in the open literature for non-porous plates. The effects of the exponent graded and porosity factors are investigated.     

Conjugate heat transfer inside a porous channel

Analytical and numerical analyses have been performed for fully developed forced convection in a fluid-saturated porous medium channel bounded by two parallel plates. The channel walls are assumed to be finite in thickness. Conduction heat transfer inside the channel wall is also accounted and the full problem is treated as a conjugate heat transfer problem. The flow in the porous material is described by the Darcy–Brinkman momentum equation. The outer surfaces of the solid walls are treated as isothermal. A temperature dependent volumetric heat generation is considered inside the solid wall only. Analytical expressions for velocity, temperature, and Nusselt number are obtained after simplifying and solving the governing differential equations with reasonable approximations. Subsequent results obtained by numerical calculations show an excellent agreement with the analytical results.     

On flow of a fourth‐grade fluid with heat transfer

The influence of heat transfer on the steady flow of a fourth‐grade fluid between two stationary parallel porous plates is studied. The flow is engendered under the application of a constant pressure gradient. The concept of homotopy analysis method is utilized for the series solution of the governing problem. Numerical solution has been also carried out. In addition, both analytic and numerical solutions are compared. The variations of embedded parameters into the solution are predicted through the graphical representations. Copyright © 2010 John Wiley & Sons, Ltd.     

The effect of radial diffusion on the performance of a liquid-liquid displacement process

The effect of radial diffusion on the performance of a liquid-liquid displacement process is considered in fluid flow between porous parallel plates and through a porous tube, as examples of a two-zone problem in unsteady-state mass transfer. The double Laplace transformation is applied to the system equations. In obtaining the inversion of the Laplace transformed equations the first inversion (with respect to the transformed dimensionless axial distance) is performed by use of the residue method, and then the second inversion (with respect to the transformed dimensionless time) is performed by use of the numerical Laplace transform technique advanced by Bellman et al. A numerical example is shown and discussed.     

Natural convection flow with solidification between two vertical plates filled with a porous medium

Quasi-steady solidification between two vertical flat plates filled with a saturated porous medium has been investigated. The medium is homogeneous and isotropic. The convection flow of liquid takes place in the porous medium in the variable space between the two walls. One of the vertical walls is set to a temperature lower than the solidification temperature of the medium and therefore a frozen crust is formed on this wall. The second wall has a high temperature then the fusion temperature of the medium. The problem has been simplified by assuming laminar flow and the Brinkman and the Oberbeck–Bousinesq’s approximations. The results are presented in terms of the velocity for different properties of the porous medium. Various velocities are displayed in dependence of the Rayleigh and Darcy numbers. The study indicates that asymmetric boundary conditions have an important effect on the temperature and flow field. In addition, the growth of the thickness of the frozen layer with time has been derived from a simple analytical solution of the interface energy equation.     

Compression of a plastic porous material between rotating plates

The problem of a plane flow of a rigid-plastic porous material between two rotating rough plates with no material flux through the point of their rotation and with a uniform distribution of porosity at the initial instant is considered under the assumption that the material behavior follows the cylindrical yield condition and the associated flow rule. The solution reduces to consecutive calculation of several ordinary integrals. It is demonstrated that the solution behavior depends on the angle between the plates, and the value of porosity at a certain stage of the deformation process can be equal to zero. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 128–135, July–August, 2009.     

Hydromagnetic rotating flow of third grade fluid

This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.     

Unsteady hydromagnetic Couette flow through a porous medium in a rotating system

This paper investigates the unsteady hydromagnetic Couette fluid flow through a porous medium between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system using boundary layer approximation. The fluid is assumed to be Newtonian and incompressible. Laplace transform technique is adopted to obtain a unified solution of the velocity fields. Such a flow model is of great interest, not only for its theoretical significance, but also for its wide applications to geophysics and engineering. Analytical expressions for the steady state velocity and shear stress on the plates are obtained, and the case of single oscillating plate is also discussed. The influence of pertinent parameters on the flow is delineated, and appropriate conclusions are drawn.     

Effects of Temperature-Dependent Viscosity on Forced Convection Inside a Porous Medium

Considering the exponential viscosity–temperature relation, effect of temperature-dependent viscosity on forced convection of a liquid through a porous medium, bounded by isoflux parallel plates, is investigated numerically based on the general model of momentum transfer. Local effects of viscosity variation on the distribution of velocity and temperature are analyzed. Moreover, global aspects of the problem are investigated where corrections are proposed for total pressure drop and the fully developed Nusselt number, in the form of out/in viscosity ratio. Results are obtained over a wide range of permeabilities from clear (of solid material) fluid to very low permeability, where for constant properties one expects a nearly slug flow.     

NON-AXISYMMETRIC MIXED BOUNDARY VALUE PROBLEM FOR DYNAMIC INTERACTION BETWEEN SATURATED POROUS FOUNDATION AND RECTANGULAR PLATE$^{\bf 1)}$

在同一界面的不同区域具有多种边界条件, 称之为混合边界, 这是一个熟知的力学问题. 对这类问题进行精确分析时, 必须要进行混合边值问题的求解. 而对于一般的三维非轴对称情形, 混合边值问题的求解往往存在数学困难. 本文利用Hilbert定理和双重Fourier变换, 给出了一种求解三维非轴对称混合边值问题的解析方法, 利用该方法对具有混合透水边界的饱和多孔地基上矩形板的振动弯曲进行了解析研究(板与地基接触面为不透水边界, 其余为透水边界). 首先, 基于Kirchhoff理论和Biot多孔介质理论建立矩形板与饱和多孔地基的动力控制方程, 进行耦合求解. 针对板土接触面和非接触面的混合边值问题, 采用双重Fourier变换构造出两对二维对偶积分方程, 以接触应力和接触面孔隙压力为基本未知量, 用Jacobi正交多项式将未知量展开, 再利用Schmidt法对二维对偶积分方程完成求解, 最终推导出板土系统在动力作用下的位移和应力解析式. 通过将本文计算模型退化为单一弹性地基, 与已有研究结果进行对比, 验证了本文方法的正确性和有效性. 最后, 通过数值算例, 对饱和多孔地基上矩形板的动力响应及参数影响做出分析和讨论. 此外, 本文提出的解析法具有一般性, 可广泛应用于复杂接触问题和多场耦合问题的求解.     

饱和多孔地基与矩形板动力相互作用的非轴对称混合边值问题

在同一界面的不同区域具有多种边界条件, 称之为混合边界, 这是一个熟知的力学问题. 对这类问题进行精确分析时, 必须要进行混合边值问题的求解. 而对于一般的三维非轴对称情形, 混合边值问题的求解往往存在数学困难. 本文利用Hilbert定理和双重Fourier变换, 给出了一种求解三维非轴对称混合边值问题的解析方法, 利用该方法对具有混合透水边界的饱和多孔地基上矩形板的振动弯曲进行了解析研究(板与地基接触面为不透水边界, 其余为透水边界). 首先, 基于Kirchhoff理论和Biot多孔介质理论建立矩形板与饱和多孔地基的动力控制方程, 进行耦合求解. 针对板土接触面和非接触面的混合边值问题, 采用双重Fourier变换构造出两对二维对偶积分方程, 以接触应力和接触面孔隙压力为基本未知量, 用Jacobi正交多项式将未知量展开, 再利用Schmidt法对二维对偶积分方程完成求解, 最终推导出板土系统在动力作用下的位移和应力解析式. 通过将本文计算模型退化为单一弹性地基, 与已有研究结果进行对比, 验证了本文方法的正确性和有效性. 最后, 通过数值算例, 对饱和多孔地基上矩形板的动力响应及参数影响做出分析和讨论. 此外, 本文提出的解析法具有一般性, 可广泛应用于复杂接触问题和多场耦合问题的求解.      

A numerical study of unsteady gas-solid flow between parallel porous plates submitted to a magnetic field

This paper studies unsteady laminar flow of dusty conducting fluid between parallel porous plates with temperature dependent viscosity and the Network Simulation Method (NSM) is used to solve the governing nonlinear partial differential equations. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates that are assumed to be porous. The NSM is applied to solve the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. With this method, only discretization of the spatial co-ordinates is necessary, while time remains as a real continuous variable. The velocity and temperature are studied for different values of the viscosity and magnetic field parameters.     

考虑相变的近场动力学热?力耦合模型及多孔介质冻结破坏模拟

多孔介质的传热传质现象广泛存在于自然界和工业领域中. 低温条件可能导致多孔介质中的组分发生相变, 并由此诱发材料损伤, 甚至导致结构失效破坏. 对这类破坏现象的预测需要精细化建模, 以能够反映物质的相变过程和材料的破坏特征. 本文采用热焓法改写经典的热传导方程, 在近场动力学框架下, 建立了一种考虑物质相变的热?力耦合模型, 发展了交错显式求解的数值计算方法, 进行了方板角冻结、热致变形和多孔介质冻结破坏等问题的模拟, 得到了方板的冻结特征、温度场和变形场的分布规律以及多孔介质的冻结破坏过程, 与试验和其他数值方法的结果具有较好的一致性. 研究表明, 本文所建立的考虑物质相变的近场动力学热?力耦合模型能够反映材料的非局部效应和物质相变潜热的影响, 准确捕捉相变过程中液固界面的演化特征, 再现多孔介质中材料相变、基质热致变形和冻结破坏过程, 突破了传统连续性模型求解这类破坏问题时面临的瓶颈, 为深入研究多孔介质冻融破坏过程和破坏机理提供了有效途径.      

Numerical analysis of fluid flow and mass transfer in a channel with a porous bottom wall

The flow of a solution between parallel plates is considered. The bottom plate is porous, while the top one is an impermeable solid. A computer program based on the control volume approach was developed to analyse the flow and concentration fields. The effects of the slip at the porous wall on the velocity and particle concentration distributions were investigated. It was observed that as the slip increases, the concentration on the porous wall decreases and the maximum velocity moves towards the porous wall. The concentration on the porous wall increases in the flow direction. This increase in the particle concentration along the porous wall may cause a reduction of the porosity and hence a variation in the suction rate along the porous wall. In order to take this effect into account, a linearly varying transverse velocity along the porous wall was considered. The results were compared with the data available in the literature.     

Effect of ion slip on the time-varying Hartmann flow of a non-Newtonian viscoelastic fluid with heat transfer

Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.     

Problem of a randomly oriented crack in a box-shaped shell

This paper deals with the stress state of a box-shaped shell formed by two semi-infinite plates joined at a right angle. The plates are homogeneous but have different thicknesses. The shell is weakened by a finite rectilinear crack of unit length which reaches one edge of the shell. The orientation of the crack and the load on its edges are arbitrarily chosen. The problem is solved with the assumption that the thickness of the plates is small compared to the length of the crack, which allows an asymptotic formulation of the problem. The problem is reduced to a special type of Riemannian vector problem in which the stress-intensity factor allows matrix factorization in accordance with Khrapkov’s scheme. The asymptotes of the resulting solution and the stress-intensity factor are examined in relation to the thickness of the shell and the angle formed by the crack and the edge of the shell. Translated from Prikladnaya Mekalinika, Vol. 34, No. 12, pp. 48–54, December, 1998.     

Investigation of passive oscillations of flexible splitter plates attached to a circular cylinder

This paper presents a numerical study to address wake control of a circular cylinder subjected to two-dimensional laminar flow regime using single and multiple flexible splitter plates attached to the cylinder. Three different cases are presented in the study, covering cylinders with one, two and three horizontally attached splitter plates while the locations of the plates around the cylinders are varied. The length of the splitter plates was equal to the cylinder diameter and Reynolds number was 100. Due to the flexibility of the plates, the problem was modeled as a Fluid–Structure Interaction (FSI) problem and the commercial finite element software, Comsol Multiphysics, was utilized to solve this problem using Arbitrary Lagrangian–Eulerian (ALE) method. Vortex shedding frequency and fluid forces acting on the cylinder are investigated, along with a comprehensive parametric study to identify the optimum arrangement of the plates for maximum drag reduction and maximum vortex shedding frequency reduction. The numerical results associated to the flexible splitter plates are also compared with the corresponding rigid splitter plate cases investigated in a previous study. Moreover, the tip amplitude of the plates and the maximum strains were measured in order to find an optimum position for placing a piezoelectric polymer to harvest energy from the flow.     

Some Steady MHD Flows of the Second Order Fluid

The exact analytic solutions of two problems of a second order fluid in presence of a uniform transverse magnetic field are investigated. The governing equation is of fourth order ordinary differential equation and is solved using perturbation method. In the first problem we discuss the flow of a second order fluid due to non-coaxial rotations of a porous disk and a fluid at infinity. In second problem the flow of a second order conducting fluid between two infinite plates rotating about the same axis is investigated, with suction or blowing along the axial direction. For second order conducting fluid it is observed that asymptotic solution exists for the velocity both in the case of suction and blowing.