微极液体在两个多孔圆盘间的MHD流动及其热传导

两个平行的无限大多孔圆盘,圆盘表面有均匀注入时,数值地研究圆盘间不可压缩导电微极流体,在横向外加磁场作用下的轴对称稳定层流.运用von Krmn的相似变换,将非线性运动的控制方程转化为无量纲形式.使用基于有限差分格式的算法,在相应的边界条件下,求解简化后耦合的常微分方程组.讨论Reynolds数、磁场参数、微极参数和Prandtl数,对流动速度和温度分布的影响.在特殊情况下,所得结果与已有文献的工作有着很好的一致性.研究表明,圆盘表面的传热率随着Rynolds数、磁场参数和Prandtl数的增加而增加;剪切应力随着注入的增加而减少,但它随着外部磁场的加强而增加.和Newton流体相比较,微极流体的剪切应力因素较弱,有利于聚合体加工过程中流动和温度的控制.     

MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity

In this work, the effects of slip velocity on the flow and heat transfer for an electrically conducting micropolar fluid over a permeable stretching surface with variable heat flux in the presence of heat generation (absorption) and a transverse magnetic field are investigated. The governing partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the slip parameter on the flow, micro-rotation and temperature profiles as well as on the local skin-friction coefficient, the wall couple stress and the local Nusselt number are presented graphically. The numerical results of the local skin-friction coefficient, the wall couple stress and the local Nusselt number are given in a tabular form and discussed.     

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.     

Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation

A mathematical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristic on steady two-dimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field. Momentum boundary layer equation takes into account of transverse magnetic field whereas energy equation takes into account of Ohmic dissipation due to transverse magnetic field, thermal radiation and non-uniform source effects. An analysis has been performed for heating process namely the prescribed wall heat flux (PHF case). The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations which are then linearized by quasi-linearization method and solved very efficiently by finite-difference method. Favorable comparisons with previously published work on various special cases of the problem are obtained. The effects of various physical parameters on velocity, temperature, concentration distributions are presented graphically and in tabular form.     

Convective flows of micropolar fluids from radiate isothermal porous surfaces with viscous dissipation and Joule heating

In this study, the steady laminar free-forced convective flow and heat transfer of micropolar fluids past a vertical radiate isothermal permeable surface with viscous dissipation and Joule heating is investigated numerically. The local similarity solutions for the flow, microrotation (angular velocity) and heat transfer characteristics are illustrated graphically for various material parameters. The effects of the pertinent parameters on the local skin friction coefficient, plate couple stress and the rate of heat transfer are also calculated. It was shown that micropolar fluids presented lower viscous drag and heat transfer values than those of the Newtonian fluids. The effect of radiation on the rate of heat transfer in a weakly concentrated micropolar fluid is higher than a strongly concentrated micropolar fluid. Results also show that full radiation has significant effect on the rate of heat transfer compared to the linear radiation.     

Numerical simulation for natural convection of micropolar fluids flow along slender hollow circular cylinder with wall conduction effect

This paper presents a numerical analysis of the flow and heat transfer characteristics of natural convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with conduction effects. The nonlinear formulation governing equations and their associated boundary conditions are first cast into dimensionless forms by a local non-similar transformation. The resulting equations are then solved using the cubic spline collocation method and the finite difference scheme. This study investigates the effects of the conjugate heat transfer parameter, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The conjugate heat transfer parameter reduces the solid–liquid interfacial temperature, the skin friction factor and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate, interfacial temperature and skin friction factor is found to be more pronounced in a system with a greater Prandtl number. Moreover, the current results are comparing with Newtonian fluid to obtain the important results of the heat transfer and flow characteristics on micropolar fluids. It shows that an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Hiemenz flow and heat transfer of a third grade fluid

The laminar flow and heat transfer of an incompressible, third grade, electrically conducting fluid impinging normal to a plane in the presence of a uniform magnetic field is investigated. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). By means of the similarity transformation, the governing non-linear partial differential equations are reduced to a system of non-linear ordinary differential equations and are solved by a second-order numerical technique. Effects of various non-Newtonian fluid parameters, magnetic parameter, Prandtl number on the velocity and temperature fields have been investigated in detail and shown graphically. It is found that the velocity gradient at the wall decreases as the third grade fluid parameter increases.     

Nonsimilar solutions for double-diffusion boundary layers on a sphere in micropolar fluids with constant wall heat and mass fluxes

This work presents nonsimilar boundary layer solutions for double-diffusion natural convection near a sphere with constant wall heat and mass fluxes in a micropolar fluid. A coordinate transformation is employed to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. Higher vortex viscosity tends to retard the flow, and thus decreases the local convection heat and mass transfer coefficients, raising the wall temperature and concentration. Moreover, the local convection heat and mass transfer coefficients near a sphere in Newtonian fluids are higher than those in micropolar fluids.     

微极流体向受热面的MHD驻点流动

分析了有均匀横向磁场作用时,导电微极流体垂直冲击受热面时形成的二维驻点流动问题．应用适当的相似转换,将连续、动量、角动量及热量的控制方程,及其相应的边界条件,简化为无量纲形式．然后,利用以有限差分离散化为基础的算法,求解简化了的自相似非线性方程．用Richardson外推法,进一步求精其结果．以图表形式表示磁场参数、微极性参数、Prandtl数对流动和温度场的影响,说明了其解的重要特性．研究表明,随着磁场参数的增大,速度和热边界层厚度变小了．与Newton流体相比较,微极流体的剪应力和传热率出现明显的减少,这对聚合物生产过程中流体的流动和热量控制是有益的．     

Effect of double stratification on MHD free convection in a micropolar fluid

This paper analyzes the flow and heat and mass transfer characteristics of the free convection on a vertical plate with variable wall temperature and concentration in a doubly stratified micropolar fluid. A uniform magnetic field is applied normal to the plate. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration are presented graphically for various values of magnetic parameter, coupling number, thermal and solutal stratification parameters. In addition, the Nusselt number, the Sherwood number, the skin-friction coefficient, and the wall couple stress are shown in a tabular form.     

Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction

An analysis is carried out to study the flow, chemical reaction and mass transfer of a steady laminar boundary layer of an electrically conducting and heat generating fluid driven by a continuously moving porous surface embedded in a non-Darcian porous medium in the presence of a transfer magnetic field. The governing partial differential equations are converted into ordinary differential equations by similarity transformation and are solved numerically by using the finite element method. The results obtained are presented graphically for velocity, temperature and concentration profiles, as well as the Sherwood number for various parameters entering into the problem.     

A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow

Many practical applications, which have an inherent interest of physical and mathematical nature, involve the hydrodynamic flow in the presence of a magnetic field. Magnetic fluids comprise a novel class of engineering materials, where the coexistence of liquid and magnetic properties provides us with the opportunity to solve problems with high mathematical and technical complexity. Here, our purpose is to examine the micropolar magnetohydrodynamic flow of magnetic fluids by considering a colloidal suspension of ferromagnetic material (usually non‐conductive) in a carrier magnetic liquid, which is in general electrically conductive. In this case, the ferromagnetic particles behave as rigid magnetic dipoles. Thus, the application of an external magnetic field, apart from the creation of an induced magnetic field of minor significance, will prevent the rotation of each particle, increasing the effective viscosity of the fluid and will cause the appearance of an additional magnetic pressure. Despite the fact that the general consideration consists of rigid particles of arbitrary shape, the assumption of spherical geometry is a very good approximation as a consequence of their small size. Our goal is to develop a general three‐dimensional theoretical model that conforms to physical reality and at the same time permits the analytical investigation of the partial differential equations, which govern the micropolar hydrodynamic flow in such magnetic liquids. Furthermore, in the aim of establishing the consistency of our proposed model with the principles of both ferrohydrodynamics and magnetohydrodynamics, we take into account both magnetization and electrical conductivity of the fluid, respectively. Under this consideration, we perform an analytical treatment of these equations in order to obtain the three‐dimensional effective viscosity and total pressure in terms of the velocity field, the total (applied and induced) magnetic field and the hydrodynamic and magnetic properties of the fluid, independently of the geometry of the flow. Moreover, we demonstrate the usefulness of our analytical approach by assuming a degenerate case of the aforementioned method, which is based on the reduction of the partial differential equations to a simpler shape that is similar to Stokes flow for the creeping motion of magnetic fluids. In view of this aim, we use the potential representation theory to construct a new complete and unique differential representation of magnetic Stokes flow, valid for non‐axisymmetric geometries, which provides the velocity and total pressure fields in terms of easy‐to‐find potentials, via an analytical fashion. Copyright © 2009 John Wiley & Sons, Ltd.     

Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited

This paper considers the effects of radiation on the flow near the two-dimensional stagnation point of a stretching sheet immersed in a viscous and incompressible electrically conducting fluid in the presence of an applied constant magnetic field. The external velocity and the stretching velocity of the sheet are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by the Keller-box method. The features of the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The results indicate that the heat transfer rate at the surface decreases in the presence of radiation.     

Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited

This paper considers the effects of radiation on the flow near the two-dimensional stagnation point of a stretching sheet immersed in a viscous and incompressible electrically conducting fluid in the presence of an applied constant magnetic field. The external velocity and the stretching velocity of the sheet are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by the Keller-box method. The features of the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The results indicate that the heat transfer rate at the surface decreases in the presence of radiation.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink

An analysis has been carried out to study the flow and heat transfer characteristics for MHD viscoelastic boundary layer flow over an impermeable stretching sheet with space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink), viscous dissipation, thermal radiation and magnetic field due to frictional heating. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied vertically in the flow region. The governing partial differential equations for the flow and heat transfer are transformed into ordinary differential equations by a suitable similarity transformation. The governing equations with the appropriate conditions are solved exactly. The effects of viscoelastic parameter and magnetic parameter on skin friction and the effects of viscous dissipation, non-uniform heat source/sink and the thermal radiation on heat transfer characteristics for two general cases namely, the prescribed surface temperature (PST) case and the prescribed wall heat flux (PHF) case are presented graphically and discussed. The numerical results for the wall temperature gradient (the Nusselt number) are presented in tables and are discussed.     

Peristaltic motion of a magnetohydrodynamic micropolar fluid in a tube

This study is concerned with the magnetohydrodynamic flow of a micropolar fluid in a circular cylindrical tube. The equations governing the flow are modeled using the assumptions of long wavelength and low Reynolds number. It is found that the governing equations are coupled partial differential equations for the flow velocity and the microrotation. The finite difference scheme is used to integrate the equations and the results are graphically presented and discussed. Special emphasis is given to the effects of micropolar fluid parameters, tube wall peristaltic amplitude and magnetic parameter on the transverse profiles of velocity and microrotation as well as pumping characteristics and trapping phenomena.     

Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the homotopy analysis method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the magnetic parameter, buoyancy parameter and rotation parameter on the surface shear stresses and surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear stresses and surface heat transfer is in good agreement with the numerical solution given in reference [H. S. Takhar, A. J. Chamkha, G. Nath, Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat Mass Transfer 37 (2001) 397].     

The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

Numerical simulation of flow of a micropolar fluid between a porous disk and a non-porous disk

Two dimensional steady, laminar and incompressible motion of a micropolar fluid between an impermeable disk and a permeable disk is considered to investigate the influence of the Reynolds number and the micropolar structure on the flow characteristics. The main flow stream is superimposed by constant injection velocity at the porous disk. An extension of Von Karman’s similarity transformations is applied to reduce governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. An algorithm based on finite difference method is employed to solve these ODEs and Richardson’s extrapolation is used to obtain higher order accuracy. The numerical results reflect the expected physical behavior of the flow phenomenon under consideration. The study indicates that the magnitude of shear stress increases strictly and indefinitely at the impermeable disk while it decreases steadily at the permeable disk, by increasing the injection velocity. Moreover, the micropolar fluids reduce the skin friction as compared to the Newtonian fluids. The magnitude of microrotation increases with increasing the magnitude of R and the micropolar parameters. The present results are in excellent comparison with the available literature results.     

Group theoretic method for unsteady free convection flow of a micropolar fluid along a vertical plate in a thermally stratified medium

The group theoretic approach is applied for solving the problem of unsteady natural convection flow of micropolar fluid along a vertical flat plate in a thermally stratified medium. The application of two-parameter transformation group reduces the number of independent variables in the governing system consisting of partial differential equations and a set of auxiliary conditions from three to only one independent variable, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. Numerical solution of the velocity, microrotation and heat transfer have been obtained. The possible forms of the ambient temperature variation with position and time are derived.