Unsteady MHD flow of a non-Newtonian fluid on a porous plate

This paper deals with the study of the MHD flow of non-Newtonian fluid on a porous plate. Two exact solutions for non-torsionally generated unsteady hydromagnetic flow of an electrically conducting second order incompressible fluid bounded by an infinite non-conducting porous plate subjected to a uniform suction or blowing have been analyzed. The governing partial differential equation for the flow has been established. The mathematical analysis is presented for the hydromagnetic boundary layer flow neglecting the induced magnetic field. The effect of presence of the material constants of the second order fluid on the velocity field is discussed.     

Nonaxisymmetric Free Convection Flow over a Rotating Disk in a Viscoelastic fluid with Magnetic Field

The non axisymmetric motion produced by a buoyancy-induced secondary flow of a viscoelastic fluid over an infinite rotating disk in a verticalplane with a magnetic field applied normal to the disk has been studied.The governing Navier Stokes equations and the energy equation admit a self similar solution. The system of ordinary differential equations has been solved numerically using Runge-Kutta Gill subroutine.The turning moment for the viscoelastic fluid is found to be less than that of the Newtonian fluid but the turning moment is increased due to the magnetic parameter. The resultant force due to the buoyancy-induced secondary flow increases with the magnetic parameter but reduces as the viscoelastic parameter increases. The quantity of fluid, which is pumped outwards due to the centrifuging action of the disk, for the viscoelastic fluid is more than that of the Newtonian fluid. The buoyancy-induced secondary flow boundary layer is much thicker than the primary boundary layer thickness. The thermal boundary layer due to the primary flow increases with the magnetic parameter decreases as the viscoelastic parameter increases. The heat transfer increases with the viscoelastic parameter but decreases as the magnetic parameter increases. The effect of the viscoelastic parameter is more pronounced on the secondary flow than on the primary flow.     

Hydromagnetic effects on the three-dimensional flow past a porous plate

Hydromagnetic effects on the three-dimensional flow of an electrically conducting viscous incompressible fluid past a porous plate with periodic suction has been analysed. The uniform flow is subjected to a transversely applied magnetic field. The mathematical analysis is presented for the hydromagnetic boundary layer flow neglecting the induced magnetic field. Approximate solutions for the components of velocity field and the skin-frictions due to them are obtained and discussed with the help of a graph and tables.     

Unsteady hydromagnetic rotating flow of a conducting second grade fluid

The purpose of this work is to investigate the hydromagnetic oscillatory flow of a fluid bounded by a porous plate, when the entire system rotates about an axis normal to the plate. The fluid is assumed to be non-Newtonian (second grade), incompressible and electrically conducting. The magnetic field is applied transversely to the direction of the flow. Such a flow model has great significance not only of its theoretical interest, but also for applications to geophysics and engineering. The resulting initial value problem has been solved analytically for steady and unsteady cases. The analysis of the obtained results showed that the flow field is appreciably influenced by the material parameter of the second grade fluid, the applied magnetic field, the imposed frequency, rotation and suction and blowing parameters. It is observed in a second grade fluid that a steady asymptotic hydromagnetic solution exists for blowing and resonance which is different from the hydrodynamic situation.     

二阶流体在旋转坐标系中的三维管道流动

就两个水平板构成的旋转系统,在磁场作用下分析二阶磁流体在其间的流动.下表面是一块可伸展的平面,上面是一块多孔的固体平板.选用合适的变换,将质量和动量的守恒方程,简化为耦合的非线性常微分方程组.应用最强大的分析技术,即同伦分析法(HAM),得到该非线性耦合方程组的级数解.结果用图形给出,并详细地讨论了无量纲参数Re,λ,Ha2,α和K2对速度场的影响.     

Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation

The effect of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media has been studied in the presence of radiation and magnetic field. The plate surface is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or blowing and has a power-law variation of both the wall temperature and concentration. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. Numerical calculations are carried out, for various values of the dimensionless parameters of the problem, which include a variable viscosity, chemical reactions, radiation, magnetic field, porous medium and power index of the wall temperature parameters. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.     

Flow of a Reiner‐Rivlin fluid between two infinite coaxial rotating disks

Present study deals with the steady flow and heat transfer of a non‐Newtonian Reiner‐Rivlin fluid between two coaxially rotating infinite disks. Using similarity transformations, the governing equations are reduced to a set of nonlinear, highly coupled ordinary differential equations and by means of an effective analytical method called homotopy analysis method; analytical solutions are constructed in series form. Different cases, such as, when one disk is at rest and the other is rotating with constant angular velocity, two disks rotating with different angular velocities in same as well as opposite sense, two disks rotating with same angular velocities in opposite sense, are discussed. The effects of non‐Newtonian parameter, Reynolds number, are also discussed, and results are presented graphically.     

Magnetohydrodynamic non-Darcy mixed convection heat transfer from a vertical heated plate embedded in a porous medium with variable porosity

A numerical model is developed to study magnetohydrodynamics (MHD) mixed convection from a heated vertical plate embedded in a Newtonian fluid saturated sparsely packed porous medium by considering the variation of permeability, porosity and thermal conductivity. The boundary layer flow in the porous medium is governed by Forchheimer–Brinkman extended Darcy model. The conservation equations that govern the problem are reduced to a system of non-linear ordinary differential equations by using similarity transformations. Because of non-linearity, the governing equations are solved numerically. The effects of magnetic field on velocity and temperature distributions are studied in detail by considering uniform permeability (UP) and variable permeability (VP) of the porous medium and the results are discussed graphically. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in increasing the flow field and the rate of heat transfer for variable permeability case. The important finding of the present work is that the magnetic field has considerable effects on the boundary layer velocity and on the rate of heat transfer for variable permeability of the porous medium. Further, the results obtained under the limiting conditions were found to be in good agreement with the existing ones.     

Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption

The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.     

Couette flow of a third grade fluid with rotating frame and slip condition

An incompressible third grade fluid occupies the porous space between two rigid infinite plates. The steady rotating flow of this fluid due to a suddenly moved lower plate with partial slip of the fluid on the plate is analysed. The fluid filling the porous space between the two plates is electrically conducting. The flow modeling is developed by employing a modified Darcy’s law. A numerical solution of the governing problem consisting of a non-linear ordinary differential equation and non-linear boundary conditions is obtained and discussed. Several limiting cases of the arising problem can be obtained by choosing suitable parameters.     

Soret and Dufour effects on MHD slip flow with thermal radiation over a porous rotating infinite disk

In this investigation, thermal radiation effect over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour diffusion effects is investigated. The partial differential equations governing the problem under consideration are transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically using fourth order Runge–Kutta based shooting method. The effects of the magnetic interaction parameter, slip flow parameter, Soret number, Dufour number, Schmidt number, radiation parameter, Prandtl number and suction parameter on the fluid velocity, temperature and concentration distributions in the regime are depicted graphically and are analyzed in detail. The corresponding skin-friction coefficients, the Nusselt number and the Sherwood number are also calculated and displayed in tables showing the effects of various parameters on them.     

Peristaltic motion of a magnetohydrodynamic generalized second‐order fluid in an asymmetric channel

We investigate the peristaltic motion of a magnetohydrodynamic (MHD) generalized second‐order fluid in an asymmetric channel. The governing equations are first modeled and then numerically solved under the long wavelength approximation. Attention has been focused to analyze the shear‐thinning and shear‐thickening effects of the investigated non‐Newtonian fluid, the influence of the magnetic force on the flow, especially the trapping, pumping characteristics caused by the peristalsis of the walls. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Heat transfer and Couette flow of a chemically reacting non‐linear fluid

In this paper we study the flow and heat transfer in a chemically reacting non‐linear fluid between two long horizontal parallel flat plates that are at different temperatures. The top plate is sheared, whereas the bottom plate is fixed. The fluid is modeled as a generalized power‐law fluid whose viscosity is also assumed to be a function of the concentration. The effects of radiation are neglected. The equations are made dimensionless and the boundary value problem is solved numerically; the velocity and temperature profiles are obtained for various dimensionless numbers. Published in 2009 by John Wiley & Sons, Ltd.     

Exact solution for rotating flows of a generalized Burgers’ fluid in a porous space

This article considers the oscillatory flows of a generalized Burgers’ fluid on an infinite insulating plate when the fluid is permeated by a transverse magnetic field. The effects of Hall current are taken into account. Modified Darcy’s law for a generalized Burgers’ fluid has been used to discuss the flows in a porous medium. The governing time dependent equations in a rotating frame are first developed and then solved for the two problems. The influence of various emerging parameters is discussed through various graphs. The solutions for the Newtonian, second grade, Maxwell, Oldroyd-B and Burgers’ fluids can be obtained from our solutions as the limiting cases.     

Analytic solution of natural convection flow of a non‐newtonian fluid between two vertical flat plates by using decomposition method

An analysis has been performed to study the natural convection of a non‐Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non‐Newtonian nature of fluid on the heat transfer are studied. The governing boundary layer and temperature equations for this problem are reduced to an ordinary form and are solved by Adomian decomposition method (ADM) and numerical method. Velocity and temperature profiles are shown graphically. The obtained results are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and non‐linear equations and so can be found widely applicable in engineering and science. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1384–1395, 2010     

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.     

On a free boundary problem in ground freezing

We consider a boundary value problem describing the stationary flow of a non‐Newtonian fluid through the frozen ground, with a free interface between the liquid and the solid phases. We prove the existence of at least one weak solution of the problem. Copyright © 2000 John Wiley & Sons, Ltd.     

On the Rayleigh problem for a Sisko fluid in a rotating frame

The unsteady rotating flow of a Sisko fluid bounded by a suddenly moved infinite flat plate is investigated. The fluid is electrically conducting in the presence of a transverse applied time-dependent magnetic field. A highly non-linear differential equation resulting from the balance of momentum and mass, coupled with appropriate boundary and initial conditions is solved numerically. The numerical solutions for different values of the parameters are compared and discussed.     

Hydromagnetic fluctuating flow of a couple stress fluid through a porous medium

The equations of a polar fluid of hydromagnetic fluctuating through a porous medium are cast into matrix form using the state space and Laplace transform techniques the resulting formlation is applied to a variety of problems. The solution to a problem of an electrically conducting polar fluid in the presence of a transverse magnetic field and to a probem for the flow between two parallel fixed plates is obtained. The inversion of the Laplace transforms, is carried out using a numerical approach. Numerical results for the velocity, angular velocity distribution and the induced magnetic field are given and illustrated graphically for each problems.     

Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles

Magneto-hydrodynamics and thermal radiation effects on heat and mass transfer in steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a fluid saturated porous media in the presence of the thermophoresis particle deposition effect is studied in this paper. The governing equations are transformed by special transformations. Brownian motion of particles and thermophoretic transport are considered in the flow equations. The magnetic field is considered to be applied. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting similarity equations are solved numerically by the fourth-order Runge–Kutta method with shooting technique. Many results are obtained and representative set is displayed graphically to illustrate the influence of the various parameters on the wall thermophoretic deposition velocity, concentration, temperature and velocity profiles.