Analytical approach to heat and mass transfer in MHD free convection from amoving permeable vertical surface

An analytical study is performed on heat and mass transfer in MHD‐free convection from a moving permeable vertical surface and the results are compared with previous works on this phenomenon to test the validity. The coupled equations of boundary layer are transformed from their non‐linear form to ordinary form using similarity transformation and then are solved by a newly developed method, homotopy analysis method. Having different base functions, homotopy analysis method provides us with great freedom in choosing the solution of a nonlinear problem. Solving the boundry layer equations, the effects of different parameters such as magnetic field strength parameter (M), Prandtl number (Pr), Schmidt number (Sc), buoyancy ratio and suction/blowing parameter (f_w) on velocity, temperature, and concentration profiles are taken into consideration. Obtained results show that increment of magnetic field strength parameter (M) leads to decrease in velocity profile. Copyright © 2011 John Wiley & Sons, Ltd.     

The effect of mass transfer on MHD free convective radiating flow over an impulsively started vertical plate embedded in a porous medium

The laminar convective heat and mass transfer flow of an incompressible, viscous, electrically conducting fluid over an impulsively started vertical plate with conduction-radiation embedded in a porous medium in presence of transverse magnetic eld has been studied. An exact solution is derived by solving the dimensionless governing coupled partial differential equations. As the equations are nonlinear, so Laplace transform technique is used to solve it. The eects of important physical parameters on the velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been analyzed through graphs. The results of the present study agree well with the previous solutions obtained without mass transfer. After the consideration of mass transfer, some dierent results are noticed. Applications of the present study arise in material processing systems and different industries.     

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．     

Boundary layer problem of MHD system with non-characteristic perfect conducting wall

In this paper, we study the boundary layer problem for the incompressible MHD system with the magnetic field having a non-characteristic perfect conducting wall boundary condition. Using the multi-scale analysis and asymptotic expansion approach, we can construct the approximate solutions for the viscous and diffuse MHD system, and utilize the careful energy method to prove the validity of the approximate solutions.     

Viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow with diffusion

We establish viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow by the mathematical validity of the Prandtl boundary layer theory with fixed diffusion. The convergence is verified under various Sobolev norms, including the L^∞(H¹) norm.     

MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical plate is studied numerically, taking into account the effects of Ohmic heating and viscous dissipation. A uniform magnetic field is applied perpendicular to the plate. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. Both the aiding-buoyancy mode and the opposing-buoyancy mode of the mixed convection are examined. The velocity and temperature profiles as well as the local skin friction and local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, the Eckert number and the suction/injection parameter, f_w. For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase owing to suction of fluid, increasing the Richardson number, Ri (i.e. the mixed convection parameter) or decreasing the Eckert number. This trend reverses for blowing of fluid and decreasing the Richardson number or decreasing the Eckert number. It is disclosed that the value of Ri determines the effect of the magnetic parameter on the momentum and heat transfer.     

Global solutions to isentropic planar magnetohydrodynamic equations with density‐dependent viscosity

In this paper, we study the isentropic compressible planar magnetohydrodynamic equations with viscosity depending on density and with free boundaries. Precisely, when the viscosity coefficient λ(ρ) is proportional to ρ^θ with θ > 0, where ρ is the density, we establish the existence of global solutions under certain assumptions on the initial data by deriving some new a priori estimates.     

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

A mathematical model is given for the magnetohydrodynamic (MHD) pipe flow as an inner Dirichlet problem in a 2D circular cross section of the pipe, coupled with an outer Dirichlet or Neumann magnetic problem. Inner Dirichlet problem is given as the coupled convection‐diffusion equations for the velocity and the induced current of the fluid coupling also to the outer problem, which is defined with the Laplace equation for the induced magnetic field of the exterior region with either Dirichlet or Neumann boundary condition. Unique solution of inner Dirichlet problem is obtained theoretically reducing it into two boundary integral equations defined on the boundary by using the corresponding fundamental solutions. Exterior solution is also given theoretically on the pipe wall with Poisson integral, and it is unique with Dirichlet boundary condition but exists with an additive constant obtained through coupled boundary and solvability conditions in Neumann wall condition. The collocation method is used to discretize these boundary integrals on the pipe wall. Thus, the proposed procedure is an improved theoretical analysis for combining the solution methods for the interior and exterior regions, which are consolidated numerically showing the flow behavior. The solution is simulated for several values of problem parameters, and the well‐known MHD characteristics are observed inside the pipe for increasing values of Hartmann number maintaining the continuity of induced currents on the pipe wall.     

Transition of MHD boundary layer flow past a stretching sheet

In this paper a study is carried out to understand the transition effect of boundary layer flow: (1) due to a suddenly imposed magnetic field over a viscous flow past a stretching sheet and (2) due to sudden withdrawal of magnetic field over a viscous flow past a stretching sheet under a magnetic field. In both the cases the sheet stretches linearly along the direction of the fluid flow. Governing equations have been non-dimensionalised and the non-dimensionalised equations have been solved using the implicit finite difference method of Crank–Nicholson type. Comparison between the steady state exact solutions and the steady state computed solutions has been carried out. Graphical representation of the dimensionless horizontal velocity, vertical velocity and local skin friction profiles of the steady state and unsteady state has been presented. Computation has been carried out for various values of the magnetic parameter M. The obtained results has been interpreted and discussed.     

Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition

The steady laminar boundary layer flow over a permeable flat plate in a uniform free stream, with the bottom surface of the plate is heated by convection from a hot fluid is considered. Similarity solutions for the flow and thermal fields are possible if the mass transpiration rate at the surface and the convective heat transfer from the hot fluid on the lower surface of the plate vary like x^−1/2, where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.     

MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method

The magnetohydrodynamics (MHD) Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a...     

Numerical study of mixed convection flow of a micropolar fluid towards permeable vertical plate with convective boundary condition

In this article, the mixed convective flow of a micropolar fluid along a permeable vertical plate under the convective boundary condition is analyzed. The scaling group of transformations is applied to get the similarity representation of the system of partial differential equations of the problem and then the resulting equations are solved by using Spectral Quasi-Linearisation Method. This study reveals that the dual solutions exists for certain values of mixed convection parameter. The outcomes are analyzed with dual solutions in detail. Effects of micropolar parameter, Biot number and suction/injection parameters on different flow profiles are discussed and depicted graphically.     

Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction

Analytical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generation/absorbing fluid on a continuously vertical permeable surface in the presence of a radiation, a first-order homogeneous chemical reaction and the mass flux are reported. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Graphical results for velocity, temperature and concentration profiles of both phases based on the analytical solutions are presented and discussed.     

Dual solutions in mixed convection boundary-layer flow with suction or injection

The effect of suction/injection on the laminar mixed convectionboundary-layer flow about a vertical wall in an incompressibleviscous fluid is considered. The similarity solutions are obtainedfor some values of the suction/injection parameter as well asthe mixed convection parameter for three particular cases: uniformtemperature, uniform heat flux and stagnation flow. The resultingsystem of non-linear ordinary differential equations is solvednumerically for both assisting and opposing flow regimes usinga finite-difference scheme known as the Keller box method. Numericalresults are obtained for the skin friction coefficient and localNusselt number as well as velocity and temperature profiles.The effects of the involved parameters on the skin frictioncoefficient and the local Nusselt number characteristics arediscussed. It is found that dual solutions exist for assistingflow, besides that usually reported in the literature for opposingflow.     

Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall

The influences of Hall current and slip condition on the MHD flow induced by sinusoidal peristaltic wavy wall in two dimensional viscous fluid through a porous medium for moderately large Reynolds number is considered on the basis of boundary layer theory in the case where the thickness of the boundary layer is larger than the amplitude of the wavy wall. Solutions are obtained in terms of a series expansion with respect to small amplitude by a regular perturbation method. Graphs of velocity components, both for the outer and inner flows for various values of the Reynolds number, slip parameter, Hall and magnetic parameters are drawn. The inner and outer solutions are matched by the matching process. An interesting application of the present results to mechanical engineering may be the possibility of the fluid transportation without an external pressure.     

Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with Hall currents and inclined magnetic field influence

A numerical solution is developed for the viscous, incompressible, magnetohydrodynamic flow in a rotating channel comprising two infinite parallel plates and containing a Darcian porous medium, the plates lying in the x–z plane, under constant pressure gradient. The system is subjected to a strong, inclined magnetic field orientated to the positive direction of the y-axis (rotational axis, normal to the x–z plane). The Navier–Stokes flow equations for a general rotating hydromagnetic flow are reduced to a pair of linear, viscous partial differential equations neglecting convective acceleration terms, for primary velocity (u′) and secondary velocity (v′) where these velocities are directed along the x and y axes. Only viscous terms are retained in the momenta equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless ordinary differential equations are solved using a robust numerical method, Network Simulation Methodology. Full details of the numerics are provided. The present solutions are also benchmarked against the analytical solutions presented recently by Ghosh and Pop [Ghosh SK, Pop I. An analytical approach to MHD plasma behaviour of a rotating environment in the presence of an inclined magnetic field as compared to excitation frequency. Int J Appl Mech Eng 2006;11(4):845–856] for the case of a purely fluid medium (infinite permeability). We study graphically the influence of Hartmann number (Ha, magnetic field parameter), Ekman number (Ek, rotation parameter), Hall current parameter (Nh), Darcy number (Da, permeability parameter), pressure gradient (Np) and also magnetic field inclination (θ) on primary and secondary velocity fields. Additionally we investigate the effects of these multiphysical parameters on the dimensionless shear stresses at the plates. Both primary and secondary velocity are seen to be increased with a rise in Darcy number, owing to a simultaneous reduction in Darcian drag force. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) but there is a decrease in secondary velocity. The study finds important applications in magnetic materials processing, hydromagnetic plasma energy generators, magneto-geophysics and planetary astrophysics.     

Global Solutions of Nonlinear Magnetohydrodynamics with Large Initial Data

A free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated. The existence, uniqueness, and regularity of global solutions are established with large initial data in H¹. It is shown that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time, although there is a complex interaction between the hydrodynamic and magnetodynamic effects. An existence theorem of global solutions with large discontinuous initial data is also established.     

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.