Steady Magnetohydrodynamic Flow Research Articles

English

This paper deals with the steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of nanofluid and heat transfer with thermal radiation past a stretching/shrinking sheet in the presence of injection are investigated numerically and simulated with Maple 18 software. Brownian motion and thermophoresis are included in employed model of nanofluid simultaneously. The system of nonlinear ordinary differential equations governing the flow is converted into a system of coupled higher order nonlinear ordinary differential equation by using similarity transformations. The results show that the flow field velocity, temperature and concentration profiles are influenced appreciably by the applied magnetic field, Brownian motion, heat radiation, porous parameter and thermophoresis particle deposition. Key words: Magnetohydrodynamics, injection, stagnation point flow, heat transfer, Brownian motion, thermophoresis.

Further validation of liquid metal MHD code for unstructured grid based on OpenFOAM

In fusion liquid metal blankets, complex geometries involving contractions, expansions, bends, manifolds are very common. The characteristics of liquid metal flow in these geometries are significant. In order to extend the magnetohydrodynamic (MHD) solver developed on OpenFOAM platform to be applied in the complex geometry, the MHD solver based on unstructured meshes has been implemented. The adoption of non-orthogonal correction techniques in the solver makes it possible to process the non-orthogonal meshes in complex geometries. The present paper focused on the validation of the code under critical conditions. An analytical solution benchmark case and two experimental benchmark cases were conducted to validate the code. Benchmark case I is MHD flow in a circular pipe with arbitrary electric conductivity of the walls in a uniform magnetic field. Benchmark cases II and III are experimental cases of 3D laminar steady MHD flow under fringing magnetic field. In all these cases, the numerical results match well with the benchmark cases.

Thermal Radiation Effect in MHD Flow of Powell—Eyring Nanofluid Induced by a Stretching Cylinder

AbstractIn this paper, the steady magnetohydrodynamic (MHD) boundary layer flow of Powell—Eyring nanofluid over a stretching cylinder is discussed. Analysis is performed in the presence of thermal radiation. Variable temperature and concentration are assumed at the surface of cylinder. The arising governing equations of momentum, energy, and concentration are transformed into nonlinear ordinary differential equations by appropriate transformations. Convergent solutions of the governing equations are found. The behavior of pertinent parameters on the velocity, temperature, and concentration profiles are depicted graphically and analyzed comprehensively in detail. The presented results are also compared with the previous published work in the limiting sense.

Magnetohydrodynamic Boundary Layer Flow of Non-Newtonian Fluid and Combined Heat and Mass Transfer about an Inclined Stretching Sheet

The steady magneto hydrodynamic (MHD) boundary layer flow and combined heat and mass transfer of a non-Newtonian fluid over an inclined stretching sheet have been investigated in the present analysis. The effects of the flow parameters on the velocity, temperature, species concentration, local skin friction, local Nusselt number, and Sherwood number are computed, discussed and have been graphically represented in figures and tables for various values of different parameters. The numerical results are carried out for several values of the combined effects of magnetic parameter M, stretching parameter λ, Prandtl number Pr, Eckert number Ec, Schmidt number Sc, Soret number S0, slip parameter A and Casson parameter n on velocity, temperature and concentration profiles and also the skin-friction coefficient f "(0) local Nusselt number -θ'(0) and local Sherwood number -ψ'(0) are discussed and presented in tabular form. The results pertaining to the present study indicate that the velocity profiles decrease as the increase of magnetic field parameter, but reverse trend arises for the effect of Casson parameter and stretching ratio parameter for both Newtonian and non-Newtonian fluids. The temperature profiles increase forthe effect of magnetic parameter, Prandtl number and Eckert number in case of Newtonian and non-Newtonian fluids. The concentration profile increases for the effect of Soret number while concentration profile decreases for the increasing values of Schmidt number, magnetic parameter, Prandtl number and Eckert number for both Newtonian and non-Newtonian fluids. By considering the cooling plate the numerical results for the skin-friction coefficient f "(0) , local Nusselt number -θ'(0) and local Sherwood number -ψ'(0) are presented in Tables 1-3.

Radiation Effect of MHD on Cu-water and Ag-water Nanofluids Flow over a Stretching Sheet: Numerical Study

Recently, the flow and heat transfer of nanofluids has attracted much attention due to their wide applications in industry and engineering. In this paper, the authors introduce numerical investigation for the effect of radiation on the steady magnetohydrodynamic (MHD) flow and heat transfer of Cu-water and Ag-water nanofluids flow over a stretching sheet. In addtion, the effects of various physical parameters such as, radiation, solid volume fraction, suction/injection and magnetic on involved phenomena are discussed in details through graphs. The numerical results reveal that as parameter of radiation increases, the rate of energy transported to the fluid increases, consequently an increase in temperature occurs. Also, the velocity profile of the Ag–water nanoi¬‚uid is relatively less than that of the Cu–water nanoi¬‚uid by increasing the volume fraction and suction/injection parameters while, the converse is valid in the case of the temperature profile. Finally, It is observed that the Ag–water nanoi¬‚uid has higher skin friction coefficient than the Cu–water nanoi¬‚uid while, a converse behaviour is found in the case of the Nusselt number.

Steady Stagnation Point Flow and Heat Transfer Over a Shrinking Sheet with Induced Magnetic Field

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a shrinking sheet is studied. The effects of an induced magnetic field and thermal radiation are taken into account. Velocity and thermal slip conditions have also been incorporated in the study. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using Newton’s linearization method. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented graphically and in tabular form. Study reveals that the surface velocity gradient and heat transfer are enhanced by decreasing magnetic parameter.

Ion slip effect on a steady flow through a circular pipe of a dusty conducting Oldroyd 8-constant fluid

In this paper, a steady magnetohydrodynamic (MHD) flow of a dusty incompressible electrically conducting Oldroyd 8-constant fluid through a circular pipe is examined with considering the ion slip effect. A constant pressure gradient in the axial direction and an external uniform magnetic field in the perpendicular direction are applied. A numerical solution is obtained for the governing nonlinear momentum equations by using finite differences. The effect of the ion slip, the non-Newtonian fluid characteristics, and the particle-phase viscosity on the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is reported.

Effect of Induced Magnetic Field on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer on a Stretching Sheet

In this paper, the steady magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous electrically conducting fluid over a stretching sheet has been investigated. Velocity and thermal slip conditions have been incorporated in the study. The effects of induced magnetic field and thermal radiation have also been duly taken into account. The nonlinear partial differential equations arising out of the mathematical analysis of the problem are transformed into a system of nonlinear ordinary differential equations by using similarity transformation and boundary layer approximation. These equations are solved by developing an appropriate numerical method. Considering an illustrative example, numerical results are obtained for velocity, temperature, skin friction, and Nusselt number by considering a chosen set of values of various parameters involved in the study. The results are presented graphically/in tabular form.

Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method

Purpose – The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field. Design/methodology/approach – The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials. Findings – The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems. Originality/value – In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

In this paper, the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet is investigated in the presence of velocity and thermal slips. With the help of similarity transformations, the governing Navier–Stokes and the energy equations are reduced to ordinary differential equations, which are then solved numerically using a shooting technique. Interesting solution behavior is observed for the similarity equations with multiple solution branches for certain parameter domain. Fluid velocity increases due to the increasing value of the velocity slip parameter resulting in a decrease in the temperature field. Temperature at a point increases with increase in the thermal slip parameter. The effects of the slips, stretching/shrinking, and the magnetic parameters on the skin friction or the wall shear stress, heat flux from the surface of the sheet, velocity, and temperature profiles are computed and discussed.

Rarefaction wave in relativistic steady magnetohydrodynamic flows

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.

Numerical investigation on MHD micropolar fluid flow toward a stagnation point on a vertical surface with heat source and chemical reaction

In this paper, the steady magnetohydrodynamic (MHD) mixed convection stagnation point flow of an incompressible and electrically conducting micropolar fluid past a vertical flat plate is investigated. The effects of induced magnetic field, heat generation/absorption and chemical reaction have been taken into account during the present study. Numerical solutions are obtained by using the Runge–Kutta fourth order scheme with shooting technique. The skin friction and rate of heat and mass transfer at the bounding surface are also calculated. The generality of the present study is assured of by discussing the works of Ramachandran et al. (1988), Lok et al. (2005) and Ishak et al. (2008) as particular cases. It is interesting to note that the results of the previous authors are in good agreement with the results of the present study tabulated which is evident from the tabular values. Further, the novelty of the present analysis is to account for the effects of first order chemical reaction in a flow of reactive diffusing species in the presence of heat source/sink. The discussion of the present study takes care of both assisting and opposing flows. From the computational aspect, it is remarked that results of finite difference (Ishak et al. (2008)) and Runge–Kutta associated with shooting technique (present method) yield same numerical results with a certain degree of accuracy. It is important to note that the thermal buoyancy parameter in opposing flow acts as a controlling parameter to prevent back flow. Diffusion of lighter foreign species, suitable for initiating a destructive reaction, is a suggestive measure for reducing skin friction.

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic (MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper (Cu), Silver (Ag), Alumina (Al2O3) and Titanium Oxide (TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.

Asymptotic Analysis of Non-Newtonian Fluid Flow in a Microchannel under a Combination of EO and MHD Micropumps

Asymptotic solution for the shear stress distributions and velocity profiles of steady electroosmotic (EO) and magnetohydrodynamic (MHD) flows are obtained in a parallel flat plate microchannel. A fully-developed flow is considered and the fluid obeys a constitutive relation based in a simplified Phan-Thien-Tanner model. The effect of the following dimensionless parameters on the fluid flow control is predicted: the viscoelastic parameter and the Hartmann number. The momentum equation, boundary conditions and the constitutive rheological model are combined to formulating a nonlinear differential equation to solve the shear stress, which is expanded in a regular expansion series in powers of small Hartmann numbers. This limit of small Hartmann numbers and low electrical conductivity in the buffer solution correspond to the range where the electric and magnetic effects can be used to move a charged solution in the flow control and sample handling in biomedical and chemical analysis.

Numerical Study on Steady Magnetohydrodynamics (MHD) Flow and Heat Transfer in a Heated Rectangular Electrically Insulated Duct under the Action of Strong Oblique Transverse Magnetic Field

laminar magnetohydrodynamics flow and heat transfer of an electrically conducting fluid in a rectangular duct in the presence of oblique transverse magnetic field is considered. The walls of the duct are electrically insulated and kept at constant temperature( ). The fluid is kept in motion by a constant pressure gradient and the viscous and Joule dissipations are considered in the energy equation. The dimensionless coupled partial differential equations are solved numerically employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature are visualized in terms of graphics for different values of oblique angle( ), Hartmaan number , Prandtl number and the aspect ratio , the ratio of the length to the breadth. Keywordsflow, electrically insulated walls, rectangular duct, heat

Induced Magnetic Field Effects on Mixed Convection

Steady magnetohydrodynamic mixed convective flow of viscous and incompressible fluid in vertical walls having linear axial temperature variation along the surface is studied. Induced magnetic field produced by motion of electric conducting fluid is taken account. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved analytically for three different cases depending upon the values of the Rayleigh number and Hartmann Number. Graphical representation of the analytical solution shows that the flow pattern is of parabolic type for low Rayleigh number whereas there is a reverse type flow pattern for higher Rayleigh numbers. The nature of flow pattern can be changed formation changes from parabolic type to reversal type as the value of Rayleigh number increases. The increases strength of magnetic field is to decrease magnitude of fluid velocity, induced magnetic field and skin-friction.

Effects of Magnetic Field and Thermal Radiation on Stagnation Flow and Heat Transfer of a Power-Law Fluid over a Shrinking Sheet

An analysis is made on the steady two-dimensional boundary layer magnetohydrodynamic (MHD) stagnation-point flow and radiative heat transfer of an electrically conducting power-law fluid over a shrinking sheet which is shrunk in its own plane with a velocity proportional to the distance from a fixed point. The similarity transformations are used to transform the boundary layer equations into a system of nonlinear ordinary differential equations which are then solved numerically using shooting technique. It is found that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on the magnetic parameter (M) and the power-law index parameter (n). The results pertaining to the present study indicate that as the strength of the magnetic parameter increases, the range of α where similarity solutions exist gradually increases. It is also observed that the temperature at a point decreases with increase in M for the first solution branch, whereas it increases with increase in M for the second solution branch. The reported results are in good agreement with the available published work in the literature.

Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid

We consider the analysis of the second law of thermodynamics applied to an electrically conducting incompressible nanofluid fluid flowing over a porous rotating disk in the presence of an externally applied uniform vertical magnetic field. This study has applications in rotating magneto-hydrodynamic (MHD) energy generators for new space systems and also thermal conversion mechanisms for nuclear propulsion space vehicles. Von Karman transformations are employed to transform the governing equations into a system of nonlinear ordinary differential equations. The entropy generation equation is derived as a function of velocity and temperature gradient. This equation is non-dimensionalized using geometrical and physical flow field-dependent parameters. The velocity profiles in radial, tangential and axial directions, temperature distribution, averaged entropy generation number and Bejan number are obtained. A very good agreement is observed between the obtained results of the current study and those of previously published studies. The effects of physical flow parameters such as magnetic interaction parameter, suction parameter, nanoparticle volume fraction and the type of nanofluid on all fluid velocity components, temperature distribution, averaged entropy generation number and Bejan number, skin friction coefficient and Nusselt number are examined and analyzed and the path for optimizing the entropy is also proposed. In addition, this simulation represents the feasibility of using magnetic rotating disk drives in novel nuclear space propulsion engines and this model has important applications in heat transfer enhancement in renewable energy systems and industrial thermal management.

MHD boundary layer flow due to a moving wedge in a parallel stream with the induced magnetic field

The present analysis considers the steady magnetohydrodynamic (MHD) laminar boundary layer flow of an incompressible electrically conducting fluid caused by a continuous moving wedge in a parallel free stream with a variable induced magnetic field parallel to the wedge walls outside the boundary layer. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations in the form of a two-point boundary value problem (BVP) and then solved numerically using a finite difference scheme known as the Keller box method. Numerical results are obtained for the velocity profiles and the skin friction coefficient for various values of the moving parameter λ, the wedge parameter β, the reciprocal magnetic Prandtl number α and the magnetic parameter S. Results indicate that when the wedge and the fluid move in the opposite directions, multiple solutions exist up to a critical value of the moving parameter λ, whose value depends on the values of S and β. MSC: 34B15, 76D10.

Steady MHD Flow of a Dusty Incompressible Non-Newtonian Oldroyd 8-Constant Fluid in a Circular Pipe

The steady magneto-hydrodynamic flow of a dusty incompressible electrically conducting and non- Newtonian Oldroyd 8-constant fluid through a circular pipe is examined considering the Hall effect. A constant pressure gradient is imposed in the axial direction of the pipe while an external uniform magnetic field is applied in the perpendicular direction. A numerical solution for the governing nonlinear momentum equations is obtained using the method of finite differences. The effect of the Hall current, the non-Newtonian fluid characteristics and the particle-phase viscosity on the velocity, the volumetric flow rates, and the skin friction coefficients of both the fluid and the particle phases is investigated.