Linear oscillatory hydromagnetic flow between two coaxial cylinders

Hydromagnetic flow between two coaxial circular cylinders is discussed when the inner cylinder oscillates axially under a radial magnetic field. Exact solution is given for the case of a perfectly conducting fluid. Expressions for velocity, induced magnetic field, current density, electric field, viscous drag and energy transfer are derived and expressed in polar forms so as to facilitate the study of magnitude and phase variations. Current sheets are found to exist on the two boundaries.     

Couette flow of a third-grade fluid with variable magnetic field

This investigation deals with the analytic solution for the time-dependent flow of an incompressible third-grade fluid which is under the influence of a magnetic field of variable strength. The fluid is in an annular region between two coaxial cylinders. The motion is induced due to an inner cylinder with arbitrary velocity. Group theoretic methods are employed to analyse the nonlinear problem and a solution for the velocity field is obtained analytically.     

Hall effects on hydromagnetic flow of an Oldroyd 6-constant fluid between concentric cylinders

The hydromagnetic flow of an electrically conducting, incompressible Oldroyd 6-constant fluid between two concentric cylinders is investigated. The flow is generated by moving inner cylinder and/or application of the constant pressure gradient. Two non-linear boundary value problems are solved numerically. The effects of material parameters, pressure gradient, magnetic field and Hall parameter on the velocity are studied. The graphical representation of velocity reveals that characteristics for shear thinning/shear thickening behaviour of a fluid is dependent upon the rheological properties.     

Pulsating magnetohydrodynamic flow in an annular channel

Pulsating laminar flow of a viscous incompressible electrically conducting fluid in an annular channel between two infinitely long circular cylinders under a radial impressed magnetic field is considered. The solutions of magnetohydrodynamic equations have been obtained on the assumption that the space between two cylinders is small compared to their mean radius. The solutions were also obtained on the assumption of small magnetic Reynolds number with special consideration of those for low and high frequencies.     

Flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders in the presence of magnetic field

In this paper, the flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders has been investigated in the presence of magnetic field. For this purpose, the constitutive equation of such a fluid flow was simplified, and the existence of the solution to the governing equation was established using Schauder's fixed point theorem. Using the finite difference method, the numerical solution of the non-dimensionalized form of the established governing equation was obtained. The effect of sundry parameters such as the rotating speed of the cylinders, the physical properties of fluid, and magnetic field intensity on the fluid velocity field was studied as well.     

The wall jet flow of a conducting gas over a permeable surface in the presence of a variable transverse magnetic field

The effects of the magnetic field, Mach number and the permeability parameter on the wall jet flow (radial or plane) of an electrically conducting gas spreading over a permeable surface have been investigated. Taking the Prandtl number of the fluid as unity and assuming a linear relationship between viscosity and temperature, it is found that similar solutions for the velocity distribution exist for a specified distribution of the normal velocity along the wall and the corresponding distribution of the transverse magnetic field. Previous non-magnetic flow results have been improved by adopting a new and simple transformation of variables.     

Study of magnetohydrodynamic pulsatile flow in a constricted channel

The present work reports the study of steady and pulsatile flows of an electrically conducting fluid in a differently shaped locally constricted channel in presence of an external transverse uniform magnetic field. The governing nonlinear magnetohydrodynamic equations simplified for low conducting fluids are solved numerically by finite difference method using stream function-vorticity formulation. The analysis reveals that the flow separation region is diminished with increasing values of magnetic parameter. It is noticed that the increase in the magnetic field strength results in the progressive flattening of axial velocity. The variations of wall shear stress with increasing values of the magnetic parameter are shown for both steady and pulsatile flow conditions. The streamline and vorticity distributions in magnetohydrodynamic flow are also shown graphically and discussed.     

Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field

The boundary layer flow of a second grade fluid over a permeable stretching surface with arbitrary velocity and appropriate wall transpiration is investigated. The fluid is electrically conducting in the presence of a constant applied magnetic field. An exact solution to the nonlinear flow problem is presented.     

Exact solutions for the flow of a viscoelastic fluid induced by a circular cylinder subject to a time dependent shear stress

The velocity field and the adequate shear stress corresponding to the flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a longitudinal time dependent shear to the fluid. The solutions that have been obtained, presented under integral and series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. They can be easy particularizes to give the similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of the relaxation time and the fractional parameter, as well as a comparison between models, is shown by graphical illustrations.     

Effect of aligned magnetic field on the steady viscous flow past a circular cylinder

The steady viscous incompressible and slightly conducting fluid flow around a circular cylinder with an aligned magnetic field is simulated for the range of Reynolds numbers 100 ? Re ? 500 using the Hartmann number, M. The multigrid method with defect correction technique is used to achieve the second order accurate solution of complete non-linear Navier–Stokes equations. The magnetic Reynolds number is assumed to be small. It is observed that volume of the separation bubble decreases and drag coefficient increases as M is increased. We noticed that the upstream base pressure increases slightly with increase of M whereas downstream base pressure decreases with increase of M. The effect of the magnetic field on the flow is discussed with contours of streamlines, vorticity, plots of surface pressure and surface vorticity.     

Time-dependent MHD Couette flow in a porous annulus

This study presents the solution for the MHD transient Couette flow in an annulus formed by two concentric porous cylinders of infinite length. The fluid flow is induced by either the impulsive or the accelerated movements of the outer cylinder. A uniform magnetic field is assumed to be applied perpendicular to the direction of flow. General solution of the governing equations is obtained using a combination of Laplace transform and the Riemann-sum approximation method of Laplace inversion. The expressions for the skin friction at the two walls are obtained in both cases. The variations of the velocity and the skin friction with respect to the Hartmann number and suction/injection parameter have been discussed. It is found out that suction accelerates the flow whereas injection retards the flow.     

Three-dimensional rotating flow induced by a shrinking sheet for suction

Series solution of magnetohydrodynamic (MHD) and rotating flow over a porous shrinking sheet is obtained by a homotopy analysis method (HAM). The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Similarity solutions of coupled non-linear ordinary differential equations resulting from the momentum equation are obtained. Convergence of the obtained solutions is ensured by the proper choice of auxiliary parameter. Graphs are sketched and discussed for various emerging parameters on the velocity field. The variations of the wall shear stress f″(0) and ?g′(0) are also tabulated and analyzed.     

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.     

Helical flow of a Bingham fluid arising from axial Poiseuille flow between coaxial cylinders

The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.     

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.     

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.     

Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a generalized Maxwell fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and after some time both cylinders suddenly begin to oscillate around their common axis with different angular frequencies of their velocities. The solutions that have been obtained are presented under integral and series forms in terms of generalized G and R functions. Moreover, these solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary Maxwell fluid are also obtained as limiting cases of our general solutions. At the end, flows corresponding to the ordinary Maxwell and generalized Maxwell fluids are shown and compared graphically by plotting velocity profiles at different values of time and some important results are remarked.     

Analytic solution for MHD flow of a third order fluid in a porous channel

The present study investigates the channel flow of a third order fluid. The fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel. Expression for velocity is developed by an analytic method, namely the homotopy analysis method (HAM). Convergence of the obtained solution is properly checked. The feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs. It is observed that unlike the flow of second grade fluid, the obtained solution for a third order fluid is non-similar. Also, the behavior of Hartmann number on the velocity is different to that of the Reynold's number.     

Comparison of the simplified and full MHD models for laminar incompressible flow past a circular cylinder

In the majority of research on incompressible magnetohydrodynamic (MHD) flows, the simplified model with the low magnetic Reynolds number assumption has been adopted because it reduces the number of equations to be solved. However, because the effect of flow on magnetic field is also neglected, the solutions of the simplified model may be different from those of the full model. As an example, the flow of an electrically conducting fluid past a circular cylinder under a magnetic field is investigated numerically using the simplified and full models in this paper. To solve the problems, two second-order compact finite difference algorithms based on the streamfunction-velocity formulation of the simplified model and the quasi-streamfunction-velocity formulation of the full model are developed respectively.Numerical simulations are carried out over a wide range of Hartmann number for steady-state laminar problems with both models. For the full model, magnetic Reynolds number (Re_m) is chosen from 0.01 to 10. The computed results show that solutions of the simplified MHD model are not exactly the same as those of the full MHD model for this flow problem in most cases even if Re_m in the full model is very low. Only in the special case that a strong external magnetic field is exerted perpendicular to the dominant flow direction, can the simplified MHD model be regarded as an approximation of the full MHD model with low Re_m.