Destabilization of the film-coated surface of an electrically conducting fluid in an alternating field exposed to irradiation with light

We examine and analyze the appearance of a surface nonuniformity in a conducting fluid under the action of an alternating electric field.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 2, pp. 267–270, February, 1989.     

Non-orthogonal stagnation-point flow of a micropolar fluid

This paper considers the problem of steady two-dimensional flow of a micropolar fluid impinging obliquely on a flat plate. The flow under consideration is a generalization of the classical modified Hiemenz flow for a micropolar fluid which occurs in the boundary layer near an orthogonal stagnation point. A coordinate decomposition transforms the full governing equations into a primary equation describing the modified Hiemenz flow for a micropolar fluid and an equation for the tangential flow coupled to the primary solution. The solution to the boundary-value problem is governed by two non-dimensional parameters: the material parameter K and the ratio of the microrotation to skin friction parameter n. The obtained ordinary differential equations are solved numerically for some values of the governing parameters. The primary consequence of the free stream obliqueness is the shift of the stagnation point toward the incoming flow.     

MHD flow of a viscoelastic fluid past a stretching surface

Summary The flow of a viscoelastic fluid past a stretching sheet in the presence of a transverse magnetic field is considered. An exact analytical solution of the governing non-linear boundary layer equation is obtained, showing that an external magnetic field has the same effect on the flow as the viscoelasticity.     

Solitary cylindrical layer of electrically conducting magnetic fluid

The possibility of the existence and stability conditions for a solitary layer of electrically conducting magnetic fluid not resting on solid walls is studied.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 5, pp. 838–843, May, 1985.     

Unsteady oscillatory stagnation-point flow of a viscoelastic fluid

The unsteady stagnation point flow of the Walters B^′ fluid is examined and solutions are obtained. It is assumed that the infinite plate at y=0 is oscillating and the fluid impinges obliquely on the plate.     

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t=0) steady and then at t>0 it becomes unsteady. The semi-similar solution of the unsteady Navier–Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier–Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier–Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time.     

MHD rotating flow of a third-grade fluid on an oscillating porous plate

Summary The rotating flow of a third-grade fluid on an oscillating porous plate in the presence of a transverse magnetic field is considered. An analytic solution of the governing nonlinear boundary layer equation is obtained. Expressions for the velocity profile are established. It is found that an external magnetic field has the same effect on the flow as the material parameters of the fluid. Further the symmetric and asymmetric nature of the solutions is discussed.     

On the flow of an electrically conducting nonlocal viscous fluid between parallel plates in the presence of a transverse magnetic field in magnetohydrodynamics

A continuum theory is constructed for the flow of an electrically conducting nonlocal viscous fluid between two nonconducting parallel plates. The flow is subject to the influence of a transverse magnetic field. The effects of long range or nonlocal interactions at a material point in the fluid arising from all material points in the rest of the fluid are taken into account by means of a nonlocal influence function. Equations of motion governing the nonlocal viscous flow are derived from localized forms of global balance laws and constitutive equations appropriate for electromagnetically active media. These field equations are analytically solved for the nonlocal velocity and the nonlocal stress fields. The effects of varying the magnetic field strength on the shear stress are investigated. The effects of such variations on the shear stress exerted on the walls of microscopic channels are also determined. Numerical computations are provided for these results.     

MHD flow of a second grade fluid in an orthogonal rheometer

The magnetohydrodynamics (MHD) flow of a conducting, homogeneous incompressible Rivlin-Ericksen fluid of second grade contained between two infinite, parallel, insulated disks rotating with the same angular velocity about two noncoincident axes, under the application of a uniform transverse magnetic field, is investigated. This model represents the MHD flow of the fluid in the instrument called an orthogonal rheometer, except for the fact that in the rheometer the rotating plates are necessarily finite. An exact solution of the governing equations of motion is presented. The force components in the x and y directions on the disks are calculated. The effects of magnetic field and the viscoelastic parameter on the forces are discussed in detail.     

MHD flow in circular expansions with thin conducting walls

The paper considers steady, inertialess flow of an incompressible, electrically conducting fluid through variable-area ducts with circular cross sections and thin, imperfectly conducting walls in the presence of strong, transverse magnetic fields. In view of previous papers for perfectly conducting walls [1] and insulating walls [2], all possible wall conductivities are now covered. The present analysis is particularly relevant to the design of fusion reactors using liquid-metal coolants. The flow is similar to that for an insulating wall, at least for the practical case of an expansion (or contraction) placed between two pipes, except that the disturbance persists for distances 0(?^{?$\text{1}\text{2}$}) upstream and downstream of the expansion instead of distances 0($\text{M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$). Here M is the (large) Hartmann number and ? is the (small) wall conductivity parameter, which is taken to be much larger than M^?1.     

An explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream

An analytic technique, namely the homotopy analysis method, is applied to study the flow and heat transfer characteristics in an electrically conducting fluid near an isothermal sheet. The sheet is linearly stretched in the presence of a uniform free stream of constant velocity and temperature. The effects of free convection and internal heat generation or absorption are also considered. Within the framework of boundary layer approximations, the explicit, totally analytic and uniformly valid solutions governed by a set of three fully coupled, highly non-linear equations are obtained, which agree well with numerical results.     

Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid

The problem of a magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid is considered for the analytical solution using homotopy analysis method (HAM). The non-linear partial differential equations are transformed to an ordinary differential equation first taking boundary layer approximations into account and then using the similarity transformations. The analytical solution is presented in the form of an infinite series. The recurrence formulae for finding the coefficients are presented and the convergence is established. The effects of the Deborah number and MHD parameter is discussed on the velocity profiles and the skin friction coefficients. It is found that the results are in excellent agreement with the existing results in the literature for the case of hydrodynamic flow.     

Unsteady second grade aligned MHD fluid flow

Summary Exact solutions are established for the equations of a class of an unsteady, plane, second grade, electrically conducting, MHD aligned fluid which undergoes isochoric motion. This class consists of flows for which the vorticity distribution is proportional to the stream function perturbed by a uniform stream.     

Natural convection of an electrically conducting fluid in a spherical layer. 1. Formulation of the problem

Natural-convection heat transfer of an electrically conducting fluid in a spherical layer modeling the earth’s liquid core is considered. The effect of different physical factors on fluid flow in a spherical interlayer is analyzed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 5, pp. 850–854, September–October, 1998.     

Squeezing flow of MHD fluid between parallel disks

Squeezing flow between parallel disks is studied for the case when one disk is porous and the other is impermeable. Viable similarity transform is used to reduce the problem to a highly nonlinear ordinary differential equation. Variation of Parameters Method (VPM) is then employed to determine the solution to resulting ordinary differential equation. Numerical solution is also obtained using R-K 4 method and comparison shows an excellent agreement between both the solutions. Effects of different physical parameters on the flow are also discussed with the help of graphs coupled with comprehensive discussions.     

MHD flow in conducting circular expansions with strong transverse magnetic fields

This paper treats the steady, inertialess flow of an incompressible, electrically conducting fluid through perfectly conducting, variable-area ducts of circular cross section in the presence of strong transverse magnetic fields. The problem is of fundamental importance in the design of liquid-lithium cooling systems for fusion reactors, of liquid-metal MHD generators and of MHD machinery in metallurgy. First we find that, if a straight pipe of radius r is joined to an expansion or contraction, then the disturbance of the fully developed flow in the pipe dies out like exp ($\text{? 12.16¦x¦r}{}^{\mathrm{?1}}$), where x is distance from the join. Next we consider the flow in conical expansions with end effects neglected; and find that the flow becomes concentrated near the plane of symmetry as the divergence increases. Finally numerical schemes for determining the flow in more general expansions and contractions are outlined. Extension of the present analysis to non-circular sections is also discussed.