End effects in inviscid flow in a magnetohydrodynamic channel

1961 ◽  
Vol 11 (1) ◽  
pp. 121-132 ◽  
Author(s):  
G. W. Sutton ◽  
A. W. Carlson
Keyword(s):  
Magnetic Field ◽  
Interaction Parameter ◽  
Rectangular Cross Section ◽  
Fluid Velocity ◽  
Magnetic Interaction ◽  
Inviscid Flow ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
End Effects ◽  
Magnetic Interaction Parameter

The flow of an inviscid, incompressible electrical conducting fluid in a channel of constant rectangular cross-section is considered, when the flow enters a region which contains a magnetic field transverse to the flow and electrodes on opposite sides of the channel. This geometry is typical of a d.c. induction pump or magnetohydrodynamic generator. The conducting fluid external to the magnetic field acts as a shunt and produces a non-uniform electric potential field and hence a non-uniform Lorenz force on the fluid, and causes the fluid velocity profile to be distorted. These effects are calculated theoretically for small magnetic Reynolds number and small magnetic interaction parameter. It is found that the velocity at the centre-line of the channel is retarded and at the walls the velocity is accelerated. The fractional change of velocity at the wall is equal to approximately 0·44 times a modified magnetic interaction parameter.

Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number

1998 ◽  
Vol 358 ◽  
pp. 299-333 ◽  
Author(s):  
OLEG ZIKANOV ◽  
ANDRE THESS
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Boundary Conditions ◽  
Interaction Parameter ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetic Interaction Parameter

The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.

scholarly journals Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

2016 ◽  
Vol 21 (3) ◽  
pp. 667-681 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Unsteady Mixed Convection ◽  
Phase Angles

Abstract An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., $T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$ . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

The (5d10 + 5d96s) – 5d96p transitions in Tl IV, Pb V, and Bi VI

1990 ◽  
Vol 68 (3) ◽  
pp. 284-292 ◽  
Author(s):  
Y. N. Joshi ◽  
A. J. J. Raassen ◽  
A. A. Van der Valk
Keyword(s):  
Least Squares ◽  
Hyperfine Structure ◽  
Interaction Parameter ◽  
Magnetic Interaction ◽  
Spin Orbit ◽  
Magnetic Effects ◽  
Magnetic Interaction Parameter

The spectra of thallium, lead, and bismuth were photographed in the region 600–2000 Å using sliding spark and triggered spark sources. The (5d10 + 5d96s)–5d96p transitions in Tl IV, Pb V, and Bi VI were investigated. Earlier level values were revised and new lines were classified. Hyperfine structure splittings were observed for many lines in Tl IV and Bi VI. Least squares fitted calculations were done for each spectra. The deviations between the calculated and observed level values showed that parametric descriptions using only the spin-orbit magnetic interaction parameter to describe magnetic effects is not sufficient in the 5d-shell spectra.

scholarly journals Gravitation modulation impact on MHD free convection flow of micropolar fluid

2020 ◽  
Vol 17 (2) ◽  
pp. 199-218
Author(s):  
Sanjib Sengupta ◽  
Reshmi Deb
Keyword(s):  
Magnetic Field ◽  
Skin Friction ◽  
Micropolar Fluid ◽  
Perturbation Technique ◽  
Rotational Velocity ◽  
Fluid Velocity ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Induced Magnetic Field ◽  
Modulation Parameter

In this paper, a theoretical study is carried out on unsteady three dimensional, laminar, free convective flow of micropolar fluid with Hall effect, Joule heating and heat sink under gravitation modulation. A uniform transverse magnetic field is applied normal to the plate along the fluid region. The magnetic Reynolds number is considered to be small due to incomparability of applied and induced magnetic field, as such the influence of induced magnetic field can be neglected. The multi parameter perturbation technique is used to solve the governed dimensionless equations. The fluid velocity profile, temperature profile and the concentration profiles are discussed with the aid of graphs and tables. The coefficient of skin friction and couple stresses are numerically computed in addition to Nusselt number and Sherwood number. The result reveals that the linear velocity increases due to escalation in gravitation modulation parameter values but for intensification in values of gravitation modulation parameter, a reverse effect is observed for the rotational velocity. A comparative analysis shows that the skin friction coefficient is less in micropolar fluid than the corresponding Newtonian fluids.

scholarly journals Effect of variable viscosity on laminar convection flow of an electrically conducting fluid in uniform magnetic field

2002 ◽  
pp. 49-62 ◽  
Author(s):  
S. Chakraborty ◽  
A.K. Borkakati
Keyword(s):  
Magnetic Field ◽  
Flat Plate ◽  
Uniform Magnetic Field ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Conducting Fluid ◽  
Fluid Viscosity ◽  
Electrically Conducting ◽  
Viscosity Parameter ◽  
Electrically Conducting Fluid

The flow of a viscous incompressible electrically conducting fluid on a continuous moving flat plate in presence of uniform transverse magnetic field, is studied. The flat plate which is continuously moving in its own plane with a constant speed is considered to be isothermally heated. Assuming the fluid viscosity as an inverse linear function of temperature, the nature of fluid velocity and temperature in presence of uniform magnetic field are shown for changing viscosity parameter at different layers of the medium. Numerical solutions are obtained by using Runge-Kutta and Shooting method. The coefficient of skin friction and the rate of heat transfer are calculated at different viscosity parameter and Prandt l number. .

Analysis On the Inception of the Magnetohydrodynamic Flow Instability in the Annular Linear Induction Pump Channel

2021 ◽  
Author(s):  
Ruijie Zhao ◽  
Xiaohui Dou ◽  
Qiang Pan ◽  
ZHANG Desheng ◽  
Bart van Esch
Keyword(s):  
Magnetic Field ◽  
Pressure Gradient ◽  
Lorentz Force ◽  
Flow Rate ◽  
Flow Instability ◽  
Fluid Velocity ◽  
Magnetic Reynolds Number ◽  
Wave Number ◽  
Magnetic Flux Density ◽  
Linear Induction

Abstract Flow instability is the intricate phenomenon in the Annular Linear Induction Pump when the pump runs at off-design working condition. A 3D numerical model is built to simulate the flow in the pump channel. The pump heads at different flow rates are accurately predicted by comparing with experiment. The simulation results show the fluid velocity is circumferentially non-uniform in the pump channel even at the nominal flow rate. The flow in the middle sector continuously decelerates to nearly zero with the reducing flow rate. Reversed flow occurs in the azimuthal plane, followed by vortex flow. The reason for the heterogeneous velocity field is attributed to the mismatch between non-uniform Lorentz force and relatively even pressure gradient. It is seen that the flow in the region of small Lorentz force has to sacrifice its velocity to match with the pressure gradient. An analytic expression of the axial Lorentz force is then developed and it is clearly demonstrated the Lorentz force could be influenced by the profiles of velocity and radial magnetic flux density. The coupling between velocity and magnetic field is studied by analyzing the magnitudes of different terms in the dimensionless magnetic induction equation. It is found the dissipation term is determined not only by the magnetic Reynolds number but the square of wave number of the disturbance in each direction. The smaller disturbing wave number weakens the dissipating effect, resulting in the larger non-uniform magnetic field and axial Lorentz force.

The force on a sphere moving through a conducting fluid in the presence of a magnetic field

1961 ◽  
Vol 11 (1) ◽  
pp. 133-142 ◽  
Author(s):  
J. R. Reitz ◽  
L. L. Foldy
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Pressure Distribution ◽  
Magnetic Field Line ◽  
Potential Flow ◽  
Uniform Magnetic Field ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Joule Dissipation ◽  
Hydrodynamic Motion

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written $\bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$ where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.

Numerical Investigation of Slip Effects on Hydromagnetic Flow Due to a Rotating Porous Disk in a Nanofluid with Internal Heat Absorption

2017 ◽  
Vol 33 (3) ◽  
pp. 375-386
Author(s):  
S. P. Anjali Devi ◽  
T. Elakkiya Priya
Keyword(s):  
Differential Equations ◽  
Interaction Parameter ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Internal Heat ◽  
Magnetic Interaction ◽  
Heat Absorption ◽  
Slip Parameter ◽  
Suction Parameter ◽  
Magnetic Interaction Parameter

AbstractIn recent days, nanofluids have derived the attention of researchers, scientists and engineers due to their abundant applications in Engineering and technology and specific applications such as Electronics cooling, vehicle cooling, medical applications including cancer therapy and so on. Motivated by these applications of nanofluids, this work is mainly concerned with the convective heat transfer of nanofluids. MHD slip flow of nanofluids with heat absorption over a rotating disk subjected to suction has been analyzed. Two types of nanofluids such as copper-water nanofluid and silver-water nanofluid are considered for the present study. The system of axisymmetric nonlinear partial differential equations governing the hydromagnetic steady flow and heat transfer are reduced to nonlinear ordinary differential equations by introducing suitable similarity transformations. The resulting non-linear ordinary differential equations are solved numerically by most efficient Nachtsheim-Swigert shooting iteration technique for satisfaction of asymptotic boundary conditions along with Runge – Kutta Fehlberg Method. The flow field is affected by the presence of physical parameters, such as magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, whereas the temperature field is addionally affected by magnetic interaction parameter, suction parameter, internal heat absorption parameter and solid volume fraction. With the amplifying effect in magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, the radial and tangential velocities decline. Axial velocity gets decelerated for increasing magnetic interaction parameter and slip parameter whereas it gets accelerated for growing effect of suction parameter and solid volume fraction. The temperature of the fluid within the boundary layer enhances with the increasing effect of magnetic interaction parameter and solid volume fraction while it reduces for increasing values of the suction parameter and internal heat absorption parameter. Also the values of radial and tangential skin friction coefficients and Nusselt number are obtained numerically and are tabulated.

Motion of a sphere through a conducting fluid in the presence of a strong magnetic field

1956 ◽  
Vol 52 (2) ◽  
pp. 301-316 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Fluid Velocity ◽  
Steady Motion ◽  
Conducting Fluid ◽  
Two Dimensional ◽  
Conducting Sphere ◽  
Straight Lines ◽  
As If

ABSTRACTThe steady motion of a perfectly conducting sphere in an inviscid conducting fluid in the presence of a strong magnetic field is discussed. It is shown that if the fluid velocity is ultimately steady then it is two-dimensional, and a cylinder of fluid whose generators are parallel to the direction of the field moves with the sphere as if solid. The streamlines outside are straight lines if the sphere moves in the direction of the field but have to execute sharp turns if it moves at right angles to the field. The motion to be expected in practice is discussed using an analogy.

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