Peristaltically induced transport of a MHD biviscosity fluid in a non-uniform tube

We have analyzed an incompressible flow of electrically conducting biviscosity fluid through an axisymmetric non-uniform tube with a sinusoidal wave under the considerations of long wavelength and low Reynolds number. In our analysis we are taking into account the induced magnetic field. The analytic solution has been obtained from which the axial velocity, the axial induced magnetic field and the axial pressure gradient have been derived. The results for the pressure rise ΔP_λ(t), frictional force per wavelength F_λ(t) and the axial induced magnetic field h_z have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the magnetic Prandtl number p_m, the magnetic field parameter M, the Reynolds number Re, the upper limit apparent viscosity coefficient β, and the time averaged mean flow rate θ.     

Linear instability of plane Couette and Poiseuille flows

It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Re_th ≈ 139, which agrees with the experimental value of Re_th ≈ 150 ± 5 [16, 17]. This new result of the linear theory of hydrodynamic stability is obtained by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction. It is established that previous notions about linear stability of this flow at arbitrarily large Reynolds numbers relied directly upon the assumed separation of spatial variables of the field of disturbances and their longitudinal periodicity in the linear theory. By also abandoning these assumptions for plane Poiseuille flow, a new threshold Reynolds number Re_th ≈ 1035 is obtained, which agrees to within 4% with experiment—in contrast to 500% discrepancy for the previous estimate of Re_th ≈ 5772 obtained in the framework of the linear theory under assumption of the “normal” shape of disturbances [2].     

The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump

The forced convection of nanofluid flow in a long microchannel is studied numerically according to the finite volume approach and by using a developed computer code. Microchannel domain is under the influence of a magnetic field with uniform strength. The hot inlet nanofluid is cooled by the heat exchange with the cold microchannel walls. Different types of nanoparticles such as Al₂O₃ and Ag are examined while the base fluid is considered as water. Reynolds number are chosen as Re=10 and Re=100. Slip velocity and temperature jump boundary conditions are simulated along the microchannel walls at different values of slip coefficient for different amounts of Hartmann number. The investigation of magnetic field effect on slip velocity and temperature jump of nanofluid is presented for the first time. The results are shown as streamlines and isotherms; moreover the profiles of slip velocity and temperature jump are drawn. It is observed that more slip coefficient corresponds to less Nusselt number and more slip velocity especially at larger Hartmann number. It is recommended to use Al₂O₃-water nanofluid instead of Ag-water to increase the heat transfer rate from the microchannel walls at low values of Re. However at larger amounts of Re, the nanofluid composed of nanoparticles with higher thermal conductivity works better.     

Crystallographic,magnetic, and electrical properties of thin <Emphasis Type="Italic">Re</Emphasis><Subscript>0.6</Subscript>Ba<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> epitaxial films (<Emphasis Type="Italic">Re</Emphasis> = La,Pr, Nd,Gd)

Thin Re_0.6Ba_0.4MnO₃ epitaxial films (Re = La, Pr, Nd, Gd) grown on (001)SrTiO₃ and (001)ZrO₂(Y₂O₃) single crystal substrates have been prepared and studied. All the films were found to have a cubic perovskite structure, with the exception of the film with Re = La, which revealed rhombohedral distortion of the perovskite cell. The temperature dependences of the electrical resistivity and magnetoresistance pass through a maximum near the Curie point T_C, where the magnetoresistance reaches a colossal value. The magnetization isotherms M(H) are superpositions of a magnetization that is linear in field (like that of an antiferromagnet) and a weak spontaneous magnetization. The magnetic moment per formula unit is substantially smaller than that expected under complete ferro-or ferrimagnetic ordering. The magnetizations of samples cooled in a magnetic field (FC samples) and with no field applied (ZFC samples) differ by an amount that persists up to the highest measurement fields (50 kOe). The M(T) dependence obtained in strong magnetic fields is close to linear. Hysteresis loops of the FC samples are shifted along the field axis. The above magnetic and electric properties of thin films are explained in terms of two coexisting magnetic phases, which are due to strong s-d exchange coupling.     

Two- and three-dimensional waves in falling film flow in the nonlaminar flow regime: an NMR study

Nuclear magnetic resonance (NMR) velocity-encoded imaging results as well as propagators are presented for the nonlaminar flow regime of falling films. The film is generated by a continuous flow of silicon oil along a vertical poly(methyl methacrylate) plate. While the film remains purely laminar for a film Reynolds number Re_f=0.5, it exhibits laminar-wavy behavior for 1.0≤Re_f≤2.5. In this range, a laminar residual film can be distinguished from averaged waves near the surface of the film from measurements of the flow velocity ν₂ along the direction of gravity as a function of the coordinatex normal to the plate. The perpendicular velocity components, ν _x and ν _y are zero within the accuracy of the measurement, indicating that the wave motion is two-dimensional in the laminar-wavy case. For higher Re_f the waves are found to be three-dimensional, a straightforward division into a residual film and waves in ν _z is lost and the waves extend over the whole thickness of the film.     

Magnetic stabilization,transition and energy analysis in the Marangoni driven Full-Zone at low Prandtl numbers

The linear stability of the Marangoni-driven Full-Zone is investigated for low Prandtl number fluids. A constant and uniform magnetic field is applied along the axial axis of the liquid bridge to stabilize the axisymmetric base state. Dramatic contraction of the flow circulation in both radial and azimuthal directions is observed with moderate magnetic fields. The numerical solution utilizes a vorticity transport formulation and high resolution spectral collocation scheme with Chebyshev polynomial basis functions. Critical transitions to three-dimensional, stationary flows are observed up to Ha = 300 for Pr = 0.02 and Ha = 500 for Pr = 0.001. A hydrodynamically driven instability is suggested by the perturbation flows and confirmed through an energy analysis.     

Solution to the paradox of the linear stability of the Hagen-Poiseuille flow and the viscous dissipative mechanism of the emergence of turbulence in a boundary layer

It has been shown that the conclusion of the linear instability of the Hagen-Poiseuille flow at finite Reynolds numbers requires the refusal of the use of the traditional “normal” form of the representation of disturbances, which implies the possibility of separation of variables describing disturbances as functions of the radial and longitudinal (along the axis of a tube) coordinates. In the absence of such separation of variables in the developed linear theory, it has been proposed to use a modification of the Bubnov-Galerkin theory that makes it possible to take into account the difference between the periods of the longitudinal variability for different radial modes preliminarily determined by the standard application of the Galerkin-Kantorovich method to the evolution equation of extremely small axisymmetric disturbances of the tangential component of the velocity field. It has been shown that the consideration of even two linearly interacting radial modes for the Hagen-Poiseuille flow can provide linear instability only in the presence of the mentioned conditionally periodic longitudinal variability of disturbances along the axis of the tube, when the threshold Reynolds number Re_th(p) is very sensitive to the ratio p of two longitudinal periods each describing longitudinal variability for its radial disturbance mode. In this case, the threshold Reynolds number can tend to infinity, Re_th(p) → ∞, only at p = p _k = k, p = p _1/k = 1/k, and \(p = p_{\sqrt k } = [k + 1 \pm \sqrt {(k + 1)^2 - 4} ]/2\) , where k = 1, 2, 3, …. The minimum Reynolds number Re_th(p) ≈ 448 (at which p ≈ 1.527) for the linear instability of the Hagen-Poiseuille flow quantitatively corresponds to the condition of the excitation of Tollmien-Schlichting waves in the boundary layer, where Re_th = 420. Similarity of the mechanisms of linear viscous dissipative instability for the Hagen-Poiseuille flow and Tollmien-Schlichting waves has been discussed. Good quantitative agreement has been obtained between the phase velocities of the vortex disturbances and the experimental data on the velocities of the leading and trailing edges of turbulent “puffs” propagating along the axis of the tube.     

Unsteady analysis of six-DOF motion of a 6:1 prolate spheroid in viscous fluid

Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6.     

Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

In this paper we investigate the effects of external electric and magnetic fields on a three-dimensional harmonic oscillator with axial symmetry. The energy spectrum of such a system is non-degenerate due to the presence of the magnetic field. The degeneracy of the energy spectrum in the absence of a magnetic field is discussed. The influence of electric and magnetic fields, as well as the frequencies of the oscillator on the probability distribution function is analyzed. Optical transition probabilities are examined by deriving the selection rules in dipole approximation for the quantum numbers n _p , m _l and n _z . Employing stationary perturbation theory, the effects of deformations of the potential energy function on the oscillatory states are analyzed. Such models have been used in literature in analysis of spectra of axially symmetrical molecules and cylindrical quantum dots.     

Self-field effects on electron dynamics in a three-dimensional helical wiggler free-electron laser with axial magnetic field

An analytic linear theory of the electron dynamics in a three-dimensional helical wiggler free electron laser (FEL) with axial magnetic field is presented. Orbits are obtained by perturbing the steady state-trajectories in order to determine the characteristic frequencies Ω_± of the FEL. The effect of the self-fields on electron dynamics is studied and modified steady-state orbits and their stabilities have been analysed considering variation of electron energy and density. Among the features encountered is that in both group-I and group-II, one of the characteristic frequencies may have either signs affecting then the stability of the motion, while in group-II operation a repulsion of the frequencies at a pseudocrossing leads to highly perturbed trajectories when the wiggler frequency is approximately half the cyclotron frequency. Self-fields effects can significantly impair the stability of the electron orbits. For group-I orbits, they are more important for higher wiggler frequencies and lower beam energies. For group-II orbits, they remain less important for higher wiggler frequencies and lower beam energies before reaching the inversion zone, then they behave as for group-I orbits. It should be remarked that self-fields shift the inversion zone towards higher cyclotron frequencies the thing that is obtained by either decreasing the wiggler frequency or increasing the beam energy. It is shown that the axial velocity-induced self-magnetic field has a diamagnetic effect for both groups orbits, while the wiggler-induced self-magnetic field has a diamagnetic effect for group-I orbits and a paramagnetic effect for group-II orbits. The paramagnetic and diamagnetic effects are more important for higher beam energies and densities.     

Magnetic properties of R2Re2Si2C (R=Ho and Er)

We have investigated magnetic properties of R₂Re₂Si₂C (R=Ho and Er) using magnetic susceptibility, magnetization and heat capacity measurements. Both the materials order antiferromagnetically. The ordering temperatures (T_N) for Ho₂Re₂Si₂C and Er₂Re₂Si₂C are, ∼8.8 and ∼7.6 K, respectively. Our measurements indicate crystal field effects in the bulk properties of both these compounds. The experimental results have been analyzed by taking into account the effect of crystalline electric field and magnetic exchange interaction.     

High-field magnetoresistance and Hall effect in Bi2Sr2CuO x single crystals

We investigated the in-plane magnetoresistance and the Hall effect of high-quality Bi₂Sr₂CuO_x single crystals with T _c (midpoint) = 3.7–9.6 K in dc magnetic fields up to 23 T. For T < 10 K, the crystals show the classical positive magnetoresistance. Starting at T ≈ 14 K, an anomalous negative magnetoresistance appears at low magnetic fields; for T ≥ 40 K, the magnetoresistance is negative in the whole studied range of magnetic fields. Temperature and magnetic field dependences of the negative-magnetoresistance single crystals are qualitatively consistent with the electron interaction theory developed for simple semiconductors and disordered metals. As is observed in other cuprate superconductors, the Hall resistivity is negative in the mixed state and changes its sign with increasing field. The linear T-dependence of cotθ_H for the Hall angle in the normal state closely resembles that of the normal-state resistivity as expected for a Fermi liquid picture.     

BCS-like behaviour in the superconducting state of itinerant antiferromagnetic CrRe alloys

Measurements of the heat capacity and the magnetic susceptibility have revealed BCS-like behaviour in the superconducting state of itinerant antiferromagnetic Cr_1?xRe_x alloys for x = 0.30) and 0.26. The thermodynamic quantities, such as electronic heat capacity and thermodynamic critical field have been reproduced with the BCS theory with the energy gap Δ = (1.76 ± 0.05)k_BT_s, where T_S is the superconducting transition temperature for the corresponding system: T_S = 3.61 K (2.35 K) for x = 0.30 (0.26).     

Flow visualization of relaminarization phenomena in curved pipes and the related measurements

Flow visualization results for secondary flow phenomena at the exit of 90° and 180° bends and helically coiled pipes (1, 2 and 5 turns), (radius of curvatureR _c=381 mm, inside pipe diameterd=37.5 mm, curvature ratiod/2R _c=0.049) and in the downstream straight pipe (l/d=30) are presented to study the stabilizing (relaminarization) effect in curved pipes with fully developed entry turbulent air flow and the destabilizing (re-transition from laminar to turbulent flow) effect in the downstream straight region. The entry Reynolds numbers areRe=2200, 3200, 4300 and 5300). The related measurement results using a hot-film anemometer are presented for developing profiles of the time-mean streamwise velocity distribution and the axial turbulence intensity field in the 180° return bend and in the downstream straight pipe for Reynolds numbersRe=3200, 4300, 6300 and 8200. The time traces showing the output of the hot-film sensor are also presented for developing fluctuating velocity field in the 180° bend and in the downstream straight pipe for the same Reynolds number range. Some aspects of the relaminarization phenomena in curved pipes and the re-transition phenomena from laminar to turbulent flow in the downstream straight pipe are clarified by the present experimental investigation.     

Magnetic linear birefringence in Yb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> gallate garnet

The magnetic linear birefringence and the magnetic susceptibility of Yb₃Ga₅O₁₂ gallate garnet was investigated experimentally in the temperature range 78–295 K. It was shown that, in this temperature range, the magnetic linear birefringence of the garnet studied depends linearly on inverse temperature 1/T. The magnitude of this effect is determined only by the part of the crystal magnetization that is due to the difference in the thermal population of the ground state of the Yb³⁺ ion rather than the total magnetization. The results obtained are interpreted within the microscopic theory. According to this theory, the magnetic linear birefringence is determined by the quadrupole moment of the magnetoactive ion, which is induced by an external magnetic field.     

Simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Fresh cement mortar is a type of workable paste,which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering.In this paper,Papanastasiou’s model for Bingham fluids is solved by using the multiplerelaxation-time lattice Boltzmann model(MRT-LB).Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou’s model provides a good approximation of realistic Bingham plastics for values of m108.For lower values of m,Papanastasiou’s model is valid for fluids between Bingham and Newtonian fluids.The MRT-LB model is validated by two benchmark problems:2D steady Poiseuille flows and lid-driven cavity flows.Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability.We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle.Besides the rich flow structures obtained in this work,the dynamics fluid force on the round particle is calculated.Results show that both the Reynolds number Re and the Bingham number Bn afect the drag coefcients CD,and a drag coefcient with Re and Bn being taken into account is proposed.The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed.Finally,the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields.These results help simulation of fresh concrete flowing in porous media.     

Magnetic configurations of hexagonal iron rhenium multilayers

We present ab initio calculation of the electronic structure and magnetic properties of Fe/Re multilayers assuming hcp crystallographic phase. The system is modeled according to recent structural analysis which shows that Fe/Re has bct(0 0 1) ordering for 0⩽t_Re⩽8 Å after which a structural phase transition occurs to an hcp phase. Antiferromagnetic and ferromagnetic orders appear more stable than the nonmagnetic (NM) state, only when the Fe atoms begin to adopt an expanded volume of about 27% accompanied by an axial distortion (c/a=1.42). The sizeable magnetic moments calculated on Fe atoms contrast with the paramagnetic bulk hcp. These results are discussed and compared with recent experimental data on hcp Fe/Re superlattices and also with magnetic properties of Fe/Ru multilayers.     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

Analysis of magnetohydrodynamic flow of a fractional viscous fluid through a porous medium

The aim of this paper is to investigate the exact general solutions of the incompressible viscous fluid flow by using the time-fractional Caputo–Fabrizio derivative. The flow of the fluid is subject to the motion of a plane wall, embedded in a porous medium under the influence of magnetic field. The corresponding non-dimensional governing fractional differential equation with appropriate initial and boundary conditions is solved by means of integral transforms namely, Laplace and Fourier transforms. Solutions are expressed as a sum of steady and transient parts, for the sinusoidal oscillations of the plane wall. The influence of involved physical parameters are discussed graphically. Specifically, it has been observed that the effective permeability K_eff reduces the time taken to reach the steady state.     

Effect of neutral pressure on the He plasma flow measurement in a linear device

Axial and azimuthal flow velocities have been measured in a linear plasma device called NAGDIS-II (NAGoya DIvertor Simulator-II), along with plasma density and electron temperature, using a vector Mach probe composed of two Mach probes, one of which is for the axial flow, and the other is for the azimuthal flow. To study the effect of neutral pressure on the deduction of the Mach numbers, the ratio of upstream to downstream currents are measured by changing the neutral pressure for the deduction of flow velocities. Helium plasma was generated with pressure of 2–35 mTorr. Since the ion gyro-radius at the magnetic flux of 300 G is larger than the probe size, an unmagnetized collisionless Mach probe theory was used for the deduction of Mach numbers and their variations. In order to check the range of collisionality, plasma density (n_e = 10¹⁰–10¹¹ cm^?3) and electron temperature (T_e = 2–9 eV) are measured by a single electric probe using a conventional collisionless probe theory. Variations of Mach number, electron temperature and plasma density with collisionless models are to be compared with those using collisional models for different pressures where ionization and ion-neutral collision are included. Mach numbers by the collisionless model are found to be overestimated by 120% for the maximum difference even in weakly collisional plasmas. A clear flow reversal exists in the axial direction with higher pressure plasma, even in the linear machine. Azimuthal flows are also measured simultaneously along with axial flows, yet they seem to be very small in the present cold ion plasma (T_i/T_e << 1).