On the propagation of sonic discontinuities in the unsteady flow of a perfect gas

The magnitude of discontinuities of the first derivatives of flow quantities in the unsteady flow of a perfect gas are shown to satisfy Riccatti equations along the orthogonal trajectories of sonic singular surfaces $\text{S(t)}$. These equations are greatly simplified if they are transformed to equations along the bicharacteristic curves in the characteristic manifold $\text{Σ = U S(t)}$. When this is done an explicit criteria for the decay or “blow up” of sonic discontinuities can be given.     

Unsteady hydromagnetic couette flow in a rotating system

Unsteady hydromagnetic flow of an electrically conducting viscous incompressible fluid in a rotating system under the influence of a uniform transverse magnetic field is investigated when one of the plates is set into motion with the time dependent velocity $\text{U(t)}$ in its own plane. Two cases of interest, namely, impulsive start as well as accelerated start of the moving plate are discussed. The asymptotic behaviour of the solution is also analysed for both small and large time to highlight the transient approach to the final steady state and effects of rotation parameter as well as Hartmann number. The shear stresses at the moving plate due to the primary and secondary flows are derived in both cases. It is found that the shear stress components due to the primary flow decrease, whereas that due to the secondary flow increase with the increase in rotation parameter.     

Double diffusive flow of a hydromagnetic nanofluid in a rotating channel with Hall effect and viscous dissipation: Active and passive control of nanoparticles

The investigation of simultaneous effects of Hall current and viscous dissipation on three-dimensional magnetohydrodynamic nanofluid flow in a horizontal rotating channel with active and passive control of nanoparticles, is carried out. The lower sheet is considered stretching while the upper sheet is kept fixed. Mathematical model is developed using boundary layer and scale analysis approach. Similarity transformation technique is employed to translate the governing partial differential equations into ordinary differential equations. The bvp4c solver of MATLAB is employed to solve transformed equations. Computations for nanofluid velocity, nanofluid temperature distribution and distribution of nanoparticles along with skin friction co-efficient and Nusselt number, are carried out for a range of values of pertinent flow parameters. A comparative analysis of effect of $\text{CuO}$ and ${\text{Al}}_2{\text{O}}_3$ nanoparticles on velocity, temperature, nanoparticle distribution, skin friction coefficient and Nusselt number is carried out. Rate of heat transfer at the lower sheet is observed to be a decreasing function of magnetic field whereas this physical quantity is getting enhanced as the volume fraction of nanoparticles are increased.     

Deceleration of a porous rotating disk in a viscous fluid

The flow due to a rotating disk decelerating with an angular velocity inversely proportional to time with either surface suction (or injection) which again varies with time is investigated. The unsteady Navier-Stokes equations are transformed to non-linear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using a globally convergent homotopy method. The flow depends on two non-dimensional parameters, namely an unsteadiness parameter $\text{S}$ and a suction (or injection) parameter $\text{A}$. Some interesting numerical results are presented graphically and discussed.     

Analysis of the steady motions of complex rotating systems

This paper develops a practical computational framework for analyzing the steady motions of complex rotating systems. Ignorable coordinates corresponding to the translational or rotational invariances of a closed system can always be used in order that the effective potential functional $\text{W}$ for the relative motion depends only upon the relative configuration. However, the stationary values (steady motions) of $\text{W}$ can be determined by an essentially unconstrained calculational procedure even when $\text{W}$ is expressed most simply with Cartesian coordinates. It is shown that the angular velocity of any fixed rotating configuration (FRC) must paralled a principal axis when some mild assumptions about the nonrigidity of the system are fulfilled. This property implies that every distinct FRC corresponds to a stationary value of $\text{W}$. The discussion includes examples of $\text{N-}\text{body}$ problems and a spin-stabilized kilometer-wave orbiting telescope. Random or systematic searching and a quasi-Newton algorithm are used to compute minima of $\text{W}$.     

Hydromagnetic stability of helical flows permeated by a magnetic field with a radial component

In this paper, we have studied the linear stability of the nondissipative helical flow of an incompressible perfectly conducting fluid between two concentric cylinders permeated by a non-zero radial magnetic field. It is found that a rigidly rotating column of a perfectly conducting fluid permeated by a magnetic field [($\text{A/r}$), ($\text{C/r}$), $\text{B}{}_0$], where $\text{A, C, B}{}_0$ are constants, is stable for all infinitesimal disturbances.     

The systematic construction of liapunov functionals in the linear stability of conservative steady flows

The linearized equations of motion for small perturbations about a state of steady flow of a conservative dynamical system, when expressed in appropriate variables, admit a class of explicit constants of motion. The construction of Liapunov functionals from these constants of motion is discussed, with applications to plane parallel flow of an inviscid incompressible fluid and plane parallel flow of an inviscid, compressible, electrically charged fluid. Bounds on the $\text{L}{}_2\text{-}\text{norms}$ of certain system variables are obtained.     

Fluid flow through an array of fixed particles

Slow flow of an incompressible viscous fluid is studied in an array of a great number of small fixed solid particles. The particles size ? and the distance η between two neighbouring solids are such that $\text{??η?1}$. Using perturbation methods it is proved that Brinkman's law occurs really for a critical size of particles; for larger particles the fluid filtration is governed by the Darcy's law and smaller solids do not influence the flow. The 3 and 2-dimensional cases are studied.     

Viscous dissipation effects on mixed convection about a rotating sphere

The effect of viscous dissipation on mixed convection flow about a rotating sphere is investigated analytically. A method based on Merk's type of series expansions is used to obtain the heat transfer rate and the skin-friction coefficients. Numerical computations were carried out for Eckert number Ec ranging from 0 to 0.1, rotation parameter B = 0, 1, 4 and buoyancy parameter ranging from 0 to 1 at various angular positions. As viscous dissipation increases heat transfer rate decreases. It is found that for Ec > 0, a critical value of B (say B_cri) exist such that $\text{Nu Re}{}_{\mathrm{R}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ increases as B increases up to B = B_cri and then decreases. B_cri decreases with Ec when the angle is fixed or decreases with angle when Ec is fixed. When Ec > 0, possibly there exist a λ, say λ_cri, such that $\text{Nu Re}{}_{\mathrm{R}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ increases with λ up to λ = λ_cri and then decreases. Also the effect of viscous dissipation on skin friction is investigated.     

The problem of a griffith crack in micropolar elasticity

In the linear theory of micropolar elasticity the problem of Griffith crack in a transverse field of constant uniaxial tension is studied. The problem is reduced to three Fredholm integral equations of the second kind. These equations, which have the same kernel, are solved numerically. The stress environment at the tips of the crack is found to depend on, apart from Poisson's ratio and a material length parameter τ, another parameter $\text{N}$ which characterises the coupling of the microstructure with the displacement field. $\text{N}$ does not occur in the analogous problem in couple stress theory. Classical results are recovered in the limits: (i) $\text{N}$ tends ot zero (τ fixed) and (ii) τ tends to zero ($\text{N}$ is of the same order of magnitude as τ or of lower order).     

Structure helimagnetique de NaMnCrF6

In NaMnCrF₆ the three magnetic sublattices Cr₁, Cr₂ and Mn order below 21K. The propagation vector $\text{q}\text{= (0, 0, 0.018)}$ implies a very large magnetic unit-cell ($\text{? 278}$ A along $\text{c}$). The configuration of the moments is helical and generated by rotating a ferrimagnetic colinear mode in an oblique plane.     

Stability of microstretch fluid motions

Criteria of stability of the unsteady motion of incompressible microstretch fluid in an arbitrary time-dependent domain are obtained using a general energy method introduced by Serrin. It is shown that the original motion is stable in the mean if either of the two sets of numbers ($\text{?}{}_1$,$\text{?}{}_2$,$\text{?}{}_3$) or ($\text{σ}{}_1$, $\text{σ}{}_2$,$\text{σ}{}_3$) consists of positive numbers only. These numbers are expressible in terms of the various Reynolds numbers of the original motion. The theorems giving the stability criteria are universal in the sense that they do not depend on the geometry of the domain or the actual distribution of the flow field quantities. The decay of energy of the flow in a rigid and fixed container as well as a theorem on the uniqueness of steady flows are deduced.     

Conductance Calculation Of Slot Channels with Variable Cross Section

The range of operation pressures of non‐contact vacuum pumps may reach six decades, and flow regime in slot channels of the rotor mechanism may vary from molecular flow to viscous flow. This article is a continuation of a series of authors‘ publications dedicated to the development of a method which makes it possible to calculate promptly the conductance of slot channels with complex contoured geometry with the minimal clearance at a certain point along gas flow direction for all three gas flow regimes: molecular, transient and viscous. The numerical solution of the differential equations system (equations of motion, energy, continuity and state) is used for calculation of mass flow rate in transient gas flow regime. On the basis of the numerical calculation results the relationship is obtained which represents a smooth joining of the data for molecular and viscous flow regimes. Verification of the model and the obtained relationship is carried out by comparison of numerical calculation results of gas mass flow rate and conductance with experimental data obtained by blowing‐through of slot channels. The maximal deviation of calculation according to the obtained relationship from the experiment does not exceed 14%, the average uncertainty being less than 8%, which makes it possible to recommend it for practical application in transient flow regime.     

Flow separation in a viscous parabolic shear past a cylinder

Low Reynolds number parabolic shear flow past a circular cylinder, placed asymetrically with its centre at a distance $\text{k}$ from the shear axis, is investigated employing matching technique. The analysis of flow separation indicates coalescion of wakes with increasing $\text{k}$. The drag is governed by a parameter λ which changes sign depending on the magnitude of $\text{k}$, while the torque is proportional to $\text{k}$. The case of a rotating cylinder including free rotation is also discussed.     

Une modelisation du comportement magnetique d'un compose de l'iridium pentavalent: LaLi12Ir12O3

A new interpretation is proposed for the magnetic properties of perovskite-type iridium (+V) oxide $\text{LaLi}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{Ir}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{O}{}_3$. In its unusual +5 oxidation state iridium has a t⁴_2ge⁰_g configuration. The magnetic susceptibility has been calculated assuming cubic symmetry of the crystal field and a Coulomb repulsion of the same order of magnitude than spin-orbit coupling. Fitting of the experimental data leads to a single spin-orbit constant $\text{ζ ? 3470}\text{cm}{}^{\mathrm{?1}}$ close to that of previously investigated Ir(+V) compounds.     

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel $\text{d}$ to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.     

Existence of periodic solutions of the equations of incompressible microstretch fluid flow

The flow of incompressible microstretch fluid is governed by a system of differential equations involving the velocity vector $\text{q}$, the microprotation vector $\text{v}$ and the scalar $\text{v}$ representing the microstretch of the fluid element. Let $\text{R = R(t)}$ be a bounded domain in space and let the field ($\text{q}$, $\text{v}$, $\text{v}$) be prescribed at each point of the boundary $\text{?R(t)}$. If the domain $\text{R(t)}$ and the boundary data depend periodically on the time $\text{t}$, it is shown that under some assumptions on the initial distribution of the flow fields and the material constants of the fluid, there exists a unique, stable, periodic solution of the microstretch flow equations in $\text{R(t)}$, taking the prescribed values on the boundary $\text{?R(t)}$ (Theorem 2 of the paper). The proof rests on some relations describing the rate of decay of the energy functionals corresponding to the difference of two microstretch flows in the domain that have the same density and gyration parameters and are subject to the same boundary conditions.     

The rectilinear oscillations of a spheroid in a micropolar fluid

The paper examines the oscillatory flow of incompressible micropolar fluid arising from the harmonic oscillation of a spheroid rectilinearly along its axis of symmetry under the assumption of small amplitude of oscillation. The velocity and microrotation are obtained and the drag experienced by the spheroid is determined. The drag parameters $\text{K}$ and $\text{K'}$ are numerically evaluated.     

Convective instability of a layer of a ferromagnetic fluid rotating about a vertical axis

Thermal instability in a layer of a ferromagnetic fluid rotating about a vertical axis and permeated by a vertical magnetic field is investigated within the framework of linear theory. Overstability cannot occur if the Prandtl number $\text{P > 1}$. For overstable oscillations, Rayleigh number is plotted as a function of wave number for several values of the magnetization parameter $\text{M}{}_3$. Critical Rayleigh number is found to decrease with increase in $\text{M}{}_3$.