Laminar flow in an annulus between two concentric rotating porous spheres

Summary An analysis is presented for the steady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric porous spheres with injection/suction at their boundaries. The inner sphere rotates with constant angular velocity about its own fixed axis, while the outer sphere is stationary. A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique. The solution obtained is in the form of a power series expansion in terms of the rotational Reynolds number Re, and an injection/suction Reynolds number Re _w , and is valid for small values of these parameters. Results for the velocity distributions, streamlines, and viscous torques for various values of the flow parameters Re, Re _w , and radius ratios are presented. Viscous torques at the inner and outer spheres are compared with those obtained from the numerical solution of the Navier-Stokes equations, in order to find the range of Re and Re _w for which this solution is accurate.     

Thermal radiation effects on magnetohydrodynamic mixed convection flow of a micropolar fluid past a continuously moving semi-infinite plate for high temperature differences

Summary An analysis is presented to study the effect of radiation on magnetohydrodynamic mixed convective steady laminar boundary layer flow of an optically thick electrically conducting viscous micropolar fluid past a moving semi-infinite vertical plate for high temperature differences. A uniform magnetic field is applied perpendicular to the moving plate. The density of the micropolar fluid is assumed to reduce exponentially with temperature. The usual Boussinesq approximation is neglected because of the high temperature differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting governing equations are transformed using a similarity transformation and then solved numerically by applying an efficient technique. The effects of radiation parameter R, magnetic parameter M, couple parameter Δ and density/temperature parameter n on the velocity, angular velocity and temperature profiles as well as the local skin friction coefficient, wall couple stress and the local Nusselt number are presented graphically and in tabular form.     

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 $\text{M}{}_3$.     

Investigating binary mixtures fluidized using a porous plate

The aim of this study was to give a simple correlation to give a first-approximation value for the minimum fluidizing velocity of a binary system. In contrast to many previous studies into predicting the minimum fluidizing velocity of a binary system fluidized using a porous plate distributor, this investigation proposes a purely empirical correlation for estimating the values of u_M, u_S and u_FF based on plotting Archimedes' number against Reynolds' number using experimental data from a wide range of sources. This produced correlations based on the general form Ar = A · Re^B, which were shown to compare well with actual results.     

Flow past an accelerated horizontal plate in a rotating fluid

Summary A semi-infinite mass of an incompressible viscous fluid bounded by an infinite flat plate is initially rotating with uniform angular velocity about an axis normal to the plate. An analysis is presented for the subsequent flow when the plate started impulsively from rest relative to the rotating fluid moves with uniform acceleration in its own plane. It is found that when 0, the velocity profiles for varying times are nonsimilar in contrast to the velocity profiles which are similar in the absence of rotation (=0). At a given instant, the velocity component along the direction of motion of the plate decreases with an increase in rotation but the transverse velocity component (induced by the Coriolis force) increases with increasing rotation. Due to the gradual thinning of the boundary layer with rotation, both the skin-friction components along and transverse to the direction of motion of the plate increase with increasing rotation. A study of the asymptotic behavior of the velocity field for large time reveals a novel feature of the flow; it develops inertial oscillations with frequency 2, which grow with time. This behavior has not been reported in the absence of rotation.     

Combined radiation and mixed convection from a vertical wall with suction/injection in a non–Darcy porous medium

Summary. Mixed convection flow of an absorbing fluid up a uniform non–Darcy porous medium supported by a semi-infinite ideally transparent vertical flat plate due to solar radiation is considered. The external flow field is assumed to be uniform, the effect of the radiation parameter in the boundary layer adjacent to the vertical flat plate with fluid suction/injection through it is analyzed in both aiding and opposing flow situations. It is observed that the similarity solution is possible only when the fluid suction/injection velocity profile varies as x^–1/2. The velocity and temperature profiles in the boundary layer and the heat transfer coefficient are presented for selected values of the parameters. It is observed that the Nusselt number increases with the increase in the radiation parameter and also when the value of the surface mass flux parameter moves from the injection to the suction region.     

Hydromagnetic convection at a continuous moving surface

Summary Exact solution for hydromagnetic convection at a continous moving surface with uniform suction is obtained. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow at a surface of finite length. Moreover, this is an exact solution of the complete Navier-Stokes equations (including, buoyancy force-term). The solutions for the velocity and skin friction are evaluated numerically for several sets of values of the parameters;G, the Grashof number,P, the Prandtl number, andM, the Hartmann number. It is observed that there is a reverse flow in the boundary-layer due to heating of the fluid (close to the moving surface). That is, whenT _w>T , the fluid in the boundary-layer will be heated up and thus the free convection currents will set in. Also, it is observed that, there is an increase in the skin friction (absolute) with increasingG, P andM.With 7 Figures     

Hydrodynamic contact between a rotating roll and a semipermeable tray

A viscous fluid flow in the gap between a side surface of a rotating roll and a rectangular cavity with a semipermeable bottom surface is considered in the Reynolds approximation.Notation x, y, z Cartesian coordinates - U peripheral velocity of the roll - W translational velocity of the tray - h gap height - h ₀ minimum gap - side gap - v _x,v _y,v _z velocity components - K coefficient of channel wall permeability - P,504-1 dimensional and dimensionless pressures - R roll radius - S channel width - fluid viscosity - angle - x₀,₁, , dimensional and dimensionless coordinates of the flow zone boundaries - dimensionless permeability - friction - ,q geometrical simplexes - dimensionless variable - Q bulk flow rate of fluid - F buoyancy force - N power - I ₁,I ₂ integral parameters of flow - ₁, ₂ angular velocities of rotor and cylinder - _c fluid density - q gravity acceleration - Re Reynolds number - R ₁,R ₂ radii of cylinder and rotor in a granulator Volgograd Technical University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 612–618, July–August, 1995.     

MHD combined free and forced convection flow through two parallel porous walls

Summary The flow of a viscous conducting fluid between two parallel plates of infinite length (one of which is at rest and the other moving parallel to itself with a linear axial temperature variation) under the influence of a uniform transverse magnetic field is considered. It is assumed that the fluid is injected into the channel through the lower wall and sucked from the channel through the upper wall with the same velocityv ₀. The velocity and temperature distributions, the coefficient of skin friction and the rate of heat transfer coefficient are evaluated. The effects of magnetic parameterM, the suction Reynolds numberR, the Grashoff numberG and Binkmann numberB on the above mentioned physical quantities are investigated.With 21 Figures     

Hydrodynamic study of a rotating MHD flow in a cylindrical cavity by ultrasound Doppler shift method

An experimental study of a steady laminar magnetohydrodynamic (MHD) flow driven by a rotating disk at the top of a cylindrical cavity filled with water or mercury is presented. The velocity distributions were analysed using the ultrasound velocity (UVP) measuring technique. The uniform and constant applied magnetic field is directed along the axis of the cavity. The measurements were compared with results obtained from a numerical model based on a finite volume computational fluid dynamics (CFD) model. The effects of the magnetic field, the fluid and wall electrical conductivities, and the wall thickness are investigated through the conductance ratio k which characterises the influence of the wall on the closure of the electric current distribution. The other relevant parameters are the Hartmann number M, and the Reynolds number Re. The study was performed essentially for different values of Re ? 30,000 and M ? 260. There were close agreement between numerical results, the present ultrasonic measurements and other reported experimental and numerical works. The experiments have revealed something that has not been predicted numerically, the sidewall layer is unstable for special conditions of Hartmann and Reynolds numbers.     

Investigation of laminar-turbulent transition in supersonic boundary layers in an axisymmetric aerophysical flight complex and in a model in a wind tunnel in the presence of heat transfer and suction of air

Analysis is made of the problems associated with laminar-turbulent transition in wall boundary layers, as well as of scale effects observed in the investigation of laminar-turbulent transition in wind tunnels and laminarization of flow. Flight-performance data are given on the Reynolds number and on the gradient criterion of stability at the beginning of transition on the nose part of the Oblako aerophysical complex in the presence of heat transfer for the numbers Re _{L, ∞} ≤ 2 × 10⁷, M_∞ ≤ 2.0, and acceleration a ≤ 12g. Experimental data are given on laminarization of flow past a porous plate in a wind tunnel under the effect of suction for M_∞ = 2.5. The theory of Emmons turbulent spots is generalized to the flight conditions of flow past the nose part of the Oblako aerophysical flight complex in the presence of heat transfer and to the case of laminar-turbulent transition on a porous plate for M_∞ = 2.5 in the presence of suction of air.     

Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study)

Summary. In this paper, an analysis is presented to study the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations which are solved numerically by using the Chebyshev finite difference method (ChFD). Numerical results are carried out for various values of the dimensionless parameters of the problem. The numerical results show variable density, variable viscosity, variable thermal conductivity and micropolar parameters, which have significant influences on the azimuthal and the angular velocities and temperature profiles, shear stress, couple stress and the Nusselt number. The numerical results have demonstrated that with increasing temperature ratio parameter the azimuthal velocity decreases. With increasing variable viscosity parameter the temperature increases, whereas the azimuthal and the angular velocities decrease. Also, the azimuthal and the angular velocities increase and the temperature decreases as the variable conductivity parameter increases. Finally, the pressure increases as the suction parameter increases.     

Boundary length and internal surface area measurements in porous materials with elliptical pores

Formulae are derived for the stereological determination of boundary length per unit area,B _A, and surface density,S _v, in materials with elliptically shaped pores. These relationships are valid for two-phase solids with orthotropically distributed internal surfaces (surfaces that can be mapped onto an ellipsoid). Maximum and minimum mean intercept length measurements in a plane are needed to calculateB _A. Mean intercept length measurements in the three principal directions of porous symmetry are necessary to calculateS _v. If the principal directions are not known they can be found by calculating the eigenvectors of a second rank tensor called the mean intercept length tensor. In a material with a transversely isotropic distribution of internal surfaces (surfaces that can be mapped onto a spheroid), mean intercept length measurements along and transverse to the axis of symmetry are needed to calculateS _v.     

Boundary layer flow of a dusty fluid over a semi-infinite flat plate

Summary Both the drag force due to slip and the transverse force due to slip-shear have been considered in boundary layer equations. The solution has been found in a power series of non-dimensionalx, x being the distance in the down-stream direction. Solutions for high slip region and small slip region characterised byx1 andx1 respectively, have been found separately. In the high slip region the effect of increase in concentration parameter of the dust particles is to increase the magnitude of the longitudinal fluid phase velocityu. Also the magnitude of the longitudinal particle slip velocityu _p -u is becoming maximum on the plate and decreasing along the plate withx. The transverse particle velocityv _p is independent of but it is directly proportional to , the transverse force coefficient. An interesting result is thatv _p is assuming small positive value on the plate. The transverse force has taken an important role in migration of particles away from the plate. In the small slip region the flow of dust particles is mainly governed by the fluid-phase. The effect of on the flow field in this region is to decrease the boundary layer thickness. In this region the particles are having some tendency to accumulate near the plate. Lastly, it has been found that the shearing stress, skinfriction and the dimensionless drag-coefficient on the plate increase with increase of .With 5 Figures     

EMHD free-convection boundary-layer flow from a Riga-plate

The electro-magnetohydrodynamic (EMHD) free-convection flow of a weakly conducting fluid (e.g. seawater) from an electromagnetic actuator is considered. The actuator is a so called Riga-plate which consists of a spanwise aligned array of alternating electrodes and permanent magnets mounted on a plane surface. This array generates a surface-parallel Lorentz force which decreases exponentially in the direction normal to the (horizontal) plate. The free-convection boundary-layer flow induced by this body force is investigated numerically and analytically. It is shown that a certain length and velocity scale exists on which the flow characteristics are independent of the material properties of the fluid, as well as of the structural and functional parameters of the actuator. These universal velocity profiles are calculated numerically at different distances x from the leading edge and are discussed in some detail, both for the impermeable and the permeable Riga-plate when; in the latter case, a uniform lateral suction or injection of the fluid is applied. For the flow characteristics analytical approximations are reported. The asymptotic suction profiles approached for large values of x are given in exact analytical form. From a mathematical point of view the basic equations of the present boundary-value problem resemble those of the classical Blasius problem with an inhomogeneous forcing instead of an external flow and, accordingly, a homogeneous asymptotic condition.     

Optimization models for the machine scheduling problem with a single flexible maintenance activity

The majority of machine scheduling literature assumes that machines are available at all times. However, this assumption is inappropriate in certain real world situations. This study addresses the single machine and parallel machine scheduling problems, where machines are flexibly maintained and total tardiness is used as a performance measure. Machine M _k should be scheduled for maintenance for a constant time, w _k . It is assumed that the maintenance period [u _k , v _k ] is set in advance and that the maintenance time, w _k , does not exceed the maintenance period (i.e., w _k ≤v _k ?u _k ). The time u _k (v _k ) is the earliest (or latest) time at which machine M _k starts (or stops) its maintenance. Two cases, resumable and unresumable, are considered in the single machine and parallel machine problems. Eight mixed binary integer programming models are developed to derive the optimal schedule for the problem, and size complexity and computer solution times are provided to demonstrate the models' efficiency.     

Numerical solution of micropolar fluid flow between a rotating and a porous stationary disc

The steady flow of an incompressible micropolar fluid between a rotating and a stationary disc is studied when a uniform suction is applied on the stationary disc. The nonlinear coupled equations involving velocity and microrotation components have been solved numerically using quasilinearisation technique. The pressure coefficient at any radius r of the rotating disc varies linearly with micropolar parameter R. The three velocities and microrotation components have been displayed graphically. It is observed that for low suction and high rotation, both radial and axial flows are of cellular type for small R but turn unidirectional for large values of R. The flow regimes are completely reversed in the case of blowing.     

The 3-D spread of saltation sand over a flat bed surface in aeolian sand transport

This paper investigated the 3-D motion of saltation sand by high-speed photography and stereo particle image velocimetry (SPIV). By the high-speed camera, the sand particle trajectories in the transverse plane near bed surface have been obtained. It could be found that the collision between the particle and the bed surface would in principle cause the transverse motion of the particle regardless of the change of the wind direction. Based on SPIV, The three-dimensional velocities of the sand particles in the wind–sand flow have been obtained by combining the velocity data from double CCD cameras. The three-dimensional velocity of the sand particle was resolved into three component velocities in the paper, i.e. the streamwise velocity u, the vertical velocity v and the transverse velocity w. The distribution of the transverse velocities w of the sand particles approximated symmetrical. The peak value of the PDF (probability density function) of velocity w fell down obviously with the increase of the wind speed when the sand sizes were equal to or less than 125 μm. When the sand sizes were larger than 125 μm, the peak value of the PDF of w was almost constant with the change of the wind speed. Although the increments of v with the increase of the wind speed were larger than that of w, the velocity w of the sand particle appeared to be much larger than its velocity v in general. Moreover, it was near one fourth probability that the quantity of the particle velocity w was one order higher than that of its velocity v. The inclination angle between w and u of the sand would be less than 60° and the inclination angle between the v and u would be less than 20° integrally.     

Doppler shift in third and fourth sound in 3He-4He mixtures

The Doppler-shifted velocity of third sound in a system where the superfluid flows with velocity v _s is given. The calculations are to first order in v _s/u₃ where u ₃ is the third-sound velocity in the rest frame. We take into account the effects of the pressure and ³He concentration gradients normal to the substrate. Corresponding calculations for fourth sound are also given.Supported in part by the GFK, West Germany, through the Israel National Council for Research and Development.     

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.