Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Universality in the fast orientational relaxation near isotropic-nematic transition

Detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out to investigate the emergence of criticality in the single-particle orientational relaxation near the isotropic-nematic (IN) phase transition. The simulations show a sudden appearance of a power-law behavior in the decay of the second-rank orientational relaxation as the IN transition is approached. The simulated value of the power-law exponent is 0.56, which is larger than the mean-field value (0.5) but less than the observed value (0.63) and may be due to the finite size of the simulated system. The decay of the first-rank orientational time correlation function, on the other hand, is nearly exponential but its decay becomes very slow near the isotropic-nematic transition, The zero-frequency rotational friction, calculated from the simulated angular Velocity correlation function, shows a marked increase near the IN transition.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Unsteady free convection flow in the stagnation-point region of a rotating sphere

The unsteady free convection boundary-layer flow in the forward stagnation-point region of a sphere, which is rotating with time-dependent angular velocity in an ambient fluid, has been studied. Both constant wall temperature and constant hear flux conditions have been considered. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The skin friction and the heat transfer are enhanced by the buoyancy force. The effect of the buoyancy force is found to be more pronounced for smaller Prandtl numbers than for larger Prandtl numbers. For a given buoyancy force, the heat transfer increases with an increase in Prandtl number, but the skin friction decreases.

MHD Flow of a 2nd 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.

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

On the magnetohydrodynamic flow between eccentrically rotating disks

The steady flow of an incompressible, viscous, electrically conducting fluid between two parallel, infinite, insulated disks rotating with different angular velocities about two noncoincident axes has been investigated; under the application of a uniform magnetic field in the axial direction. The solutions for the symmetric and asymmetric velocities are presented. The interesting feature arising due to the magnetic field is that in the central region the flow attains a uniform rotation with mean angular velocity at all rotation speeds for sufficiently large Hartmann number. In this case the flow adjusts to the rotational velocities of the disks mainly in the boundary layers near the disks. The forces on the disks are found to increase due to the presence of the applied magnetic field.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

Hip power analysis in individuals with transfemoral amputation: A different strategy different from stabilisation during gait stance

Introduction and Objectives Joint moments and joint powers during gait are widely used to determine the effects of rehabilitation programs as well as prosthetic fitting. Following the definition of power (dot product of joint moment and joint angular velocity) it has been previously proposed to analyse the 3D angle between both vectors, αMw. Basically, joint power is maximised when both vectors are parallel and cancelled when both vectors are orthogonal. In other words, αMw < 60° reveals a propulsion configuration (more than 50% of the moment contribute to positive power) while αMw > 120° reveals a resistance configuration (more than 50% of the moment contribute to negative power). A stabilisation configuration (less than 50% of the moment contribute to power) corresponds to 60° < αMw < 120°. Previous studies demonstrated that hip joints of able-bodied adults (AB) are mainly in a stabilisation configuration (αMw about 90°) during the stance phase of gait. [1, 2] Individuals with transfemoral amputation (TFA) need to maximise joint power at the hip while controlling the prosthetic knee during stance. Therefore, we tested the hypothesis that TFAs should adopt a strategy that is different from a continuous stabilisation. The objective of this study was to compute joint power and αMw for TFA and to compare them with AB. Methods Three trials of walking at self-selected speed were analysed for 8 TFAs (7 males and 1 female, 46±10 years old, 1.78±0.08 m 82±13 kg) and 8 ABs (males, 25±3 years old, 1.75±0.04, m 67±6 kg). The joint moments are computed from a motion analysis system (Qualisys, Goteborg, Sweden) and a multi-axial transducer (JR3, Woodland, USA) mounted above the prosthetic knee for TFAs and from a motion analysis system (Motion Analysis, Santa Rosa, USA) and force plates (Bertec, Columbus, USA) for ABs. The TFAs were fitted with an OPRA (Integrum, AB, Gothengurg, Sweden) osseointegrated implant system and their prosthetic designs include pneumatic, hydraulic and microprocessor knees. Previous studies showed that the inverse dynamics computed from the multi-axial transducer is the proper method considering the absorption at the foot and resistance at the knee. Results The peak of positive power at loading response (H1) was earlier and lower for TFA compared to AB. Although the joint power is lower, the 3D angle between joint moment and joint angular velocity, αMw, reveals an obvious propulsion configuration (mean αMw about 20°) for TFA compared to a stabilisation configuration (mean αMw about 70°) for AB. The peaks of negative power at midstance (H2) and of positive power at preswing / initial swing (H3) occurred later, lower and longer for TFA compared to AB. Again, the joint powers are lower for TFA but, in this case, αMw is almost comparable (with a time lag), demonstrating a stabilisation (almost a resistance for TFA, mean αMw about 120°) and a propulsion configuration, respectively. The swing phase is not analysed in the present study. Conclusion The analysis of hip joint power may indicate that TFAs demonstrated less propulsion and resistance than ABs during the stance phase of gait. This is true from a quantitative point of view. On the contrary, the 3D angle between joint moment and joint angular velocity, αMw, reveals that TFAs have a remarkable propulsion strategy at loading response and almost a resistance strategy at midstance while ABs adopted a stabilisation strategy. The propulsion configuration, with αMw close to 0°, seems to aim at maximising the positive joint power. The configuration close to resistance, with αMw far from 180°, might aim at unlocking the prosthetic knee before swing while minimising the negative power. This analysis of both joint power and 3D angle between the joint moment and the joint angular velocity provides complementary insights into the gait strategies of TFA that can be used to support evidence-based rehabilitation and fitting of prosthetic components.

On the magnetohydrodynamic flow between eccentrically rotating disks

The steady flow of an incompressible, viscous, electrically conducting fluid between two parallel, infinite, insulated disks rotating with different angular velocities about two noncoincident axes has been investigated; under the application of a uniform magnetic field in the axial direction. The solutions for the symmetric and asymmetric velocities are presented. The interesting feature arising due to the magnetic field is that in the central region the flow attains a uniform rotation with mean angular velocity at all rotation speeds for sufficiently large Hartmann number. In this case the flow adjusts to the rotational velocities of the disks mainly in the boundary layers near the disks. The forces on the disks are found to increase due to the presence of the applied magnetic field.

Secondary flow of Rivlin-Ericksen fluids between two concentric spheres oscillating about a fixed diameter

The paper deals with the study of the nature of secondary flow of aRivlin-Ericksen fluid, contained between two concentric spheres, which perform oscillations about a fixed diameter. The steady part of the secondary flow is discussed in detail in the following three cases (i) the outer sphere at rest, the inner oscillating, (ii) the two spheres oscillating with the same angular velocity in the same sense and (iii) the spheres oscillating with the same angular velocity in opposite sense. In a previous paper, a similar problem was discussed for theOldroyd fluids. We find that the secondary flow is strongly dependent on the common frequency of oscillation of the two spheres and on the rotational nature of the motion for the present investigation also. Certain contrasting features of interest between the secondary flow field of the two fluids are also noted.

A semi-classical model of the electron containing tachyonic matter

It is shown that the mass of the electron could be conceived as the energy associated with its spinning motion and the angular velocity is such that the linear velocities at the surface exceed the velocity of light; this in fact accounts for its stability against the centrifugal forces in the core region.

An accurate numerical integration scheme for finite rotations using rotation vector parametrization

A numerical integration procedure for rotational motion using a rotation vector parametrization is explored from an engineering perspective by using rudimentary vector analysis. The incremental rotation vector, angular velocity and acceleration correspond to different tangent spaces of the rotation manifold at different times and have a non-vectorial character. We rewrite the equation of motion in terms of vectors lying in the same tangent space, facilitating vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Nucleosome core histone complex isolated gently and rapidly in 2 M NaCl is octameric

A relatively stable specific complex of the chromatin core histones H2A, H2B, H3, and H4 has been obtained in 2 M NaCl/25 mM sodium phosphate buffer, pH 7.0. The histone core complex has an apparent specific volume of 0.73 ml/g. Its sedimentation coefficient was dependent on rotor speed (angular velocity, omega) and attained different stable values at low and high rotor speeds. The drop in sedimentation coefficient occurred sharply between omega 2 values of about 9 x 10(6) and 1.1 x 10(7) (radians/sec)2. The s020,w corresponding to zero angular velocity (1 atmosphere pressure) was 6.6 S +/- (SEM) 0.1 S. At high rotor speeds the value decreased to 3.8 S +/- 0.1 S. The core complex has a diffusion coefficient, D20,w, of 5.4 x 10(-7) cm2/sec and a molecular weight of 108,000 +/- (SD) 2500.

Sensitivity of the simulated precipitation to changes in convective relaxation time scale

The paper describes the sensitivity of the simulated precipitation to changes in convective relaxation time scale (TAU) of Zhang and McFarlane (ZM) cumulus parameterization, in NCAR-Community Atmosphere Model version 3 (CAM3). In the default configuration of the model, the prescribed value of TAU, a characteristic time scale with which convective available potential energy (CAPE) is removed at an exponential rate by convection, is assumed to be 1 h. However, some recent observational findings suggest that, it is larger by around one order of magnitude. In order to explore the sensitivity of the model simulation to TAU, two model frameworks have been used, namely, aqua-planet and actual-planet configurations. Numerical integrations have been carried out by using different values of TAU, and its effect on simulated precipitation has been analyzed. The aqua-planet simulations reveal that when TAU increases, rate of deep convective precipitation (DCP) decreases and this leads to an accumulation of convective instability in the atmosphere. Consequently, the moisture content in the lower-and mid-troposphere increases. On the other hand, the shallow convective precipitation (SCP) and large-scale precipitation (LSP) intensify, predominantly the SCP, and thus capping the accumulation of convective instability in the atmosphere. The total precipitation (TP) remains approximately constant, but the proportion of the three components changes significantly, which in turn alters the vertical distribution of total precipitation production. The vertical structure of moist heating changes from a vertically extended profile to a bottom heavy profile, with the increase of TAU. Altitude of the maximum vertical velocity shifts from upper troposphere to lower troposphere. Similar response was seen in the actual-planet simulations. With an increase in TAU from 1 h to 8 h, there was a significant improvement in the simulation of the seasonal mean precipitation. The fraction of deep convective precipitation was in much better agreement with satellite observations.