A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

Steady-State Response of Thick Rectangular Plates

The classical theory of plates neglects the effects of rotatory inertia and shear deformation, and due to this assumption it is applicable only for thin plates. Mindlin presented an improved plate theory which is fairly accurate.

Estimation of Cavitation Erosion with Incubation Periods and Material Properties

A detailed study of the normalized correlations between the incubation period tc and the properties of various materials tested in a rotating disk device indicates that, at very high intensities, the strength properties influence the duration of tc. The analysis of extensive data from other laboratories for cavitation and liquid impingement erosion also indicates that, while both energy and strength properties influence the duration of tc, the latter ones predominate for a majority of cases. A fatigue-type failure occurs during tc. For estimating the time required to pierce a metallic specimen in a rotating device a relationship tp = 160 tc0.44 is proposed. A detailed study of normalized correlations between erosion resistance (inverse of erosion rate) and tc values of different materials tested in the rotating disk shows that correlations are good. Analysis of data from eight other investigators clearly points out the validity and the usefulness of this type of prediction.

The effects of slip velocity at a membrane surface on blood flow in the microcirculation

Closed-form solutions are presented for blood flow in the microcirculation by taking into account the influence of slip velocity at the membrane surface. In this study, the convective inertia force is neglected in comparison with that of blood viscosity on the basis of the smallness of the Reynolds number of the flow in microcirculation. The permeability property of the blood vessel is based on the well known Starling's hypothesis [11]. The effects of slip coefficient on the velocity and pressure fields are clearly depicted.

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.

Microstructural study of rapidly solidified titanium eutectoid alloysstar, open

Rapid solidification of Ti-7.3wt.%Cu (near-eutectoid composition), Ti-36.2wt.%Ni and Ti-34.3wt.% Ni-5.8wt.%Si alloys has been carried out by electron beam melting and splat quenching on a water-cooled rotating copper disc. The product obtained was in the form of thin ribbons 60–100 μm thick. Transmission electron microscopy studies of Ti---Cu alloy splats showed that the microstructure consisted of a mixture of martensite and a lamellar eutectoid product. The formation of the intermetallic compound Ti2Cu involved a diffusionless ω transformation and spinodal clustering. In the case of Ti---Ni alloy the as-quenched microstructure is complex, consisting of α, transformed β and intermetallic phases. This could have arisen possibly as a result of local variation in cooling rates. Rapid solidification of Ti---Ni---Si alloy resulted in partial quenching of an amorphous phase. The amorphous phase was seen to be extremely hard (a Vickers hardness of about 800 HV).

A study on bullock carts. Part 1. Engineering analysis of the two-wheel bullock cart design

An engineering analysis of the design of two-wheel bullock carts has been carried out with the aid of a mathematical model. Non-dimensional expressions for the pull and the neck load have been developed. In the first instance, the cart is assumed to be cruising at constant velocity on a terrain with the effective coefficient of rolling friction varying over a wide range (0.001 to 0.5) and the gradient varying between +0.2 to −0.2. Subsequently, the effect of inertia force due to an acceleration parallel to the ground is studied. In the light of this analysis, two modifications to the design of the cart have been proposed and the relative merits of the current designs and the proposed designs are discussed.

A numerical study of thermocapillary flow in a rectangular cavity during laser melting

The surface tension gradient driven flow that occurs during laser melting has been studied. The vorticity-streamfunction form of the Navier-Stokes equations and the energy equation has been solved by the ‘Alternative Direction Implicit’ method. It has been shown that the inertia forces in the melt strongly influence the flow pattern in the melt. The convection in the melt modifies the isotherms in the melt at high surface tension Reynolds number and high Prandtl number. The buoyancy driven flow has been shown to be negligible compared to the surface tension gradient driven flow in laser melting.

Generation of rotationally dominated galaxies by mergers of pressure-supported progenitors

Through the analysis of a set of numerical simulations of major mergers between initially non-rotating, pressure-supported progenitor galaxies with a range of central mass concentrations, we have shown that: (1) it is possible to generate elliptical-like galaxies, with outside one effective radius, as a result of the conversion of orbital- into internal-angular momentum; (2) the outer regions acquire part of the angular momentum first; (3) both the baryonic and the dark matter components of the remnant galaxy acquire part of the angular momentum, the relative fractions depending on the initial concentration of the merging galaxies. For this conversion to occur the initial baryonic component must be sufficiently dense and/or the encounter should take place on an orbit with high angular momentum. Systems with these hybrid properties have recently been observed through a combination of stellar absorption lines and planetary nebulae for kinematic studies of early-type galaxies. Our results are in qualitative agreement with these observations and demonstrate that even mergers composed of non rotating, pressure-supported progenitor galaxies can produce early-type galaxies with significant rotation at large radii.

Relaminarization in highly accelerated turbulent boundary layers

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

A refined analysis of composite laminates

The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.

Wear resistance of cast graphitic aluminium alloys

Wear rates of several cast aluminium base alloys have been measured for lubricated rubbing against a rotating hardened steel disk. Wear rates of cast graphitic aluminium-silicon-nickel alloys were lower than those of pure Al, Al-Si and Al-Si-Ni alloys especially above pressures of 0.02 kg/mm2. The high wear resistance is attributed to the presence of graphite particles in the matrix which act as a solid lubricant. Additions of nickel alone to Al-Si alloys decrease the wear resistance. Graphitic aluminium-silicon-nickel alloys containing above 2% graphite can be mated unlubricated against the rotating steel disk after a one minute lubricated run-in period. Graphite particles may be potentially suitable to replace part of all of the tin in aluminium-tin bearing alloys.

Wear resistance of cast graphitic aluminium alloys

Wear rates of several cast aluminium base alloys have been measured for lubricated rubbing against a rotating hardened steel disk. Wear rates of cast graphitic aluminium-silicon-nickel alloys were lower than those of pure Al, Al-Si and Al-Si-Ni alloys especially above pressures of 0.02 kg/mm2. The high wear resistance is attributed to the presence of graphite particles in the matrix which act as a solid lubricant. Additions of nickel alone to Al-Si alloys decrease the wear resistance. Graphitic aluminium-silicon-nickel alloys containing above 2% graphite can be mated unlubricated against the rotating steel disk after a one minute lubricated run-in period. Graphite particles may be potentially suitable to replace part of all of the tin in aluminium-tin bearing alloys.

Wavefront filter for double-exposure holographic interferometry

Measurements of small phase shifts by double-exposure holographic interferometry are facilitated, and ambiguities in the sign of the phase shift eliminated, by introducing a background pattern of interference fringes. A simple and reliable optical system for this purpose utilizing a rotating wedge is described, with which fringes of any desired orientation and spacing can conveniently be obtained. It is shown how this system can be used under certain conditions for measurements of small mechanical deformations.

Similarities in Different Experiments of Erosion Caused by Cavitation and Liquid Impingement

Correlations of erosion resistances of materials tested in different equipment are reported. Analysis of the authors' data from rotating disk and venturi equipment indicates that there exists a good correlation between the erosion resistances of materials tested at different intensities. The study indicates that time effects on erosion are important in correlations of this type. The erosion resistances of materials tested in two different devices exhibit good correlations indicating a quantitative similarity between different forms of erosion. The investigations also show that the prediction of erosion resistances of materials in a field device may be made with the data from a laboratory device which may not fully reproduce the flow conditions in the field. These conclusions are also checked with data reported from other laboratories.