Non-Newtonian boundary layers on a moving cylinder

The analysis of steady laminar forced convection boundary layer of power-law non-Newtonian fluids on a continuously moving cylinder with the surface maintained at a uniform temperature or uniform heat flux is presented. Of interest were the effects of power-law viscosity index, transverse curvature, generalized Prandtl number and streamwise coordinate on the local Nusselt number as well as on the velocity and temperature profiles. The two thermal boundary conditions yield quite similar results. Comparison of the calculated results with available series expansion solutions for a Newtonian fluid shows a very good performance of the present numerical procedure.

Integral method for the calculation of incompressible two-dimensional transitional boundary layers

The method proposed here considers the mean flow in the transition zone as a linear combination of the laminar and turbulent boundary layer in proportions determined by the transitional intermittency, the component flows being calculated by approximate integral methods. The intermittency distribution adopted takes into account the possibility of subtransitions within the zone in the presence of strong pressure gradients. A new nondimensional spot formation rate, whose value depends on the pressure gradient, is utilized to estimate the extent of the transition zone. Onset location is determined by a correlation that takes into account freestream turbulence and facility-specific residual disturbances in test data. Extensive comparisons with available experimental results in strong pressure gradients show that the proposed method performs at least as well as differential models, in many cases better, and is always faster.

A Novel Method for the Uniform Incorporation of Grain-Boundary Layer Modifiers in Positive Temperature Coefficient of Resistivity Barium Titanate

The presently developed two-stage process involves diping the prefired porous disks of n-BaTiO3 in nonaqueous solutions containing Al-buty rate, Ti-isopropoxide, and tetraethyl silicate and subsequent sintering. This leads to uniform distribution of the grain-boundary layer (GBL) modifiers (Al2O3+ TiO2+ SiO2) and better control of the grain size as well as the positive temperature coefficient of resistivity characteristics. The technique is particularly suited for GBL modifiers in low concentrations (< 1%).

A sufficient criterion for Kelvin–Helmholtz instability in the magnetopause boundary‐layer region

The Kelvin–Helmholtz instability has been investigated for the magnetopause boundary‐layer region by the linearized method. The plasma in magnetosheath and magnetopause is assumed to be semi‐infinitely extended homogeneous, nondissipative, and incompressible. It is observed that, if one relation of two plasma speeds on the two sides of the magnetopause, wave number, and boundary‐layer thickness exceeds a certain threshold, the instability sets in. This new analytically sufficient criterion for excitation of instability in the three‐layer plasma flow generalizes the corresponding Chandrasekhar’s instability criterion for two‐layer plasma flow. The known results have been recovered and modified, the new results have been discovered. It is proved that the velocity threshold for the onset of instability is low when the magnitude of the magnetosheath and boundary‐layer region magnetic field and the angle between them are small. Also the threshold depends on the direction of plasma flow. The following results are observed numerically. The growth of the instability is sensitive to the magnetic field direction in the magnetosheath. A slight variation in the magnetic field direction in the second region can substantially change the relative velocity threshold for instability. When the ratio of the density of the second and third layer (magnetosphere) increases or that of the first and third layer decreases, the threshold decreases. Apart from this a necessary criterion for instability is obtained for a particular case.

Compressible MHD boundary layer in the stagnation region of a sphere

The steady laminar compressible boundary layer flow of an electrically conducting fluid in the stagnation region of a sphere with an applied magnetic field has been studied. The effects of the induced magnetic field, mass transfer, and viscous dissipation have been taken into account. Both isothermal and adiabatic wall conditions have been considered. The governing equations have been solved numerically using a shooting method. The skin friction and heat transfer are found to be strongly affected by the magnetic field, mass transfer, wall temperature and Mach number. It is found that the magnetic field reduces the heat transfer. This is a significant result which can be used in controlling the heat transfer rate. The boundary layer solutions break down as the magnetic parameter tends to a certain critical value.

Hydrodynamics of the Renn-Lubensky twist grain boundary phase, and the decoupled lamellar phase

The long-wavelength hydrodynamics of the Renn-Lubensky twist grain boundary phase with grain boundary angle 2pialpha, alpha irrational, is studied. We find three propagating sound modes, with two of the three sound speeds vanishing for propagation orthogonal to the grains, and one vanishing for propagation parallel to the grains as well. In addition, we find that the viscosities eta1, eta2, eta4, and eta5 diverge like 1/Absolute value of omega as frequency omega --> 0, with the divergent parts DELTAeta(i) satisfying DELTAeta1DELTAeta4=(DELTAeta5)2, exactly. Our results should also apply to the predicted decoupled lamellar phase.

3-Dimensional laminar boundary-layer in a constant-pressure diverging

larity solution is obtained for laminar 3D constant pressure flow with lateral streamline divergence. The similarity solution is shown to reduce to a Blasius solution for 2D flow over a flat plate. Measurements of velocity profiles are made to compare the similarity solution and are found to be in excellent agreement with the prediction

A hybrid technique of modeling of cracks using displacement discontinuity and direct boundary element method

A hybrid technique to model two dimensional fracture problems which makes use of displacement discontinuity and direct boundary element method is presented. Direct boundary element method is used to model the finite domain of the body, while displacement discontinuity elements are utilized to represent the cracks. Thus the advantages of the component methods are effectively combined. This method has been implemented in a computer program and numerical results which show the accuracy of the present method are presented. The cases of bodies containing edge cracks as well as multiple cracks are considered. A direct method and an iterative technique are described. The present hybrid method is most suitable for modeling problems invoking crack propagation.

Effect of strain rate on the high-temperature low-cycle fatigue properties of a nimonic PE-16 superalloy

Strain-rate effects on the low-cycle fatigue (LCF) behavior of a NIMONIC PE-16 superalloy have been evaluated in the temperature range of 523 to 923 K. Total-strain-controlled fatigue tests were per-formed at a strain amplitude of +/-0.6 pct on samples possessing two different prior microstructures: microstructure A, in the solution-annealed condition (free of gamma' and carbides); and microstructure B, in a double-aged condition with gamma' of 18-nm diameter and M23C6 carbides. The cyclic stress response behavior of the alloy was found to depend on the prior microstructure, testing temperature, and strain rate. A softening regime was found to be associated with shearing of ordered gamma' that were either formed during testing or present in the prior microstructure. Various manifestations of dynamic strain aging (DSA) included negative strain rate-stress response, serrations on the stress-strain hysteresis loops, and increased work-hardening rate. The calculated activation energy matched well with that for self-diffusion of Al and Ti in the matrix. Fatigue life increased with an increase in strain rate from 3 x 10(-5) to 3 x 10(-3) s-1, but decreased with further increases in strain rate. At 723 and 823 K and low strain rates, DSA influenced the deformation and fracture behavior of the alloy. Dynamic strain aging increased the strain localization in planar slip bands, and impingement of these bands caused internal grain-boundary cracks and reduced fatigue life. However, at 923 K and low strain rates, fatigue crack initiation and propagation were accelerated by high-temperature oxidation, and the reduced fatigue life was attributed to oxidation-fatigue interaction. Fatigue life was maximum at the intermediate strain rates, where strain localization was lower. Strain localization as a function of strain rate and temperature was quantified by optical and scanning electron microscopy and correlated with fatigue life.

Unsteady three-dimensional boundary layer flow due to a stretching surface

In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0 less-than-or-equal-to c less-than-or-equal-to 1) where c denotes the stretching ratio. This method fails in the saddle point region (-1 less-than-or-equal-to c less-than-or-equal-to 0) due to the occurrence of reverse flow in the y-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values at c = 0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A > 0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Non-uniform slot injection (suction) or wall enthalpy into a steady nonsimilar compressible laminar boundary layer

Steady two-dimensional and axisymmetric compressible nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and non-uniform wall enthalpy have been studied from the starting point of the streamwise co-ordinate to the exact point of separation. The effect of different free stream Mach number has also been considered. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is observed that the non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise co-ordinate has very little effect on the skin friction and thus on the point of separation.