Nonsimilar incompressible laminar boundary-layer flows in micropolar fluids

The solution of the steady laminar incompressible nonsimilar boundary-layer problem for micropolar fluids over two-dimensional and axisymmetric bodies has been presented. The partial differential equations governing the flow have been transformed into new co-ordinates having finite range. The resulting equations have been solved numerically using implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The results indicate that the separation in micropolar fluids occurs at earlier streamwise locations as compared to Newtonian fluids. The skin friction and velocity profiles depend on the shape of the body and are almost insensitive to microrotation or coupling parameter, provided the coupling parameter is small. On the other hand, the microrotation profiles and microrotation gradient depend on the microrotation parameter and they are insensitive to the coupling parameter.

Korteweg-de Vries equation for the propagation of fast ion-acoustic waves in multi-dimensions

Abstract is not available.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Effect of viscosity on internal waves from a source in a wall

The solution for a line source of oscillatory strength kept at the origin in a wall bounding a semi-infinite viscous imcompressible stratified fluid is presented in an integral form. The behaviour of the flow at far field and near field is studied by an asymptotic expansion procedure. The streamlines for different parameters are drawn and discussed. The real characteristic straight lines present in the inviscid problem are modified by the viscosity and the solutions obtained are valid even at the resonance frequency.

Quasi-simple wave solutions for acoustic gravity waves

The special class of quasi-simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically. Physics of Fluids is copyrighted by The American Institute of Physics.

Nonsimilar laminar incompressible boundary layers with vectored mass transfer

The effect of vectored mass transfer on the flow and heat transfer of the steady laminar incompressible nonsimilar boundary layer with viscous dissipation for two-dimensional and axisymmetric porous bodies with pressure gradient has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The skin friction is strongly influenced by the vectored mass transfer, and the heat transfer both by the vectored mass transfer and dissipation parameter. It is observed that the vectored suction tends to delay the separation whereas the effect of the vectored injection is just the reverse. Our results agree with those of the local nonsimilarity, difference-differential and asymptotic methods but not with those of the local similarity method.

Unsteady Incompressible Three-Dimensional Asymmetric Stagnation-Point Boundary Layers

The unsteady laminar incompressible boundary-layer flow near the three-dimensional asymmetric stagnation point has been studied under the assumptions that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. It is found that in contrast with the symmetric flow, the maximum heat transfer occurs away from the stagnation point due to the decrease in the boundary-layer thickness. The effect of the variation of the wall temperature with time on heat transfer is strong. The skin friction and heat transfer due to asymmetric flow only are comparatively less affected by the mass transfer as compared to those of symmetric flow.

On Multi-Dimensional Packets of Surface Waves

By using the method of operators of multiple scales, two coupled nonlinear equations are derived, which govern the slow amplitude modulation of surface gravity waves in two space dimensions. The equations of Davey and Stewartson, which also govern the two-dimensional modulation of the amplitude of gravity waves, are derived as a special case of our equations. For a fully dispersed wave, symmetric about a point which moves with the group velocity, the coupled equations reduce to a nonlinear Schrödinger equation with extra terms representing the effect of the curvature of the wavefront.

Time reversal technique for health monitoring of metallic structure using Lamb waves

Time reversal active sensing using Lamb waves is investigated for health monitoring of a metallic structure. Experiments were conducted on an aluminum plate to study the time reversal behavior of A(0) and S-0 Lamb wave modes under narrow band and broad band pulse excitation. Damage in the form of a notch was introduced in the plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. Time-frequency analysis of the time reversed signal was carried out to extract the damage information. A measure of damage based on wavelet transform was derived to quantify the hidden damage information in the time reversed signal. It has been shown that time reversal can be used to achieve temporal recompression of Lamb waves under broadband signal excitation. Further, the broad band excitation can also improve the resolution of the technique in detecting closely located defects. This is demonstrated by picking up the reflection of waves from the edge of the plate, from a defect close to the edge of the plate and from defects located near to each other. This study shows the effectiveness of Lamb wave time reversal for temporal recompression of dispersive Lamb waves for damage detection in health monitoring applications. (C) 2009 Elsevier B.V. All rights reserved.

An analysis of sun salutation

Sun salutation is a part of yoga. It consists of a sequence of postures done with synchronized breathing. The practice of few cycles of sun salutation is known to help in maintaining good health and vigor. The practice of sun salutation does not need any extra gadgets. Also it is very much aerobic and invigorates the body and the mind.

Approximate solutions for the structure of shock waves

Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness delta n . A detailed error analysis provides explanations for this result. An asymptotic analysis of delta n for largeMach numbers shows that it scales with theMaxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.

Influence of External Light Waves on the Thermoelectric Power Under Strong Magnetic Field in Ultrathin Films, Quantum Wires and Quantum Dots of Optoelectronic Materials

In this paper, an attempt is made to study the influence of external light waves on the thermoelectric power under strong magnetic field (TPSM) in ultrathin films (UFs), quantum wires (QWs) and quantum dots (QDs) of optoelectronic materials whose unperturbed dispersion relation of the conduction electrons are defined by three and two band models of Kane together with parabolic energy bands on the basis of newly formulated electron dispersion laws in each case. We have plotted the TPSM as functions of film thickness, electron concentration, light intensity and wavelength for UFs, QWs and ODs of InSb, GaAs, Hg1-xCdxTe and In1-xGaxAsyP1-y respectively. It appears from the figures that for UFs, the TPSM increases with increasing thickness in quantum steps, decreases with increasing electron degeneracy exhibiting entirely different types of oscillations and changes with both light intensity and wavelength and these two latter types of plots are the direct signature of light waves on opto-TPSM. For QWs, the opto-TPSM exhibits rectangular oscillations with increasing thickness and shows enhanced spiky oscillations with electron concentration per unit length. For QDs, the opto-TPSM increases with increasing film thickness exhibiting trapezoidal variations which occurs during quantum jumps and the length and breadth of the trapezoids are totally dependent on energy band constants. Under the condition of non-degeneracy, the results of opto-TPSM gets simplified into the well-known form of classical TPSM equation which the function of three constants only and being invariant of the signature of band structure.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.