Refraction of laser plane in a spherically inhomogeneous thermal boundary layer

The problem of determining the trajectories of geometrical optical rays for a model of a laser plane in a spherical thermal boundary layer is solved and equations of the projection of the laser plane passing through the layer are obtained. Qualitative variations in the pattern of refraction of rays and the projection of the laser plane for two models of the boundary layer are studied. It is shown that under definite conditions, the results of measurements of the parameters of this projection may be used to calculate the temperature field in the layer. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 35–38, May, 2006.     

Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane

Scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane is rigorously solved. The scattered field is represented by a Fourier-integral representation. To analytically represent the fields in a general-shaped groove, the groove is divided into L number of layers. Fields are then expressed in each layer as summations of 2D spatial harmonic fields with unknown coefficients. Matching the boundary conditions between layers provides a linear set of equations connecting all the unknown harmonic coefficients. Judicious use of Fourier transform on the equations resulting from matching boundary conditions at the groove aperture provides a series representation of the scattered field in the spectral domain with unknown harmonic coefficients of the first layer in the groove. A stable solution is obtained by solving the complete system of equations with an adaptive choice for the number of modes in each layer.     

On the development of a magnetohydrodynamic boundary layer

The problem of the development of a plane magnetohydrodynamic boundary layer in a viscous incompressible fluid is investigated for a time dependence of the velocity of the outer boundary of the boundary layer and of the magnetic field in the form (1). A solution of the problem is found under the assumption that the body motion starts impulsively and continues at equal acceleration.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 6, pp. 1053–1059, June, 1971.     

Boundary layer growth of a micropolar fluid

The unsteady boundary layer flow of a micropolar fluid along an infinite plate is analysed when the plate undergoes an impulsive motion in its plane. The solution is obtained by Laplace transform technique. The microstructure of the fluid is found to induce a wave-dominated flow pattern, there being two modes of wave-propagation. The characteristics of these waves, during the initial and final stages of the boundary layer growth, are discussed.     

Homogeneous Solutions of a Skew-Symmetric Problem with Mixed Boundary Conditions for a Piezoceramic Layer

On the basis of a modified scheme of homogeneous solutions significantly simplifying the Lur'e scheme, we construct homogeneous solutions for a piezoceramic layer with mixed boundary conditions imposed on its faces. We consider an electroelastic state skew-symmetric about the median plane of the layer. It is shown that the corresponding homogeneous solutions do not contain biharmonic terms and the components of the conjugate electroelastic field in the layer have the form of Fourier series with respect to the coordinate x ₃.     

Modeling of Plastic Zones in the Process of Shear Deformation of a Half Layer Containing a Crack

We study the evolution of plastic zones in a perfectly elastoplastic half layer containing a crack in its median plane under the conditions of antiplane deformation caused by displacements of the rigid faces of the half layer, deduce equations for the boundary of the continual plastic zone and its length in the plane of the crack as functions of the load, and perform the approximate analysis of the stress intensity factors of the elastic solution for the zones (the so-called linear model of the plastic zone).     

Boundary element analysis of curved cracked panels with adhesively bonded patches

A new boundary element formulation for analysis of curved cracked panels with adhesively bonded patches is presented in this paper. The effect of the adhesive layer is modelled by distributed body forces (i.e. two in‐plane forces, two moments and one out‐of‐plane force). A coupled boundary integral formulation of a shear deformable plate and two‐dimensional plane stress elasticity is used to determine bending and membrane forces along the adhesive layer taking into consideration the compatibility conditions in the patch area. Two numerical examples are presented to demonstrate the efficiency of the proposed method. It is shown that the out‐of‐plane bending behaviour and panel curvature have significant influence on the magnitude of the stress intensity factors. Copyright © 2003 John Wiley & Sons, Ltd.     

Interface waves along an anisotropic imperfect interface between anisotropic solids

First and second order asymptotic boundary conditions are introduced to model a thin anisotropic layer between two generally anisotropic solids. Such boundary conditions can be used to describe wave interaction with a solid-solid imperfect anisotropic interface. The wave solutions for the second order boundary conditions satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. They couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic substrates. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This model determines the transfer matrix which includes interfacial stiffness and inertial and coupling terms. The present results are a generalization of previous work valid for either an isotropic viscoelastic layer or an orthotropic layer with a plane of symmetry coinciding with the wave incident plane. The problem of localization of interface waves is considered. It is shown that the conditions for the existence of such interface waves are less restrictive than those for Stoneley waves. The results are illustrated by calculation of the interface wave velocity as a function of normalized layer thickness and angle of propagation. The applicability of the asymptotic boundary conditions is analyzed by comparison with an exact solution for an interfacial anisotropic layer. It is shown that the asymptotic boundary conditions are applicable not only for small thickness-to-wavelength ratios, but for much broader frequency ranges than one might expect. The existence of symmetric and SH-type interface waves is also discussed.     

Turbulent boundary layer on a chemically active surface with a negative pressure gradient

An integral method of flow analysis is discussed for a turbulent boundary layer on an ablating surface of plane and axisymmetric bodies. The results of computations are given for ablation of the surfaces of a plate and a sphere of a material similar in composition to textolite.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 3, pp. 473–478, September, 1977.     

Problem of Drying of a Layer of Combustible Forest Materials

Physical and mathematical modeling of drying of a layer of combustible forest materials (CFMs) is considered in a conjugate formulation within the framework of which the equations of a binary boundary layer and the equations of heat and mass transfer in a layer of combustible forest materials are solved. Boundary conditions for the laws of conservation of mass and energy are written on the interface of media. It is found experimentally and theoretically that the velocities of the flow and radiation strongly affect the time of drying of a layer of combustible forest materials, whereas the effect of the angle of inclination (slope) between the underlying surface and the horizontal plane is insignificant.     

驻波场中圆柱形换热管外声流特性的数值研究

基于非线性Navier-Stokes方程推导了一般性的声流控制方程,并利用有限元软件COMSOL对平面驻波声场中单根圆柱形换热管和双圆柱形换热管外包含二阶流场信息的Navier-Stokes方程进行全域求解,得到了一阶和二阶流场信息。研究了雷诺数Re和斯特劳哈尔数Sr对换热管外声流结构的影响规律。研究发现:随Re和Sr的增大,换热管边界层内的涡流区域变小,直至消失,而边界层外的涡流区域逐渐增大;且单换热管外涡流个数由8个减少到4个,双换热管外涡流个数从12个减少到8个。此外,边界层内和边界层外的涡流结构呈反向旋转;边界层外流场沿着振荡方向远离换热管,而在垂直方向流向换热管。     

Wall-bounded laminar sink flows

Summary The laminar flow near an infinite plane wall perpendicular to a line sink of constant strength is investigated in the limit of large Reynolds numbers. Self-similarity requires that fluid is issuing from the boundary layer. The inviscid flow outside the boundary layer is governed by the Euler equations. A one-parametric set of solutions to the Euler equations with appropriate boundary conditions is given. Uniqueness of the inviscid flow solution is obtained from matching with the boundary layer expansion. The solution of the boundary-layer equations is given both in closed form and numerically. It is found that at the edge of the boundary layer the vorticity decays algebraically.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

一类非线性奇摄动问题的激波性态

利用奇摄动理论和垂直观察平面技巧,在适当的条件下讨论了一类非线性问题激波位置的变化。分析了边界条件对于激波位置的影响,得出了当边界条件作微小的变动时,激波位置将产生较大的偏移,甚至由区间内部层偏移至边界层的结果。     

Interplay of surface effects in a thin nematic liquid crystal layer

Manifestations of the competition of surface effects in a thin nematic liquid crystal (LC) layer are considered. It is shown that the LC director field lines remain straight irrespective of the preferred anchoring angles at the LC boundary surfaces. The angle between the director field lines and the plane of the LC layer depends on these preferred anchoring angles and on the Rapini-Papoular energy ratio at the boundary surfaces. There are two possible director orientations differing by 90°. Switching between these states can be induced by chemical factors or by external fields. In contrast to the well-known Fréedericksz transition, the work required for such switching is partly performed by the competing surfaces. Hence, the LC layer switching only requires overcoming the difference between the Rapini-Papoular energies, which can be rendered small by properly selecting LC-substrate pairs.     

Boundary layer scattering measurements with a charge-coupled device camera lidar

A CCD-based bistatic lidar (CLidar) system has been developed and constructed to measure scattering in the atmospheric boundary layer. The system uses a CCD camera, wide-angle optics, and a laser. Imaging a vertical laser beam from the side allows high-altitude resolution in the boundary layer all the way to the ground. The dynamic range needed for the molecular signal is several orders of magnitude in the standard monostatic method, but only approximately 1 order of magnitude with the CLidar method. Other advantages of the Clidar method include low cost and simplicity. Observations at Mauna Loa Observatory, Hawaii, show excellent agreement with the modeled molecular-scattering signal. The scattering depends on angle (altitude) and the polarization plane of the laser.     

The effect of thermal radiation on the propagation of temperature waves in a semitransparent medium

The propagation of temperature waves arising as a result of periodic external thermal stimulation is investigated in a plane layer of semitransparent absorbing and radiating medium without scattering. The classification of temperature waves on the basis of two dimensionless parameters is suggested. It is rigorously demonstrated that not more than two temperature waves may simultaneously exist in a gray semi-infinite medium. The relative contribution of radiation to complex heat transfer is estimated. The system of equations of radiative-conductive heat transfer is reduced to a single integral equation on the boundary. The effect of reflection on the boundary is discussed.     

Mode III fracture of a magnetoelectroelastic layer: exact solution and discussion of the crack face electromagnetic boundary conditions

This paper develops a closed-form solution for anti-plane mechanical and in plane electric and magnetic fields in a magnetoelectroelastic layer of finite thickness. Explicit expressions for the stresses, electric fields, and magnetic fields, together with their intensity factors are obtained for the extreme cases for impermeable and permeable cracks. Solutions for some special cases, such as a magnetoelectroelastic layer with infinite thickness, are also obtained. Applicability of the crack face electromagnetic boundary conditions is discussed. It is found that the crack profile is important in obtaining the correct electromagnetic fields and their intensity factors. The stress intensity factor, however, does not depend on the crack face electromagnetic boundary condition assumptions.     

Similar solutions of boundary layer equations in the presence of a magnetic field

The author investigates the problem of a plane boundary layer in a viscous incompressible fluid with high conductivity in the presence of a magnetic field. The class of potential flows for which the system examined in [1] reduces to an ordinary system is determined.     

Stresses Near a Disk-Shaped Sharp Slot with Tangential Contact Interaction Between Its Surfaces

We propose a new statement of the problem of elastic equilibrium of a disk-shaped slot whose surfaces are loaded by an arbitrary normal load vanishing on its front according to a certain law. By the method of discontinuous Weber-Schafheitlin integrals, it is shown that, in this case, there exists a unique state of elastic equilibrium with regular distribution of stresses over the front of the slot. According to the concept of boundary layer, the jump of tangential stresses formed on the surfaces of the slot due to the continuity of the components of the vector of local rigid rotation Ω on its front is continued in the plane of the slot and guarantees the validity of the equilibrium conditions provided that the normal stresses are equal to zero (the effect of boundary layer). The numerical analysis shows that the jump of tangential stresses in the boundary layer outside the slot rapidly decreases with the distance from the front in complete agreement with the Saint-Venant principle. If a jump of tangential stresses on the surfaces of the slot is absent (and exists outside the slot), then these surfaces have a kink in the front of the slot and the volume strains possess a logarithmic singularity. This situation can be regarded as the limiting state corresponding to the onset of plastic deformation or brittle fracture. If the tangential stresses do not have jump in the entire plane of the slot, then the solution of the problem does not exist. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 3, pp. 71–84, May–June, 2005.