Analytical solution for shock waves in dusty gases

Summary The structure of one dimensional shock waves is investigated using the Navier-Stokes equations for the gas phase and the particle phase. The resulting system of four ordinary nonlinear differential equations is reduced to a system of two autonomous nonlinear differential equations which are solved analytically. This solution is obtained formally by neglecting the viscosity (=0).     

Analytical solution of time periodic electroosmotic flows: analogies to Stokes' second problem.

Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter kappa, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of kappa reveals interesting physics, ranging from oscillatory "pluglike" flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz-Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Helmholtz-Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large kappa values show inflection points very near the walls with localized vorticity extrema that are stronger than the Stokes layers. This have the potential to result in low Reynolds number flow instabilities. It is also shown that, unlike the steady pure electroosmotic flows, the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height.     

Analytical solution for bonded wedges under thermal stresses

After a change in temperature, high stresses leading to destruction may occur in bonded dissimilar materials near the point of the interface line intersection with the edge. In terms of linear elasticity, these high stresses are described by the singular terms of the stress field expansion at the corner point. In the present paper, the explicit representation of the singular terms and exact values of the stress intensity factors in the case of infinite wedge-shaped joint geometry are obtained by the Mellin transform technique. Systematic comparison with the FEM results for samples of finite size has shown that the values of stress intensity factors are in good agreement if the singularity is not too strong (the singularity orders _k<0.2). With the stronger singularity, the analytical solution is in qualitative agreement with the FEM one, such that it can be used for fast parametrical study of finite samples as well.     

A second order finite element method for the one-dimensional Stefan problem

We describe a finite element method for the one-dimensional Stefan problem. The elements are quadrilaterals of the space-time plane which are determined at each time-step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank-Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equal to 2.     

Schiff碱化合物的分子二阶非线性极化率

报道采用溶致变色法测算了6个给体－受体共轭型希夫碱化合物的分子二阶非线性极化率,探讨了分子结构与非线性光学活性的关系。研究表明取代基的电子性质、取代位置、分子共轭链长度等均影响分子的二阶非线性极化率,在这些化合物的电子吸收光谱中,最大吸收波长在350nm以下,而二阶非线性极化率范围在10^－29－10^－28esu数量级,非线性光学活性较强而光吸收截止波长却较短,具有很好的应用前景。     

A second order cone complementarity approach for the numerical solution of elastoplasticity problems

In this paper we present a new approach for solving elastoplastic problems as second order cone complementarity problems (SOCCPs). Specially, two classes of elastoplastic problems, i.e. the J ₂ plasticity problems with combined linear kinematic and isotropic hardening laws and the Drucker-Prager plasticity problems with associative or non-associative flow rules, are taken as the examples to illustrate the main idea of our new approach. In the new approach, firstly, the classical elastoplastic constitutive equations are equivalently reformulated as second order cone complementarity conditions. Secondly, by employing the finite element method and treating the nodal displacements and the plasticity multiplier vectors of Gaussian integration points as the unknown variables, we obtain a standard SOCCP formulation for the elastoplasticity analysis, which enables the using of general SOCCP solvers developed in the field of mathematical programming be directly available in the field of computational plasticity. Finally, a semi-smooth Newton algorithm is suggested to solve the obtained SOCCPs. Numerical results of several classical plasticity benchmark problems confirm the effectiveness and robustness of the SOCCP approach.     

Nonclassical thermal effects in Stokes' second problem

Summary The MCF model is used to study the nonclassical heat conduction effects in Stoke's second problem. The structure of the waves and the influence of the thermal relaxation time on the temperature and velocity fields are investigated. The displacement thickness, skin friction and the rate of the heat transfer at the plate are determined.     

Numerical solution of the inverse heat-conduction problem for determining thermal constants

We investigate the solution of the inverse heat-conduction problem for a cylinder, based on a series expansion of a thermal constant in powers of temperature, and the determination of the series coefficients by a direct-search method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 6, pp. 1058–1061, December, 1977.     

Sturm-liouville problem for a differential equation of second order with discontinuous coefficients

Using, as an example, a special Sturm-Liouville boundary-value problem for a differential equation of second order with discontinuous coefficients, the authors describe a method of constructing a closed orthonormalized system of functions that is common to the entire domain of determination. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 4, pp. 748–753, July–August, 2000.     

A unified generalized thermoelasticity solution for the transient thermal shock problem

A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem.     

Effects of slip on Graetz problem of power law fluids with second kind boundary condition

Abstract

The linear convective instabilities of a fluid layer of binary alloy, cooled from above and consequently frozen at the bottom, are considered. Due to the density jump across the freezing interface, some light material is then released and diffused by pressure and composition gradients. As a result of a low cooling rate, the effect of thermal buoyancy is insignificant and the freezing interface advances upward at a slow speed by accumulating the solidified binary alloy. As Schmidt number P_L approaches infinity, instabilities set in stationarily at the marginal state. Cellular convective modes are possible, provided a destabilizing compositional profile occurs in the fluid layer, while morphological modes, associated with non‐cellular convection, require a constitutional supercooling near the freezing interface. In the absence of a constitutional supercooling, morphological modes are not important and cellular convective modes become dominant.     

Analytical solution for the simultaneous heat and mass transfer problem in air washers

An analytical solution approach for the simultaneous heat and mass transfer problem in air washers operating as evaporative coolers is presented. A one-dimensional model using the coupled mass and energy balance equations in the air washer is presented. Then, starting from a linear approach for the experimental curve of the air saturation, an analytical solution for the model was derived. The solution showed an excellent agreement with the available results found in the literature. The influence of several important parameters for the cooling process such as temperature and ambient air humidity, air flow rate and feeding water temperature, in the air cooling rate was investigated. The efficacy of the process can be greatly increased by reducing the cooling water temperature and the applied air flow rate. The analytical solution can be easily included into the models used for simulating desiccant air-conditioning systems operating in conjunction with air washers.     

Two-dimensional thermal shock problem of fractional order generalized thermoelasticity

In this study, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the fractional order generalized thermoelasticity theory. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution is applied to a specific problem of a half-space subjected to thermal shock. The inverse Fourier transforms are obtained analytically, while the inverse Laplace transforms are computed numerically. Some comparisons have been shown in figures to estimate the effect of the fractional order on all the studied fields.     

Analytical solution of stability problem for two composite half-planes compressed along interfacial cracks

The plane stability problem for two composite half-planes compressed along the interface, which contains an arbitrary number of cracks, is considered. An exact analytical solution of the problem is found for elastic and elastic–plastic, isotropic and orthotropic, compressible and incompressible half-planes in the common form for finite and small deformations. This solution was developed using complex potentials within the exact approach based on equations of the three-dimensional linearised theory of deformable bodies’ stability. Critical loads are rigorously proved to be independent of the number and disposition of interfacial cracks.     

Determination of the contact thermal resistance from the solution of the inverse problem of thermal conductivity

The contact resistance at the boundary between an orthropic reinforcing rod and an isotropic matrix is determined from the solution of the inverse probblem of thermal conductivity, using the gradient method. The suggested modification of the computational algorithm as the initial calculation of the initial period of the thermal process is shown to enhance the resolving power of the method and the choice of zeroth approximations from below is shown to ensure monotonic convergence of the solution.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 3, pp. 423–427, March, 1989.     

Parametric resonance of the thermal conductivity of molecular gases in magnetic and electric fields

Experimental data showing a resonant change in the thermal conductivity of a paramagnetic gas (NO₂) and a polar gas (NF₃) in parallel constant and alternating magnetic and electric fields are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 2, pp. 263–270, August, 1977.