Unsteady convective mass transfer in a three-zone system

A three zone unsteady state mass transfer problem is considered for flow between parallel plates. Solute is transferred from the moving zone to the other two, in one of which a first order reaction consuming the solute occurs. (An industrially important example of this situation would be the absorption of a gas from a lean mixture into a liquid-saturated ion exchange membrane.) The double Laplace transformation is applied to the system equations. In obtaining the inversion of the transformed equations the first inversion (with respect to the transformed dimensionless axial distance) is performed by use of the residue method, and then the second inversion (with respect to the transformed dimensionless time) is performed by use of the numerical technique developed by Bellman et al. Some numerical results are presented and discussed.     

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。     

State space approach to unsteady magnetohydrodynamics natural convection heat and mass transfer through a porous medium saturated with a viscoelastic fluid

A technique of the state space approach and the inversion of the Laplace transform method are applied to dimensionless equations of an unsteady one-dimensional boundary-layer flow due to heat and mass transfer through a porous medium saturated with a viscoelastic fluid bounded by an infinite vertical plate in the presence of a uniform magnetic field is described. Complete analytical solutions for the temperature, concentration, velocity, and induced magnetic and electric fields are presented. The inversion of the Laplace transforms is carried out by using a numerical approach. The proposed method is used to solve two problems: boundary-layer flow in a viscoelastic fluid near a vertical wall subjected to the initial conditions of a stepwise temperature and concentration and viscoelastic fluid flow between two vertical walls. The solutions are found to be dependent on the governing parameters including the Prandtl number, the Schmidt number, the Grashof number, reaction rate coefficient, viscoelastic parameter, and permeability of the porous medium. Effects of these major parameters on the transport behavior are investigated methodically, and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, concentration, and induced magnetic and electric field distributions, as well as the local skin-friction coefficient and the local Nusselt and Sherwood numbers.     

Dynamic response of an elastic medium containing crack

A fundamental solution for an infinite elastic medium containing a penny-shaped crack subjected to dynamic torsional surface tractions is attempted. A double Laplace–Hankel integral transform with respect to time and space is applied both to motion equation and boundary conditions yielding dual integral equations. The solution of the derived dual integral equations is based on an analytic procedure using theorems of Bessel functions and ordinary differential equations. The dynamic displacements’ field is obtained by inversion of the corresponding Laplace–Hankel transformed variable. Results of a representative example for a crack subjected to pulse surface tractions are obtained and discussed.     

A Numerical Method for Wave Propagation in Viscoelastic Stratified Porous Media

This paper presents a numerical method, a transmission matrix method, for the wave propagation in viscoelastic stratified saturated porous media. The wave propagation in saturated media, based on Biot theory, is a coupled problem. In this stratified three-dimensional model we do the Laplace transform for the time variable and the Fourier transform for the horizontal space coordinate. The original problem is transformed into ordinary differential equations with six independent unknown variables, which are only the function of the coordinate of depth. Thus, we get a transmission matrix of the wave problem for each layer. In the process of solution we use numerical method to calculate the eigenvalues and the eigenvectors of the transmission matrices. In the first step of the solution process we can obtain the wave field in the transformed space. The fast Fourier transform (FFT) method is used to do the inverse Laplace and the inverse Fourier transforms to get the solution in the time space. The detailed formulae are derived and some numerical examples are given.     

Integral transform analysis of natural convection in porous enclosures

A hybrid numerical-analytical solution for steady-state natural convection in a porous cavity is proposed, based on application of the ideas in the generalized integral transform technique. The integral transformation process reduces the original coupled partial differential equations, for temperature and stream function, into an infinite system of non-linear ordinary differential equations for the transformed potentials, which is adaptively truncated and numerically solved through well-established algorithms. The approach is applied to a vertical rectangular enclosure subjected to uniform internal heat generation. The convergence characteristics of the explicit inversion formulae are illustrated and critical comparisons with previously reported purely numerical solutions are performed.     

Magnetohydrodynamic laminar boundary-layer flow over a porous wedge with thermophoresis particle deposition in the presence of variable stream conditions

An analysis is presented to investigate the effects of thermophoresis variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by local non-similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

分形理论在煤层气非平衡吸附模型中的应用

传统的煤层气动力学模型均是建立在欧几里得几何基础上的,难以描述煤层孔隙结构的复杂性及形状的不规则性。本文以分形理论为基础,通过引入分形维数来刻画煤层孔隙结构的复杂性并考虑煤层的吸附特性、双重介质特征及介质的变形,建立基于Fick第二定律的分形介质煤层气非稳态渗流数学模型。由于流动方程的强非线性,结合各类边界条件用正则摄动法和Laplace变换得到模型在拉氏空间上的近似解析解,再利用Laplace数值反演求得实空间上的数值解。对参数进行敏感性分析并绘制了典型压力曲线,这些结果为煤层气开采提供了理论依据和试井方法。     

Unsteady flow of ground-water in an aquifer system with viscoelastic properties

The transient flow behaviour of groundwater in an aquifer-aquitard system with viscoelastic properties is studied. On the basis of previous work (Hantush, Neuman, Brutsaert, Corapcioglu), new partial-differential integral equations are assembled. The well-known equations (Hantush, Brutsaert) are special cases of these equations, which describe the flow of slightly compressible groundwater in aquifer-aquitard layers with viscoelastic properties.Analytical solutions of the coupled partial differential-integral equations are obtained by Laplace transform. The viscoelastic properties enhance the heterogeneities of an elastic aquifer system with delay and feed. Numerical inversion of the Laplace transformed drawdown is in good agreement with the analytical solutions obtained.     

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models.     

Dynamic Response of a Piezoelectric Material with a Conducting Rigid Inclusion

The problem of a conducting rigid inclusion embedded in an infinite piezoelectric matrix is considered under the action of combined electromechanical impact loads. By using integral transform techniques, the mixed initial-boundary value problem for the case of anti-plane shear load and in-plane electric field is transformed into two systems of dual integral equations, the solutions of which give the singularity coefficients of electroelastic field near the inclusion tips in closed-form in the Laplace transform domain. Numerical results for the stress singularity coefficient in the physical space are presented graphically by numerically solving the resulting Fredholm integral equation and carrying out the numerical inversion of Laplace transform for a PZT-5H material with a conducting rigid line inclusion.     

ANALYSIS OF THE HIGH-ASPECT-RATIO WING GUST RESPONSE BY TRANSFER FUNCTION METHOD1)

将传递函数法应用于大展弦比机翼的阵风响应分析。首先,基于二元机翼的运动方程和准定常片条理论建立机翼的阵风响应微分方程,对其进行Laplace变换,并转换为状态空间方程形式。然后,运用传递函数方法,获得机翼响应在频域的解析解,通过Laplace数值逆变换求得机翼在时域内的响应。通过与已有文献结果对比,验证了本文方法的正确性。最后,采用该方法求解了“1-cos”型阵风和连续大气湍流作用下的机翼响应,并对结果进行了分析讨论。     

Thermophoresis and variable viscosity effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction

An analysis is presented to investigate the effects of thermophoresis and variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Linear viscoelastic analysis of straight and curved thin-walled laminated composite beams

This paper is devoted to study the behavior, in the range of linear viscoelasticity, of shear flexible thin-walled beam members constructed with composite laminated fiber-reinforced plastics. This work appeals to the correspondence principle in order to incorporate in unified model the motion equations of a curved or straight shear-flexible thin-walled beam member developed by the authors, together with the micromechanics and macromechanics of the reinforced plastic panels. Then, the analysis is performed in the Laplace or Carson domains. That is, the expressions describing the micromechanics and macromechanics of a plastic laminated composites and motion equations of the structural member are transformed into the Laplace or Carson domains where the relaxation components of the beam structure (straight or curved) are obtained. The resulting equations are numerically solved by means of finite element approaches defined in the Laplace or Carson domains. The finite element results are adjusted with a polynomial fitting. Then the creep behavior is obtained by means of a numerical technique for the inverse Laplace transform. Predictions of the present methodology are compared with experimental data and other approaches. New studies are performed focusing attention in the flexural–torsional behavior of shear flexible thin-walled straight composite beams as well as for thin-walled curved beams and frames.     

层状横观各向同性饱和土的非轴对称动力响应

通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向Hankel变换,建立问题的状态方程;求解状态方程后,得到传递矩阵. 进而利用传递矩阵,结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform

This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail.     

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.     

Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation

This paper examined the hydromagnetic mixed convection stagnation point flow towards a vertical plate embedded in a highly porous medium with radiation and internal heat generation. The governing boundary layer equations are formulated and transformed into a set of ordinary differential equations using a local similarity approach and then solved numerically by shooting iteration technique together with Runge-Kutta sixth-order integration scheme. A representative set of numerical results are displayed graphically and discussed quantitatively to show some interesting aspects of the pertinent parameters on the dimensionless axial velocity, temperature and the concentration profiles, local skin friction, local Nusselt number and local Sherwood number, the rate of heat and mass transfer. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases.     

Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium

The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.     

弹性地基上多孔功能梯度材料矩形板的自由振动与临界屈曲载荷分析

多孔功能梯度材料(FGM)构件的特性与孔隙率和孔隙分布形式有密切关系。本文基于经典板理论,考虑不同孔隙分布形式时修正的混合率模型,研究Winkler弹性地基上四边受压多孔FGM矩形板的自由振动与临界屈曲载荷特性。首先利用Hamilton原理和物理中面的定义推导Winkler弹性地基上四边受压多孔FGM矩形板自由振动的控制微分方程并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程和边界条件进行变换,得到计算无量纲固有频率和临界屈曲载荷的代数特征方程。将问题退化为孔隙率为零时的FGM矩形板并与已有文献进行对比以验证其有效性。最后计算并分析了梯度指数、孔隙率、地基刚度系数、长宽比、四边受压载荷及边界条件对多孔FGM矩形板无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。