Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium

Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of $n$ reaction–diffusion–convection equations coupled with $n$ ordinary differential equations, which models a combustion front moving through a porous medium with $n$ parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.     

飞秒脉冲的远场反射谱特性

从平面波的角谱表示出发,得到了超短脉冲光束由分层介质表面反射的频谱特性,数值计算给出了飞秒高斯脉冲经自由空间中介质薄膜反射的远场谱分布.由于光与介质的相互作用,反射谱呈现谱线变窄、红移、蓝移以及出现旁瓣而分裂成多重谱线的现象.     

Homogenization of a degenerate parabolic problem in a highly heteregeneous mediumHomogénéisation d'un problème parabolique dégénéré dans un milieu fortement hétérogène

We consider the homogenization of a time-dependent heat transfer problem in a highly heteregeneous periodic medium made of two connected components having finite heat capacities c_α(x) and heat conductivities a_α(x), α=1,2, of order one, separated by a third material with thickness of order ε the size of the basic periodicity cell, but with conductivity λa₃(x) where a₃=O(1) and λ tends to zero with ε. Assuming only that c_i(x)?0 a.e., such that the problem can degenerate (parabolic-elliptic), we identify the homogenized problem following the values of δ=lim_ε→0ε²/λ. To cite this article: M. Mabrouk, A. Boughammoura, C. R. Mecanique 331 (2003).     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

不同水介质润滑下GCr15钢的微动磨损特性

采用液压高精度材料试验机考察了平面-球面接触GCr15钢摩擦副在海水、酸性水和洁净水等3种不同水介质润滑下的微动磨损性能．用激光扫描显微镜(LSM)观察了磨痕表面形貌．结果表明：3种水介质对钢-钢摩擦副具有明显的润滑作用，其中酸性水的润滑作用最明显；磨损体积损失同介质的润滑作用和腐蚀作用相关，在洁净水和海水介质润滑下的磨损体积损失较小，在酸性水介质润滑下的磨损体积损失较大；在海水润滑下的GCr15钢磨损表面呈现明显的点蚀特征．     

Experimental Determination of the Longitudinal Dispersivity During the Injection of a Micro-Cement Grout in a One-Dimensional Soil Column

In order to describe the basic phenomenon of miscible grout propagation during the injection in a saturated and deformable porous medium, a general mathematical model was proposed, which accounts for the existing coupling between the fluid flow analysis, the miscible grout transport, and the solid skeleton deformation, leading to a realistic prediction of the injected zone. The development of the model was made concurrently with laboratory experiments to determine the model parameters. This paper describes the determination of the longitudinal dispersivity during the transport of a micro-cement grout injected in a one-dimensional soil column, by relying on image processing analysis. The application concerned here is the injection of soils for improving their properties, that is, to reduce permeability, increase mechanical strength or reduce the deformability. The longitudinal dispersion coefficient is an essential parameter governing the mixing process and the evolution of the transition zone, and thus the injection efficiency. Finally, the comparison between simulated results from the developed model and experimental data, essential to validate the model from a phenomenological standpoint, is made.     

摩托车正时链和传动链磨损特性的研究

研究油润滑条件下摩托车发动机正时链的磨损特性,发现疲劳磨损,裂纹的形成和扩展是影响疲劳寿命的主要因素;定期刷油或滴油润滑条件下,摩托车传动链的磨损机制是磨粒磨损,并伴有疲劳磨损,销轴和套筒零件的渗层及心部组织等是影响链条磨损特性的重要因素,因为中碳调质钢经碳氮共渗后可获得弥散分布的颗粒状碳化物的表层组织及回火屈氏体的心部组织,从而显示出表层耐磨、心部强韧性好及抗塑变能力高的综合机械性能。     

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.     

Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge

An analysis has been carried out to study heat transfer characteristics of an incompressible Newtonian electrically conducting and heat generating/absorbing fluid having temperature-dependent viscosity over a non-isothermal wedge in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The wedge surface is assumed to be permeable so as to allow for possible wall suction or injection. The effects of viscous dissipation, Joule heating, stress work and thermal radiation are included in the model. The governing differential equations are derived and transformed using a non-similarity transformation. The transformed equations are solved numerically by applying a fifth-order Runge-Kutta-Fehlberg scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity and temperature profiles for a prescribed magnetic field parameter as well as the development of the local skin-friction coefficient and local Nusselt number with the magnetic field and radiation parameters are presented graphically and in tabulated form to elucidate the influence of the various physical parameters.     

Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium

The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.