Mathematical modeling of heat transfer in a heat-shielding material

The interaction of the cooling systems of permeable materials with a high-temperature gas flow is considered. The effect of the porosity and thermal properties of some metals on heat transfer is studied. It is found that increasing the thermal conductivity of the material leads to a decrease in the temperature of the heat-shielding coating and increasing the porosity to a more uniform distribution of the coolant applied on the surface and to a decrease in the heat loads on the structure to be protected.     

Instantaneous formation of a round hole in a stretched plate

Republic Intercollegiate Computer Center, Kishinev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 11, pp. 90–96, November, 1991.     

Mathematical modeling of brush seals

A computational fluid dynamics (CFD)-based model of brush seals has been developed and tested against other workers' experimental data. In the model, the brush is treated as an axisymmetric, anisotropic porous region with nonlinear resistance coefficients. The resistance coefficients are chosen through calibration against measurements. The CFD model gives predictions of flow rate, pressure distribution, velocity field, and bending forces on the bristles. The bristle forces are used in a separate calculation to estimate bristle bending and reaction forces on the shaft and backing plate. Bending in both the axial direction and the orthogonal plane are considered.     

Mathematical modeling of electrorheological materials

Received May 11, 2000 / Published online January 23, 2001     

Mathematical modeling of magneto-sensitive elastomers

Magneto-sensitive (MS) elastomers are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. These materials typically consist of micron-sized ferrous particles dispersed in an elastomer. The full system of equations for deformable MS solids in an electro-magnetic field is first considered. Then, the strain-energy functions for isotropic MS elastomers are presented and a simple phenomenological model is suggested. Finally, to illustrate some of the features of the derived model, a MS elastomer confined by parallel top and bottom plates is subjected to shear deformation under the influence of a magnetic field normal to the plates. An acceptable agreement is illustrated between numerical simulation and experimental observation.     

Mathematical modeling of magnetorheological fluids

Magnetorheological (MR) fluids are a class of smart materials whose rheological properties may be rapidly modified by the application of a magnetic field. These materials typically consist of micron-sized ferrous particles dispersed in a fluid. In the present paper, we consider the full system of equations as well as the Clausius-Duhem inequality for moving isotropic MR fluids in an electro-magnetic field. We present the material constitutive relations for a non-Newtonian incompressible MR fluid. To illustrate the validity of the constitutive relations, the flow of a MR fluid between two parallel fixed plates under the influence of a constant magnetic field perpendicular to the flow direction is considered.Received: 14 July 2003, Accepted: 18 May 2004, Published online: 22 February 2005 Correspondence to: A. Dorfmann     

Mathematical modeling of gas desorption from a gas hydrate

In gas-gashydrate reservoirs the gas is in the free and bound states. The amount of gas bound in the hydrate depends on the thermodynamic conditions. Therefore, when these conditions are varied it is possible for gas to be released from the hydrate in the desorption regime up to total dissociation of the hydrate into gas and water. Below, the problem of extraction of free and bound gas in the desorption regime is considered.Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 118–125, September–October, 1996.     

Mathematical modeling of methane flow in a borehole coal mining system

Safety in coal mining is greatly increased by the drainage of the methane content of coal seams through boreholes, simultaneously producing significant energy. The design of suitable drainage technology is based on the mathematical modeling of methane flow in coal seams. In the calculation of the methane pressure, the new mathematical model presented in this paper considers both the sorption phenomenon of methane depending upon the methane pressure and the fact that the variation in methane pressure can create a change in the stress condition of the rock and, as a consequence of this, a change in the permeability of the coal. The new mathematical model can be used for the numerical simulation of the flow processes in coal seams and methane drainage technology can be designed more accurately.     

Mathematical modeling of flows in wind turbines with a vertical axis

Flow in the rotors of wind turbines with a vertical axis of the Darrieus-Savonius type and their combinations is considered within the framework of the Navier-Stokes equations, in the two-dimensional formulation. A parametric investigation of the Darrieus rotor characteristics is carried out. For all configurations the dependence of the moment and power coefficients on the specific speed of the rotor is calculated. The possibility of the Darrieus rotor self- starting from the state of rest is investigated. The effect of nonmonotonicmoment variation for the Darrieus-type rotor is studied for the specific speeds of 0.5 to 1. A combined design of the Darrieus-Savonius rotor is considered to solve the problems due to a small moment of the Darrieus rotor during the start.     

Head-on collision between normal shock waves and a rubber-supported plate,a parametric study

The equations governing the flow resulting from a head-on collision between a normal shock wave and a rubber-supported plate are listed. The non-dimensional parameters that may affect the resulting flow are specified and their influence on the post-collision flow and waves is studied numerically. It is shown that changes in: the area-ratio between the gas and the rubber cross-sections, the incident shock wave Mach number and the mass ratio between the rubber and the plate it supports, all have significant effects on the post-collision gas and rubber responses. Changes in the rubber elasticity constant also affect the post-collision flow. The extent of the effect that changes in the above mentioned parameters have on the post-collision flow responses depends upon the loading mode used. Three different modes were studied; uni-axial stress loading, bi-axial stress loading and uni-axial strain loading.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Bridging techniques in a multi-scale modeling of pattern formation

Bridging techniques between microscopic and macroscopic models are discussed in the case of wrinkling analysis. The considered macroscopic models are related to envelope equations of Ginzburg–Landau type, but generally, they are not valid up to the boundary. To this end, a multi-scale approach is considered: the reduced model is implemented in the bulk while the full model is applied near the boundary and these two models are coupled with the Arlequin method (Ben Dhia, 1998). This paper focuses on the definition of the coupling model and the transition between two scales. Especially, a new nonlocal bridging technique is presented and compared with another recent one (Hu et al., 2011). The present method can also be seen as a guide for coupling techniques involving other reduced order models.     

MATHEMATICAL MODEL OF A JUNCTION BETWEEN LINEAR ELASTOMER AND THIN PLATE

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Mathematical modeling of volumetric material growth

Growth (resp. atrophy) describes the physical processes by which a material of solid body increases (resp. decreases) its size by addition (resp. removal) of mass. In the present contribution, we propose a sound mathematical analysis of growth, relying on the decomposition of the geometric deformation tensor into the product of a growth tensor describing the local addition of material and an elastic tensor, which is characterizing the reorganization of the body. The Blatz-Co hyperelastic constitutive model is adopted for an isotropic body, satisfying convexity conditions (resp. concavity conditions) with respect to the transformation gradient (resp. temperature). The evolution law for the transplant is obtained from the natural assumption that the evolution of the material is independent of the reference frame. It involves a modified Eshelby tensor based on the specific free energy density. The heat flux is dependent upon the transplant. The model consists of the constitutive equation, the energy balance, and the evolution law for the transplant. It is completed by suitable boundary conditions for the displacement, temperature and transplant tensor. The existence of locally unique solutions is obtained, for sufficiently smooth data close to the stable equilibrium. The question of the global existence is examined in the simplified situation of quasistatic isothermal equations of linear elasticity under the assumption of isotropic growth.     

Mathematical modeling of piezomagnetoelectric thin plates

We present the outline of the rigorous mathematical derivation of linearized piezomagnetoelectric thin plate models and focus on the results it leads to. It is in particular shown how four different models emerge from theoretical tools. New mixed ‘senso-actuator’ and ‘actuato-sensor’ behaviors appear. Moreover, the influence of all the 45 crystal symmetry classes on our models is described. We point out the extremely important structural switch-off phenomenon for which the electromagnetoelastic coupling disappear for some specific crystal classes.     

铅飞层中斜冲击波对碰马赫反射行为实验研究

采用线阵多普勒光纤探针测速技术(Doppler pins system,DPS)和高速光电分幅相机照相两种精密诊断技术,对铅飞层中斜冲击波对碰后的反射行为进行了观测。获得了飞层对碰部位速度-时间历史曲线和凸起形貌演化图像,给出了凸起轮廓发展演化过程、压力分布等实验数据和信息。结合冲击波反射理论,对铅飞层对碰区动力学现象进行了分析和解释,证实铅飞层中斜冲击波对碰后发生了马赫反射。