多孔介质平板通道传热模型的两种求解方法

基于Brinkman Darcy扩展模型和非局部热平衡模型,考虑液相和固相含有内热源的情况,建立了多孔介质平板通道传热的一般模型.分别采用直接法和间接法将液相与固相能量方程解耦,进而求得充分发展传热条件下的多孔介质温度场.与直接解耦法相比,间接解耦法可在原始边界条件下求解二阶微分方程,更加简单易行.通过对无量纲温度表达式系数以及温度分布的比较,验证了两种求解方法的等价性.在两种极限情形下,间接法所得温度分布解析解与现有文献结果相当吻合,这也在一定程度上证明了所建模型更具一般性.参数分析表明,液固两相温差随着Biot数或有效导热系数比的增大而减小,Nusselt数随着内热源比的增大而减小.     

饱和多孔介质的超粘弹性本构理论研究

为了建立能考虑固体材料、多孔固体与流体可逆和不可逆变形的饱和多孔介质超粘弹性理论,以多孔固相为参考构型,以有效应力、材料真实应力和流相真实孔压作为状态变量,结合混合物均匀化响应原理获得各项均符合热力学功共轭特征的饱和多孔介质能量平衡方程,根据非平衡热力学熵分解理论求得熵流和熵产.结果表明,超弹塑性理论是该理论的一个特例;多孔固体的总变形可分为固相间隙和材料变形两部分,间隙应变与Terzaghi有效应力构成功共轭对,材料应变与材料真实应力构成功共轭对.饱和多孔介质的自由能可分为固相和流相两部分.当固相间隙和材料变形解耦时,固相所含的自由能又可分为间隙和材料两部分.证明了Skempton有效应力不是饱和多孔介质的基本应力状态变量.     

不可压饱和多孔弹性杆动力响应的多辛方法

研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.     

饱和多孔介质中骨架的应变局部化萌生条件

应用饱和多孔介质控制方程和Liapunov稳定理论,导出了固相应力和有效应力描述的多孔介质骨架应变局部化的萌生条件．不同应力形式表达的多孔介质基体的控制方程,相应的应变局部化萌生条件的表达形式也不尽相同,其原因源于骨架本构中固液两相之间相互作用的不同描述．应用得出的Terzaghi有效应力描述的应变局部化萌生条件,可以理论解释多孔介质中固、液两相不同相对运动出现的破坏方式,如管涌、滑坡和泥石流．应用简单算例说明了应变局部化条件的具体实施方法．     

化学反应时混合对流传热传质磁流体流经多孔楔形体粘度变化及热分层影响的数值研究

在磁流体力学中,当粘滞不可压缩传热传质混合对流的导电流体,流经多孔楔形体且伴有化学反应时,对其粘度变化及热分层影响进行了分析.将楔形体壁面埋入均匀的非Darcy多孔介质中,壁面具有吸入或抽出流体的功能.通过相似变换,将边界层的控制方程写为无量纲形式.使用有限差分法,对变换后耦合的非线性常微分方程进行数值解.对无量纲参数的不同值进行数值计算时,略去三阶以上的高阶差分.图形形式给出的结果表明,这些参数对流场及其它物理量都有重要影响.与已知文献的结果比较表明,它们高度地一致.     

外形任意的多孔介质轴对称物体中充满非Newton幂律流体时的自然对流

在一个轴对称、外形任意的多孔介质二维体中,充满了有屈服应力的非Newton幂律流体时,数值分析其自由对流及其传热/传质问题．利用相似变换,将边界层控制方程及其边界条件变换为无量纲形式,然后用有限差分法求解该方程组．所研究的参数为流变常数、浮力比和Lewis数．给出并讨论了典型的速度、温度及浓度曲线．发现屈服应力参数值和非Newton流体的幂律指数对结果有着显著的影响．     

饱和的多孔介质中含夹杂时的磁流体动力学自然对流

在一个多孔介质中含倾斜矩形夹杂物时,数值地研究磁流体动力学自然对流热交换问题,矩形夹杂的边界条件为两个绝热壁和两个等温壁,使用适当的变量集,将控制方程:连续性条件、推广的Darcy定理--Forchheimer律、能量方程变换为无量纲形式,然后使用有限差分格式求解,磁效应数、Darcy-Rayleigh数、矩形夹杂物的倾斜角以及纵横比作为控制参数,得到多孔介质中含矩形夹杂物时,磁效应数和倾斜角参数影响流体流动和热交换的规律.     

各向异性粘弹性多孔介质中平面波的传播

讨论了弹性多孔介质中波的传播的（或许是）最一般的模型。考虑的介质是粘弹性的、各向异性的、多孔固体骨架，其各向异性可渗透的孔隙中充满着粘性液体。考虑一般类型的各向异性，并且介质中的衰减波作为非均质波处理。对介质中4种衰减波中的每一种，将复慢矢量分解定义为相速度、均质衰减、非均质衰减和衰减角。用一个无量纲参数来度量非均质波与其均质波的区别。利用北海沙岩的数值模型，分析传播方向、非均质参数、频率范围、各向异性对称性、骨架滞弹性和孔隙流体粘度，对该类介质中波传播特性的影响。     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

放/吸热流体在两个充满多孔材料的竖直平行板之间作不稳定的自然对流

在一个由两块无限竖直平行板组成的管道中,充满着多孔的介质材料,使用Darcy模型(Brinkman模型的推广)的动量方程,连同能量方程,计算不可压缩、粘性、放/吸热流体在该管道中的不稳定自然对流,即Couette流动.流动是由于边界平板有不对称的加热,以及作加速运动所引起.选用合理的无量纲参数,对控制方程进行简化,通过Laplace变换进行解析求解,得到闭式的速度和温度分布曲线解,随后导出表面摩擦力和传热率.发现在竖直管道中的不同剖面,流体的流动及温度分布曲线随着时间而增加,且在运动平板附近更高.特别是,流体的速度和温度随着平板间距的增加而增加,但是,表面摩擦力和热传导率随着平板间距的增加而减小.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

Nonlinear stability in microfluidic porous convection problems

This paper investigates classes of thermal convection problems which display effects which are predominant at small scales, i.e. at the microfluidic level. We concentrate on two effects. The first is the effect of local thermal non-equilibrium (LTNE), where the temperature of the saturating fluid may be different from the temperature of the solid skeleton of the porous body. The second is the effect of anisotropy where differences in the flow direction may change strongly depending on the inertia, permeability, thermal conductivity, and on the diffusion coefficient. The class of porous materials analysed are those of Forchheimer type. However, we employ a Forchheimer law recently in vogue in the literature where the nonlinear term which accounts for the variation from linear in the velocity—pressure gradient relationship is cubic in the velocity field as opposed to the classical quadratic one.

     

On Two‐Phasic Flow Problems in Elasto‐Plastic Porous Materials

In the present contribution, the formulation of the governing equations of coupled flow and deformation processes in porous materials is based on the well‐founded Theory of Porous Media (TPM) [2, 3]. Embedded in this concept, the model under consideration represents a triphasic medium of a cohesive‐frictional elasto‐plastic solid skeleton and a binary pore‐fluid, which is composed of a materially incompressible wetting phase (here water) and a materially compressible non‐wetting phase (here air). The unsaturated domain (saturation in terms of liquid saturation) of the porous medium is included in the model by the application of a suitable capillary‐pressure‐saturation relation, which takes into account the interaction of the solid skeleton and the two pore‐fluids. Furthermore, the interaction is described by Darcy's filter law including a relative permeability, which depends on the deformation of the pore space and the degree of saturation.     

Thermal transpiration for the linearized Boltzmann equation

The phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hard‐sphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number κ, the flow velocity between two plates is of the order of log κ, and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation. © 2006 Wiley Periodicals, Inc.     

On the Description of Partially Saturated Soils by the Theory of Porous Media

In this contribution, a multi‐phase soil model based on the Theory of Porous Media (TPM) is presented. The model is fully coupled in the following constitutive phases: An elasto‐plastic or elasto‐viscoplastic solid skeleton, a materially incompressible pore‐liquid (water) and a materially compressible pore‐gas (air). The interaction of the solid skeleton and the pore‐fluids is specified by a capillary pressure‐saturation relation, whereas the mobilities of the fluid phases in the pore‐space of the solid skeleton are described by the so‐called relative permeabilities. Finally, a gravity governed initial‐boundary‐value problem solved by the FE method is presented.     

Effects of variable viscosity on non-Darcy MHD free convection along a non-isothermal vertical surface in a thermally stratified porous medium

An analysis is performed for non-Darcy free convection flow of an electrically conducting fluid over an impermeable vertical plate embedded in a thermally stratified, fluid saturated porous medium for the case of power-law surface temperature. The present work examines the effects of non-Darcian flow phenomena, variable viscosity, Hartmann–Darcy number and thermal stratification on free convective transport and demonstrates the variation in heat transfer prediction based on three different flow models. The wall effect on porosity variation is approximated by an exponential function. The effects of thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation. The resulting non-similar system of equations is solved using a finite difference method. Results are presented for velocity, temperature profiles and local Nusselt number for representative values of different controlling parameters.     

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.     

Numerical study of melting in an enclosure with discrete protruding heat sources

In order to explore the capability of a solid–liquid phase change material (PCM) for cooling electronic or heat storage applications, melting of a PCM in a vertical rectangular enclosure was studied. Three protruding generating heat sources are attached on one of the vertical walls of the enclosure, and generating heat at a constant and uniform volumetric rate. The horizontal walls are adiabatic. The power generated in heat sources is dissipated in PCM (n-eicosane with the melting temperature, T_m = 36 °C) that filled the rectangular enclosure. The advantage of using PCM is that it is able to absorb high amount of heat generated by heat sources due to its relatively high energy density. To investigate the thermal behaviour and thermal performance of the proposed system, a mathematical model based on the mass, momentum and energy conservation equations was developed. The governing equations are next discretised using a control volume approach in a staggered mesh and a pressure correction equation method is employed for the pressure–velocity coupling. The PCM energy equation is solved using the enthalpy method. The solid regions (wall and heat sources) are treated as fluid regions with infinite viscosity and the thermal coupling between solid and fluid regions is taken into account using the harmonic mean of the thermal conductivity method. The dimensionless independent parameters that govern the thermal behaviour of the system were next identified. After validating the proposed mathematical model against experimental data, a numerical investigation was next conducted in order to examine the thermal behaviour of the system by analyzing the flow structure and the heat transfer during the melting process, for a given values of governing parameters.     

微极流体薄膜层通过以滑移速度移动的可渗透无限平板时流体特性变化和热辐射对流动和热传导的影响

微极流体薄膜层通过按滑移速度移动的可渗透无限竖直平板时,研究热辐射对混合对流薄膜层流动和热传导的影响.假定流体粘度和热传导率变化是温度的一个函数.对一些典型的可变参数值,应用Chebyshev谱方法,数值求解流动的控制方程.将所得结果与已发表文献的结果进行比较,结果是一致的.绘出并讨论了可变参数对速度、微旋转速度、温度分布曲线、表面摩擦因数和Nusselt数的影响.     

Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects

In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng &; Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H,and it is shown that these thermal non-equilibrium effects are strongest when H is small.