饱和纳米流体多孔介质中竖直嵌入板上边界层的非Newton流

在层流条件下,对饱和多孔介质中的竖直板,研究幂指数型非Newton流的自由对流热交换.非Newton纳米流体服从幂指数型的数学模型,模型综合考虑了Brown运动和热泳的影响.通过相似变换,将问题的偏微分控制方程组,转化为常微分方程组,得到了常微分方程组的数值解.数值解依赖于幂指数n,Lewis数Le,浮力比Nr,Brown运动参数Nb,以及热泳参数Nt.在n和Le的不同取值下,研究并讨论了对相关流体性质参数的影响和简化的Nusselt数.     

纳米流体流经热分层线性多孔伸展平面时的MHD自然对流及其Lie对称群变换

就不可压缩粘性纳米流体,流经半无限垂直伸展平面并计及热分层时,研究该流体的MHD自然对流和热交换.通过特定形式的Lie对称群变换,即单参数群变换,将所考虑问题的偏微分控制方程变换为常微分方程组.然后,使用基于打靶法的Runge Kutta Gill法进行数值求解.最后得到结论:流场、温度和纳米颗粒体积率受热分层和磁场的影响很显著.     

在柱坐标系下研究由拉伸缸引起的Casson纳米流体流动与传热传质现象

首次利用柱坐标研究速度滑移和对流表面边界条件下,由拉伸缸引起的稳态层流Casson纳米流体流动、传热及传质现象.采用恰当的相似变换将偏微分控制方程转化为高阶非线性耦合常微分方程,并通过打靶法进行数值求解,图示并详细分析了不同物理参数对速度、温度及浓度分布的影响.结果显示,速度受滑移参数的影响较大,温度和浓度分别受Biot数和Lewis数的影响较大;随着Casson参数的增大,速度下降而温度和浓度都增加;温度随着Brown(布朗)运动参数或热泳参数的增加而上升;浓度随着Brown运动参数的增大而减小,随着热泳参数的增大而增大,当热泳参数较大时,浓度出现了"回流"现象.     

传导-辐射对沿垂直平面有热泳的瞬时自然对流的影响

研究存在热辐射时,热泳微粒的沉积,对沿垂直平面瞬态自然对流边界层流动的影响,垂直平面浸没在光密灰色流体中.分析中采用Rosseland扩散近似表示辐射热通量项.将控制方程简化为抛物线型的偏微分方程组,然后在整个时间段0≤τ<∞,利用有限差分法数值求解.还得到了小数值时间和大数值时间的渐近解,发现渐近解和数值解吻合很得好.而且,流体,20℃和1个标准大气压下的空气,即Prandtl数Pr为0.7时,用图形给出了不同物理参数,即热辐射参数Rd、表面温度参数θw和热泳参数λ,对瞬时的表面剪切应力τw、表面热传输率qw和组分浓度扩散率(传质率)mw的影响,以及对瞬时的速度、温度和浓度分布曲线的影响.     

不同流条件下随温度变化的流体黏性和热泳微粒沉积对自由传热传质作用的Lie群分析

研究二维稳定不可压缩流体在竖向延伸平面上的流动.流体黏性假设为与温度相关的线性函数.对控制方程进行伸缩群变换,由于变换参数之间的关系让方程解保持不变.在找到3个绝对不变量后,推导对应动量方程的一个三阶一般微分方程和两个对应能量方程和扩散方程的二阶一般微分方程.求出具有边界条件方程的数值解,发现随着平面延伸距离增加,随温度变化的流体黏性降低让流速变慢.在平面的某个特定点处,随着黏性减少流速变慢但温度增加.热泳微粒沉积在浓度边界层起着关键作用.最后对计算结果进行讨论并给出图例.     

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.     

金属泡沫微流道热沉内流体流动与传热特性的数值研究

为改善高能量密度电子设备的冷却效率,提出了在微流道热沉内填充金属泡沫的新型热沉结构,并数值研究了金属泡沫的孔隙率、孔密度、材质(铜、镍及铝)、流体工质(水、乙二醇及纳米流体)等相关参数对微流道流动与换热特性的影响.研究结果表明:金属泡沫可以显著地强化微流道热沉的换热特性;添加金属泡沫后微流道热沉的换热性能可提高2倍以上;采用纳米流体与金属泡沫相结合的双重强化换热手段可以进一步地增强微流道热沉的冷却能力;在层流流动状态下金属泡沫微流道热沉可以对发热量为200 W/cm2的电子设备进行有效地冷却,表明其在高功率密度电子设备热管理领域具有广阔的应用前景.     

第二梯度流体的蠕变流和热传导相似解

给出了在笛卡儿坐标系中,忽略惯性的缓慢流动的二维运动方程和二阶梯度流体的传热方程．当Re1时,若从运动方程中简单地省略惯性项,则结果方程的解仍然近似有效．事实上,从无量纲的动量和能量方程也可导出这一结论．利用李群分析,知道求得的方程是对称的．李代数包括4个有限参数和一个无限参数组成的李群变换,其中一个是比例对称变换,另一个是平移变换．利用对称性求得两种不同形式的解．利用x和y坐标的平移,给出了指数形式的精确解．对于比例对称变换,更多地涉及到常微分方程,只能给出级数形式的近似解,最后讨论了某些边值问题．     

纳米流体在粘性耗散和Newton传热组合影响下的Sakiadis流动分析

就两类以水为基本流体的Newton纳米流体:内含金属颗粒铜(Cu),或者非金属颗粒二氧化钛(TiO2),研究粘性耗散和Newton传热对移动平板边界层流动的组合影响.利用相似变换,将偏微分的控制方程转换为常微分方程组,并用Runge-Kutta-Fehlberg法和打靶法,对其进行数值求解.由此得到结论,随着纳米颗粒体积分数和Newton传热的增加,移动平板表面的热交换率也增加,但是,随着Brinkmann数的增加,移动平板表面的热交换率反而减小.此外,纳米工作流体Cu-水的移动平板表面热交换率,高于纳米工作流体TiO2-水.     

热方程的非古典势对称群与不变解

主要研究了热方程与波方程的非古典势对称群生成元及相应的群不变解．研究表明对于守恒形式的偏微分方程,可通过其伴随系统求得的非古典势对称群生成元来构造其显式解．这些显式解不能由方程本身的Lie对称群生成元或Lie-B?cklund对称群生成元构造得到．     

Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect

In the present article, radiative Sutterby nanofluid flow over a stretchable cylinder is considered. The suspended swimming microorganisms have been deliberated in the fluid analysis. Different processes such as Brownian motion, thermophoresis, Joules heating, and viscous dissipation have been inspected in the presences of stratification parameters. The solutions for flow profiles have been obtained via optimal homotopy analysis method. Impacts of different physical involved variables on non-dimensional velocity, temperature, nanofluid concentration, and concentration of density of swimming microorganisms have been debated. Coefficient of skin friction, local Nusselt number, Sherwood number, and density of motile organisms have been calculated. The results reveal that Sutterby fluid parameter enhances the skin friction and has a reverse impact on the velocity, while an increase in stratification causes a declination in the flow boundary layers. The temperature of the flow is also seen to be boosted by the increment in Brownian motion parameter. Analysis of entropy generation shows that the concentration difference parameter maximizes the entropy and minimizes the dimensionless Bejan number.     

Finite element solution of double-diffusive boundary layer flow of viscoelastic nanofluids over a stretching sheet

This paper deals with the double-diffusive boundary layer flow of non-Newtonian nanofluid over a stretching sheet. In this model, where binary nanofluid is used, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The variational finite element method (FEM) is used to solve these ordinary differential equations. We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, modified Dufour number, viscoelastic parameter, Prandtl number, regular Lewis number, Dufour Lewis number, and nanofluid Lewis number on the flow field and heat transfer characteristics. Graphical display of the numerical examine are performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, reduced Nusselt, reduced Sherwood and reduced nanofluid Sherwood number distributions. The present study has many applications in coating and suspensions, movement of biological fluids, cooling of metallic plate, melt-spinning, heat exchangers technology, and oceanography.     

Numerical study of dynamic thermal conductivity of nanofluid in the forced convective heat transfer

In this work, forced convective heat transfer of nanofluid in the developing laminar flow (entrance region) in a circular tube is considered. The nanofluid thermal conductivity, as an important parameter, is considered as two parts: static and dynamic part. Simulated results show that the dynamic part of nanofluid thermal conductivity due to the Brownian motion has a minor effect on the heat transfer coefficients, on the other hand, static part of thermal conductivity including nanolayer around nanoparticle has an important role in heat transfer.     

Influence of thermophoretic diffusion of nanoparticles with Joule heating in flow of Maxwell nanofluid

The aspects of activation energy in magnetized Maxwell nanofluid flow with Brownian movement and thermophoretic diffusion have been elaborated here. Furthermore, Joule heating, variable conductivity and chemical reaction are scrutinized. The Buongiorno nanofluid thought is ratify to incorporate the importance of thermophoretic and Brownian diffusion. The attained ODEs have been solved via homotopic algorithm. The performance of operational variables is inspected. The Maxwell temperature field for Eckert number and variable conductivity factor have similar trend. The fluid concentration exaggerates for activation energy and decelerates for Brownian motion parameter. Furthermore, the brilliant outcomes attained and associated with possible existing prose accurately.     

Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study

Steady, laminar boundary fluid flow which results from the non-linear stretching of a flat surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear governing equations with associated boundary conditions are solved using variational finite element method (FEM) with a local non-similar transformation. The influence of Brownian motion number (Nb), thermophoresis number (Nt), stretching parameter (n) and Lewis number (Le) on the temperature and nanoparticle concentration profiles are shown graphically. The impact of physical parameters on rate of heat transfer (−θ′(0)) and mass transfer (−?′(0)) is shown in tabulated form. Some of results have also been compared with explicit finite difference method (FDM). Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell [16] for local Nusselt number without taking the effect of Brownian motion and thermophoresis.     

Symmetry groups and similarity solutions for the system of equations for a viscous compressible fluid

Here, using Lie group transformations, we consider the problem of finding similarity solutions to the system of partial differential equations (PDEs) governing one-dimensional unsteady motion of a compressible fluid in the presence of viscosity and thermal conduction, using the general form of the equation of state. The symmetry groups admitted by the governing system of PDEs are obtained, and the complete Lie algebra of infinitesimal symmetries is established. Indeed, with the use of the entailed similarity solution the problem is transformed to a system of ordinary differential equations(ODEs), which in general is nonlinear; in some cases, it is possible to solve these ODEs to determine some special exact solutions.     

Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions

Analysis has been conducted to analyze the stagnation point flow of nanofluid near a permeable stretched surface with convective boundary condition. The relevant problem formulation is presented in the presence of porous medium and internal heat generation/absorption. The effects of Brownian motion and thermophoresis occur in the transport equations. The velocity, temperature and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest namely Brownian motion parameters, thermophoresis parameter, permeability parameter, source/sink parameter, ratio of rate constants to free stream velocity and stretching velocity, Biot number and Prandtl number. A comparative study between the previous published and present results in a limiting sense is found in an excellent agreement.     

Similarity and dimensional analysis in the plane problem of the propagation of a vertical hydraulic fracture crack in an elastic medium

The problem of the growth of a vertical hydraulic fracture crack in an unbounded elastic medium under the pressure produced by a viscous incompressible fluid is studied qualitatively and by numerical methods. The fluid motion is described in the approximation of lubrication theory. Near the crack tip a fluid-free domain may exist. To find the crack length, Irwin’s fracture criterion is used. The symmetry groups of the equations describing the hydraulic fracture process are studied for all physically meaningful cases of the degeneration of the problem with respect to the control parameters. The condition of symmetry of the system of equations under the group of scaling and time-shift transformations enables the self-similar variables and the form of the time dependence of the quantities involved in the problem to be found. It is established that at non-zero rock pressure the well-known solution of Spence and Sharp is an asymptotic form of the initial-value problem, whereas the solution of Zheltov and Khristianovich is a limiting self-similar solution of the problem. The problem of the formation of a hydraulic fracture crack taking into account initial data is solved using numerical methods, and the problem of arriving at asymptotic mode is investigated. It is shown that the solution has a self-similar asymptotic form for any initial conditions, and the convergence of the exact solutions to the asymptotic forms is non-uniform in space and time.