DTM-BF方法和可渗透收缩壁面上带滑移速度的非稳态磁流体力学流动

研究了运动的粘性导电流体中可渗透收缩壁面上非稳态磁流体边界层流动,利用解析和数值方法对问题进行了研究,并考虑了壁面速度滑移的影响．提出了一个新的解析方法（DTM-BF）,并将其应用于求解带有无穷远边界条件的非线性控制方程的近似解析解．对所有的解析结果和数值结果进行了对比,结果显示两者非常吻合,从而证明了DTM-BF方法的有效性．另外,对不同的参数,得到了控制方程双解和单解的存在范围．最后,分别讨论了滑移参数、非稳态参数、磁场参数、抽吸/喷注参数和速度比例参数对壁面摩擦、唯一解速度分布和双解速度分布的影响．     

双曲拉伸面上的流动及其热交换

研究不可压缩粘性流体,在双曲拉伸面上的边界层流动及其热传导．分别使用级数展开法和局部非相似（LNS）法,得到解析结果和数值结果,给出了表面摩擦和Nusselt数的解析结果和数值结果,并进行了互相比较．同时发现动量和热边界层厚度,随着离前缘距离的增加而减小．众所周知,线性拉伸项方程的解,可以作为双曲拉伸首次项方程的解．     

幂律流体边界层方程的近似解析解和壁摩擦因数的近似值

对幂率流体层流平板边界层的解析解进行了研究．对该问题提供了Adomian分解方法并且推导出了问题的级数形式的近似解析解,该近似解析解具有快速收敛性和易于计算性．对不同的幂率给出了方程的近似解析解和相应的壁摩擦因数近似值,最后对近似解所推出结果和所得壁摩擦因数与文献中的数值解进行了比较验证,证实了该文提出的解析近似方法的准确性和可靠性,说明了该近似解能够应用于提供所研究问题的壁摩擦因数．     

流过半无限竖直可渗透壁面时的磁流体动力学自由对流

研究不可压缩粘性导电流体,流过半无限竖直可渗透平板时,将其偏微分形式的流动和传热的基本控制方程,应用适当的相似变换,简化为非线性的常微分方程组．对两种抽吸参数:大的和小的抽吸参数,采用摄动法得到变换后方程的近似解．数值结果表明,随着磁场参数和抽吸参数的增大,任意点的速度场在减小;磁场参数的影响,引起热边界层厚度的增大;速度和温度场随着热汇参数的增大而减小．     

高阶非线性奇摄动微分方程的三点边值问题

本文讨论了一类高阶非线性奇摄动微分方程的三点边值问题.根据小参数的不同次幂,分情况补充相应的边界条件.运用边界层函数法,构造了形式渐近解,并得到解的存在唯一性和渐近解的一致有效性.最后用数值计算结果印证了结论.     

具有多重解的非线性奇摄动问题

利用边界层法,研究了一类具有多重解的非线性奇摄动问题．在适当的假设下,通过给出外部解展开式系数及其对应边界条件的一般表达式,根据退化问题的边值作为某方程的根的重数,得到了此问题不同形式的渐近解．特别地,当这种根的重数为偶数时,问题具有二重解．另外,将相关结果应用于化学反应器理论,并通过对具有多重解的例子的渐近解和精确解的数值模拟说明如此构造的渐近解具有较高的精度．     

传热传质对有抽吸的收缩薄片上的非线性磁流体动力学边界层流动的影响

研究有抽吸作用的可收缩薄片上的磁流体动力学粘性流动.讨论了二维轴对称可收缩问题.利用相似变换给出了无量纲形式的边界层控制方程.利用现代数值技术,数值地求解变换后耦合的非线性常微分方程组,并与现有文献的结果进行了比较.得到了无量纲速度、温度、 浓度的分布, 以及表面摩擦、传热率、传质率和沉积率的数值结果,并用图形显示了与解有关的重要参数.     

幂律速度运动表面上磁流体在驻点附近的滑移流动

从理论上研究了具有非线性延伸表面的磁流体在滑移流区的动量传输问题.通过Lie群变换把控制方程组转化为常微分方程组,利用同伦分析方法求得了问题的近似解析解.获得的级数解与文献中的数值解吻合得较好.另外,利用级数解分析滑移参数、磁场强度、速度比率参数、吸入喷注参数和幂律指数对流动的影响.结果显示这些参数对壁剪切力和边界层内流场有较大的影响.     

使用解析方法获得FitzHugh-Nagumo方程新的peakon解

依据对FitzHugh-Nagumo方程的研究,通过微分变化法近似分析出FitzHugh-Nagumo方程,获得了这个方程的尖峰孤立波（peakon soliton）的解,从而获得了更多形式的peakon解,同时也分析了微分变换法（differential transform method, DTM）收敛区域和收敛速度．构建的微分变换法,结合帕德(Padé)逼近,构建一个明确的,完全解析,对FitzHugh-Nagumo方程全部有意义的尖波解．其主要思想是限制边界条件而令导数在孤立波不存在峰值,但导数的孤立波在两侧存在．结果表明,微分变换法在参数很小的情况下可以避免摄动的限制．表明这种方法提供了一种强大而有效地获得FitzHugh-Nagumo方程新的peakon解的数学方法．     

深埋隧洞围岩应力的精确解与近似解的对比分析

对不同断面形状的深埋隧洞进行了分析,比较了隧洞围岩应力解析解与通过当量半径方法得到的近似解之间的差别.首先,应用复变函数的基本理论,给出圆形、椭圆、矩形、直墙拱形等几种常见深埋隧洞围岩应力的解析表达式.其次,应用当量半径的折算形式,将其任意形状的边界转化为标准圆形断面,利用Lamé解答得到了各围岩应力分量.最后,考虑隧洞断面形状参数的变化,通过数值算例对精确解和近似解进行了比较,分析了当量半径折算形式的精确度.在此基础上,应用有限元方法验证了复变函数解析解的精确性,以椭圆、矩形和直墙拱形的复变函数解验证当量半径精确度.结果表明,当量半径的折算形式解答与精确解答之间相似程度与隧洞的断面形状和几何参数之间有着密切的关系.     

New explicit approximate solution of MHD viscoelastic boundary layer flow over stretching sheet

In this paper, the study the momentum and heat transfer characteristics in an incompressible electrically conducting non‐Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly nonlinear coupled ordinary differential equations by similarity transformations. The resultant coupled highly nonlinear ordinary differential equations are solved by means of, homotopy analysis method (HAM) for constructing an approximate solution of heat transfer in magnetohydrodynamic (MHD) viscoelastic boundary layer flow over a stretching sheet with non‐uniform heat source. The proposed method is a strong and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiry parameter, which provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics. Copyright © 2012 John Wiley & Sons, Ltd.     

The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet

In this work, the magnetohydrodynamic (MHD) boundary layer flow is investigated by employing the modified Adomian decomposition method and the Padé approximation. The series solution of the governing non-linear problem is developed. Comparison of the present solution is made with the existing solution and excellent agreement is noted.     

Boundary layer problem of MHD system with non-characteristic perfect conducting wall

In this paper, we study the boundary layer problem for the incompressible MHD system with the magnetic field having a non-characteristic perfect conducting wall boundary condition. Using the multi-scale analysis and asymptotic expansion approach, we can construct the approximate solutions for the viscous and diffuse MHD system, and utilize the careful energy method to prove the validity of the approximate solutions.     

Minimum error solutions of boundary layer equations

The minimum error solutions of boundary layer equations in the least square sense have been studied by employing the Euler-Lagrange equations. To test the method a class of problems,i.e., boundary layer on a flat plate, Hiemenz flow, boundary layer on a moving sheet and boundary layer in non-Newtonian fluids have been studied. The comparison of the results with approximate methods, like Karman-Pohlhuasen, local potential and other variational methods, shows that the present predictions are invariably better.     

HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet

In the present study, we have described the stagnation point flow of a viscous fluid towards a stretching sheet. The complete analytical solution of the boundary layer equation has been obtained by homotopy analysis method (HAM). The solutions are compared with the available numerical results obtained by Nazar et al. [Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. Int J Eng Sci 2004;42:1241–53] and a good agreement is found. The convergence region is also computed which shows the validity of the HAM solution.     

Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the homotopy analysis method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the magnetic parameter, buoyancy parameter and rotation parameter on the surface shear stresses and surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear stresses and surface heat transfer is in good agreement with the numerical solution given in reference [H. S. Takhar, A. J. Chamkha, G. Nath, Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat Mass Transfer 37 (2001) 397].     

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

A mathematical model is given for the magnetohydrodynamic (MHD) pipe flow as an inner Dirichlet problem in a 2D circular cross section of the pipe, coupled with an outer Dirichlet or Neumann magnetic problem. Inner Dirichlet problem is given as the coupled convection‐diffusion equations for the velocity and the induced current of the fluid coupling also to the outer problem, which is defined with the Laplace equation for the induced magnetic field of the exterior region with either Dirichlet or Neumann boundary condition. Unique solution of inner Dirichlet problem is obtained theoretically reducing it into two boundary integral equations defined on the boundary by using the corresponding fundamental solutions. Exterior solution is also given theoretically on the pipe wall with Poisson integral, and it is unique with Dirichlet boundary condition but exists with an additive constant obtained through coupled boundary and solvability conditions in Neumann wall condition. The collocation method is used to discretize these boundary integrals on the pipe wall. Thus, the proposed procedure is an improved theoretical analysis for combining the solution methods for the interior and exterior regions, which are consolidated numerically showing the flow behavior. The solution is simulated for several values of problem parameters, and the well‐known MHD characteristics are observed inside the pipe for increasing values of Hartmann number maintaining the continuity of induced currents on the pipe wall.     

应用逐次Taylor级数线性化法在多孔伸展界面上求解高对流Maxwell流体的磁流体动力学流动

研究不可压缩的高对流Maxwell(UCM)流体,在多孔伸展界面上作磁流体动力学(MHD)的边界层流动.利用相似变换将控制的偏微分方程,变换为非线性常微分方程.采用逐次Taylor级数线性化方法(STLM)求解该非线性问题.对所显现的参数完成速度分量的计算,介绍了表面摩擦因数的数值结果,并分析了问题所显现参数的变化.