可渗透收缩薄膜引起的三维

研究可渗透收缩薄膜上的不稳定粘性流动.通过相似变换得到相似方程.在不同的不稳定参数、质量吸入参数、收缩参数、Prandtl数下,数值地求解相似方程,得到速度和温度的分布,以及表面摩擦因数和Nusselt数等.结果发现,与不稳定的伸展薄膜不同,在质量吸入参数和不稳定参数的某一范围内,可渗透收缩薄膜上的不稳定流动存在双重解.     

磁场力作用下胀缩可渗透壁面管道非稳态流动摄动解

分析了磁场力作用下胀缩可渗透管道中的不可压缩流动．应用相似变换,控制方程被转换成非线性常微分方程,得到不同的膨胀率和Hartmann数下的奇异摄动解,并对相关的流动特征进行了详细的分析．     

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．     

等宽多孔介质壁面管道中磁流体的流动

研究等宽管道中,磁场、可渗透壁面、Darcy速度和滑动参数,对流体稳定流动的综合影响.假设管道中流动的流体是均匀的、不可压缩的Newton流体.利用Beavers-Joseph滑动边界条件,得到控制方程的解析解.详细地讨论了磁场、可渗透性、Darcy速度和滑动参数对轴向速度、滑动速度和剪应力的影响.可以看出,Hartmann数、Darcy速度、多孔参数和滑动参数,在改变流动方向,进而改变剪应力方面,起着至关重要的作用.     

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．     

同伦分析法求解非线性多孔收缩表面上黏性磁流体的流动

研究在非线性多孔收缩表面上黏性磁流体(MHD)的流动.先用相似变换简化其控制方程,然后用同伦分析法(HAM)求解该简化问题.用图表的形式对问题的相关参数进行讨论,发现在有磁流体时,收缩解存在.同时得到,在不同参数下f″(0)的解是收敛的.     

传导-辐射和磁流体组合对磁化可渗透平板自然对流影响的数值解法

研究粘性、不可压缩、导电流体,在磁化可渗透竖直平板上作自然对流时,数值地分析辐射和磁流体组合的影响.采用两种方法数值地求解非相似的控制方程:1)对所有吸入参数值ξ,采用有限差分法;2)为小数值和大数值的吸入参数值ξ,分别建立起级数的渐近解.用图形和列表形式,给出Prandtl数Pr,磁Prandtl数Pm,磁力参数S,辐射参数Rd,壁面温度θw的变化,对壁面摩擦因数、热交换率和电流密度的影响.最后分析上述物理参数对速度分布、温度分布和磁场横向分量的影响.     

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.     

考虑感应磁场影响时,伸展表面上的MHD驻点流动及其热传递

考虑感应磁场的影响,研究不可压缩粘性流体在伸展表面上,作稳定磁流体动力学(MHD)的驻点流动.通过相似变换,将非线性的偏微分方程,变换成为常微分方程.用打靶法数值地求解变换后的边界层方程,得到不同的磁场参数和Prandtl数Pr时的数值解.对a/c>1和a/c<1两种情况(其中a和c均为正值),讨论感应磁场参数对表面摩擦因数、局部Nusselt数、速度和温度的影响,绘出变化曲线并给予讨论.     

化学反应对流过半无限垂直多孔板的粘性耗散非定常磁流体流动的影响

分析了化学反应,对流过半无限竖直多孔板的、粘性耗散的、非定常的磁流体流动的影响．利用随时间变化的相似参数,将运动、能量、溶质的控制方程变换为常微分方程,并用有限单元法数值地求解所得到的常微分方程．用图形给出了不同参数对速度、温度和浓度分布的影响,用表格给出了不同物理参数值时,表面摩擦力、Nusselt数和Sherwood数的数值．     

Combined effects of non-uniform heat source/sink and thermal radiation on heat transfer over an unsteady stretching permeable surface

The present paper is concerned with the study of flow and heat transfer characteristics in the unsteady laminar boundary layer flow of an incompressible viscous fluid over continuously stretching permeable surface in the presence of a non-uniform heat source/sink and thermal radiation. The unsteadiness in the flow and temperature fields is because of the time-dependent stretching velocity and surface temperature. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum and thermal energy are reduced to a system of nonlinear ordinary differential equations containing Prandtl number, non-uniform heat source/sink parameter, thermal radiation and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge–Kutta–Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the unsteadiness parameter, thermal radiation, suction/injection parameter, non-uniform heat source/sink parameter on flow and heat transfer characteristics as well as on the local Nusselt number are shown graphically.     

Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature

The unsteady laminar boundary layer flow over a continuously stretching permeable surface is investigated. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. Effects of the unsteadiness parameter, suction/injection parameter and Prandtl number on the heat transfer characteristics are thoroughly examined.     

Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties

In this paper we present numerical solutions to the unsteady convective boundary layer flow of a viscous fluid at a vertical stretching surface with variable transport properties and thermal radiation. Both assisting and opposing buoyant flow situations are considered. Using a similarity transformation, the governing time-dependent partial differential equations are first transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by a second order finite difference scheme known as the Keller-Box method. The numerical results thus obtained are analyzed for the effects of the pertinent parameters namely, the unsteady parameter, the free convection parameter, the suction/injection parameter, the Prandtl number, the thermal conductivity parameter and the thermal radiation parameter on the flow and heat transfer characteristics. It is worth mentioning that the momentum and thermal boundary layer thicknesses decrease with an increase in the unsteady parameter.     

Unsteady viscous flow over a rotating stretchable disk with deceleration

In this work, the laminar unsteady flow over a stretchable rotating disk with deceleration is investigated. The three dimensional Navier–Stokes (NS) equations are reduced into a similarity ordinary differential equation group, which is solved numerically using a shooting method. Mathematically, two solution branches are found for the similarity equations. The lower solution branch may not be physically feasible due to a negative velocity in the circumferential direction. For the physically feasible solution branch, namely the upper solution branch, the fluid behavior is greatly influenced by the disk stretching parameter and the unsteadiness parameter. With disk stretching, the disk can be friction free in both the radial and the circumferential directions, depending on the values of the controlling parameters. The results provide an exact solution to the whole unsteady NS equations with new nonlinear phenomena and multiple solution branches.     

Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field

This paper presents a mathematical analysis of MHD flow and heat transfer to a laminar liquid film from a horizontal stretching surface. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of non-linear ordinary differential equations. Numerical solution of resulting non-linear differential equations is found by using efficient shooting technique. Boundary layer thickness is explored numerically for some typical values of the unsteadiness parameter S and Prandtl number Pr, Eckert number Ec and Magnetic parameter Mn. Present analysis shows that the combined effect of magnetic field and viscous dissipation is to enhance the thermal boundary layer thickness.     

Unsteady flow of a Maxwell fluid over a stretching surface in presence of chemical reaction

An analysis is presented for unsteady two-dimensional flow of a Maxwell fluid over a stretching surface in presence of a first order constructive/destructive chemical reaction. Using suitable transformations, the governing partial differential equations are converted to ordinary one and are then solved numerically by shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. Fluid velocity initially decreases with increasing unsteadiness parameter and concentration decreases significantly due to unsteadiness. The effect of increasing values of the Maxwell parameter is to suppress the velocity field. But the concentration is enhanced with increasing Maxwell parameter.     

Analytic solutions of unsteady boundary flow and heat transfer on a permeable stretching sheet with non-uniform heat source/sink

In this paper, we study the boundary layer flow and heat transfer on a permeable unsteady stretching sheet with non-uniform heat source/sink. The analytic solutions are obtained by using suitable similarity transformations and homotopy analysis method (HAM). Furthermore, the effects of unsteadiness parameter, Prandtl number and heat source/sink parameter on the dynamics are analyzed and discussed.     

A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method

In this paper, a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady, laminar, incompressible flow in a porous expanding channel. Dual or triple solutions for the fixed values of the wall suction Reynolds number $R$ and the expansion ratio $α$ are obtained numerically. The computed multiple solutions for the symmetric flow are validated by comparing them with approximate analytic solutions obtained by the similarity transformation and homotopy analysis method. Unlike previous works, our method deals with the Navier-Stokes equations directly and thus has no similarity and other restrictions as in previous works. Finally we use the method to study multiple solutions for three cases of the asymmetric flow (which has not been studied before using the similarity-type techniques).     

Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions

In this paper, we investigate the heat transfer of a viscous fluid flow over a stretching/shrinking sheet with a convective boundary condition. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking parameter on the temperature profiles and wall heat flux are presented and discussed. The solution is given as an incomplete Gamma function. It is found the convective boundary conditions results in temperature slip at the wall and this temperature slip is greatly affected by the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking parameters. The temperature profiles in the fluid are also quite different from the prescribed wall temperature cases.