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．

On DTM-BF Method and Dual Solutions for an Unsteady MHD Flow Over a Permeable Shrinking Sheet With Velocity Slip

The unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid was investigated analytically and numerically. The velocity slip at the solid surface was taken into account in the boundary conditions. A novel analytical method named DTM BF was proposed and applied to get the approximate analytical solutions of the nonlinear governing equation along with the boundary conditions at infinity. All analytical results were compared with the results obtained by a numerical method. The comparison showed an excellent agreement, which validated the accuracy of the DTM BF method. Moreover, the existence ranges of the dual solutions and unique solution for various parameters were obtained. The effects of velocity slip parameter, unsteadiness parameter, magnetic parameter, suction/injection parameter and velocity ratio parameter on the skin friction, the unique velocity and dual velocity profiles were explored respectively.