Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran.
Physics Department, Shahed University, Tehran, Iran.
Sci Rep. 2018 Nov 5;8(1):16358. doi: 10.1038/s41598-018-34778-w.
The equation of magneto-hydrodynamic Jeffery-Hamel flow of non-Newtonian Casson fluid in a stretching/shrinking convergent/divergent channel is derived and solved using a new modified Adomian decomposition method (ADM). So far in all problems where semi-analytical methods are used the boundary conditions are not satisfied completely. In the present research, a hybrid of the Fourier transform and the Adomian decomposition method (FTADM), is presented in order to incorporate all boundary conditions into our solution of magneto-hydrodynamic Jeffery-Hamel flow of non-Newtonian Casson fluid in a stretching/shrinking convergent/divergent channel flow. The effects of various emerging parameters such as channel angle, stretching/shrinking parameter, Casson fluid parameter, Reynolds number and Hartmann number on velocity profile are considered. The results using the FTADM are compared with the results of ADM and numerical Range-Kutta fourth-order method. The comparison reveals that, for the same number of components of the recursive sequences over a wide range of spatial domain, the relative errors associated with the new method, FTADM, are much less than the ADM. The results of the new method show that the method is an accurate and expedient approximate analytic method in solving the third-order nonlinear equation of Jeffery-Hamel flow of non-Newtonian Casson fluid.
基于新的修正 Adomian 分解方法（ADM），推导出并求解了可伸展/收缩会聚/发散通道中非牛顿 Casson 流体的磁流体 Jeffery-Hamel 流动的方程。到目前为止，在所有使用半解析方法的问题中，边界条件都没有得到完全满足。在本研究中，提出了傅里叶变换和 Adomian 分解方法（FTADM）的混合方法，以便将所有边界条件纳入我们对可伸展/收缩会聚/发散通道中非牛顿 Casson 流体的磁流体 Jeffery-Hamel 流动的解中。考虑了各种新兴参数对速度分布的影响，例如通道角度、伸展/收缩参数、Casson 流体参数、雷诺数和 Hartmann 数。使用 FTADM 的结果与 ADM 和数值 Range-Kutta 四阶方法的结果进行了比较。比较表明，对于在广泛的空间域上的递归序列的相同组件数，与新方法 FTADM 相关的相对误差远小于 ADM。新方法的结果表明，该方法是求解非牛顿 Casson 流体的三阶非线性 Jeffery-Hamel 流动方程的准确且便捷的近似解析方法。
