There are many unicellular tiny organisms which can self-propel collectively through non-Newtonian fluids by means of producing undulating deformation. Example includes nematodes, rod shaped bacteria and spermatozoa. Here we use Taylor’s swimming sheet model, with non-Newtonian fluid bounded with in a complex wavy walls of a two-dimensional channel. Oldroyd-4 constant fluid is approximated as cervical mucus and MHD effects are also considered. After utilizing lubrication and creeping flow assumption the reduced non-linear differential equation is solved (by implicit finite difference technique) so that it will satisfy the dynamic equilibrium condition for steady propulsion. For a special (Newtonian) case the expressions of swimming speed and flow rate are also presented. We also demonstrate that the rheological properties of non-Newtonian fluid can assist or resist the pack of micro-organisms (swimming sheet), while the larger undulation amplitude in swimmer’s body and magnetic field in downward direction can enhance the propulsion speed. The solution obtained via implicit finite difference method is also validated by a built in MATLAB routine bvp-4c. This built in function is based on collocation technique. Moreover an excellent correlation is achieved for both numerical methods.

有许多单细胞微小生物可以通过产生波动变形而通过非牛顿流体共同自我推进。例子包括线虫，杆状细菌和精子。在这里，我们使用泰勒的游泳板模型，在二维通道的复杂波浪壁中以非牛顿流体为边界。近似于Oldroyd-4恒定体液可考虑宫颈粘液和MHD效应。在利用润滑和蠕变流动假设后，通过隐式有限差分技术求解了简化的非线性微分方程，使其满足稳态推进的动态平衡条件。对于特殊情况（牛顿），还显示了游泳速度和流速的表达式。我们还证明，非牛顿流体的流变特性可以帮助或抵抗一堆微生物（游泳板），而游泳者身体中较大的起伏幅度和向下的磁场可以提高推进速度。通过隐式有限差分法获得的解也通过内置的MATLAB例程bvp-4c进行了验证。此内置函数基于并置技术。此外，两种数值方法都实现了极好的相关性。此内置函数基于并置技术。此外，两种数值方法都实现了极好的相关性。此内置函数基于并置技术。此外，两种数值方法都实现了极好的相关性。