The present study develops the equations that govern a steady flow of ferrofluid in a semi-porous channel (SPC) under the effects of Lorentz force. Three different base fluids namely water, kerosene and blood and magnetite as ferroparticles are used in the analysis. These equations are modeled by using the Cartesian coordinate system with the help of Berman’s similarity transformation. The partial slip condition is also considered at the lower plate of the channel. Three different methods of solution, namely the method of homotopy analysis (HAM) (analytical technique), the method of differential transformation (DTM) (semi-numerical technique) and the method of Runge-Kutta (numerical technique), are used to achieve the solution of non-dimensional, non-linear ordinary differential equations. For HAM solution, the auxiliary parameter $ħ$ delivers an effective way to regulate the convergence range of solution series whereas in DTM an approximation to the solution is obtained without any auxiliary parameter. The impact of Hartman and Reynolds number on the flow velocity are shown graphically and discussed. Finally, the comparison between the solution methods is given and found in very good agreement.

本研究提出了在洛伦兹力的作用下控制铁磁流体在半多孔通道（SPC）中稳定流动的方程。分析中使用了三种不同的基础流体，即水，煤油，血液和磁铁矿作为铁颗粒。借助Berman相似度变换，使用笛卡尔坐标系对这些方程进行建模。通道的下板也考虑了部分打滑情况。使用三种不同的解决方法，即同伦分析（HAM）方法（分析技术），微分变换（DTM）方法（半数值技术）和Runge-Kutta方法（数值技术）来实现无量纲，非线性常微分方程的解。对于HAM解决方案，辅助参数$H$提供了一种有效的方法来调节解序列的收敛范围，而在DTM中，无需任何辅助参数即可获得解的近似值。用图形显示并讨论了哈特曼数和雷诺数对流速的影响。最后，给出了解决方法之间的比较，并发现它们之间具有很好的一致性。