An analysis related to the transport of nanofluid that is confined in a channel between two orthogonal permeable walls will be investigated with the help of two numerical techniques. With the aid of the reasonable similarity changeover; the said model will be shaped into the desired non-linear equation whose behavior will be explained analytically as well as graphically where the functioning of three disparate variables such as magnetic parameter, permeable Reynold number, and channel permeable ratio will be explained precisely. The said model has been controlled by the homotopy analysis method (HAM) and then, compared through an efficient numerical method named shooting method (ShM). The profiles show that increases in the magnetic parameter decline the nanofluid flow velocity, whereas magnitude-wise raise is shown in each axial velocity profile. The radial profile raises while getting variation in wall expansion parameter from negative to positive. For the entire domain, the rate of change in velocity description enhances at the center while reduces at the surfaces. And the outcomes disclose that the wall permeable ratio has a significant impact on the solutions. Since the zero value of wall ratio refers to the particular type that Terrill has discussed.

将借助两种数值技术研究与限制在两个正交可渗透壁之间的通道中的纳米流体的传输有关的分析。借助合理的相似性转换；所述模型将形成所需的非线性方程，其行为将通过解析和图形方式进行解释，其中将精确解释三个不同变量的功能，例如磁参数、渗透雷诺数和通道渗透率。该模型先通过同伦分析法（HAM）进行控制，然后通过一种有效的数值方法——射击法（ShM）进行比较。曲线显示，磁参数的增加会降低纳米流体的流速，而在每个轴向速度曲线中都显示了幅度上的上升。径向轮廓升高，同时壁膨胀参数从负变为正。对于整个域，速度描述的变化率在中心处增加，而在表面处减小。结果表明，墙体渗透率对解决方案有重大影响。因为墙比的零值是指 Terrill 讨论过的特定类型。