Herein, we examined the impact of Brownian motion and thermophoresis on MHD stagnation-point nanofluid flow toward vertical stretching surface using the non-Newtonian Prandtl fluid model. The governing mathematical model consists of a set of nonlinear partial differential equations along with associated boundary conditions. The similarity conversion technique is adopted to convert them to nonlinear ordinary differential equations, which are then solved numerically using the Finite-Difference Crank–Nicolson Method. The simulation is performed to examine flow, heat and mass transfer due to changes in physical parameters. The study revealed that, in the buoyancy opposing flow region, the heat transfer rate increases, and the mass transfer rate decreases due to an increase in Brownian motion. Moreover, augmentation in thermophoresis effects enhances the mass transfer rate, while the heat transfer rate is not dominantly affected. It is further noticed that the FDM-based Crank–Nicolson scheme is well matched and efficient to deal with the solution of such kinds of nonlinear physical models arising in mechanics.

在此，我们使用非牛顿普朗特流体模型研究了布朗运动和热泳对 MHD 驻点纳米流体流向垂直拉伸表面的影响。控制数学模型由一组非线性偏微分方程以及相关的边界条件组成。采用相似转换技术将它们转换为非线性常微分方程，然后使用有限差分 Crank-Nicolson 方法对其进行数值求解。执行模拟以检查由于物理参数变化引起的流动、热量和质量传递。研究表明，在浮力相反的流动区域，由于布朗运动的增加，传热速率增加，传质速率降低。而且，热泳效应的增强提高了传质速率，而传热速率并未受到显着影响。进一步注意到，基于 FDM 的 Crank-Nicolson 方案匹配良好且有效处理力学中出现的此类非线性物理模型的解。