A Steady flow of two-dimensional magnetohydrodynamic non-Newtonian fluid over a stretching/shrinking sheet in the presence of nanoparticles is exemplified theoretically and numerically. In this problem, we have considered the thermal radiation and adjust the hot fluid along with the lower surface of the wall namely convective boundary-layer slip. To the best of the authors' knowledge, this parameter was here incorporated for the first time in such field of magnetofluid dynamic characteristics of conducting bio-nanofluids embedded in a porous medium. The solution of governing dimensionless problem is executed by Legendre-based collocation method (LBCM). It is vital to remark that the account for the velocity slip in the boundary conditions increases the velocity component. Also, the liquid acts as a Newtonian fluid when the Casson parameter increases. Consequently, those parameters contribute to the cooling plate, while others have the opposite effect. Thus, by selecting the appropriate fluid model and adjusting the governing parameters, the cooling/heating mechanism can be created. These results will assist the engineers in designing applications that require high-temperature nanomaterials processing operations.

在理论和数值上举例说明了在存在纳米颗粒的情况下二维磁流体动力学非牛顿流体在拉伸/收缩片上的稳定流动。在这个问题中，我们考虑了热辐射并调整了热流体沿壁面的下表面，即对流边界层滑移。据作者所知，该参数首次被纳入到嵌入多孔介质中的导电生物纳米流体的磁流体动力学特性领域。治理无量纲问题的求解采用基于勒让德的搭配法（LBCM）。重要的是要注意边界条件中的速度滑移会增加速度分量。还，当 Casson 参数增加时，液体充当牛顿流体。因此，这些参数有助于冷却板，而其他参数则具有相反的效果。因此，通过选择适当的流体模型并调整控制参数，可以创建冷却/加热机制。这些结果将帮助工程师设计需要高温纳米材料加工操作的应用。