The objective of current investigation is to perform mathematical modeling of natural convection and magnetic effects on hybrid nanomaterial convective transportation and numerically examined via new approach. The permeable terms in momentum equations based on non-Darcy approach. Mixture of (MWCNT+Fe₃O₄) with water was employed. Impacts of permeability, Rd, Lorentz force and Ra on nanomaterial treatment have been illustrated via a set of graphs. The isotherms found significantly affected due to an augment in applied magnetic field and increasing values of Darcy number while domain change in the streamlines pattern is perceived for the same intensity of magnetic and Darcy numbers. Moreover, the comparative form study is presented to show the efficiency of the CVFEM while the comparison of results is also asserted with the help of graphs. The comparative analysis is endorsing a good agreement of results with existing literature.

当前调查的目的是对混合纳米材料对流传输的自然对流和磁效应进行数学建模，并通过新方法进行数值检验。基于非达西方法的动量方程中的渗透项。采用( MWCNT +Fe ₃ O ₄ )与水的混合物。渗透率、Rd、洛伦兹力和 Ra 对纳米材料处理的影响已通过一组图表进行了说明。由于外加磁场的增加，发现等温线受到显着影响和增加达西数的值，而流线模式中的域变化被感知为相同强度的磁和达西数。此外，还提出了比较形式研究以显示 CVFEM 的效率，同时还借助图表来断言结果的比较。比较分析证实了结果与现有文献的良好一致性。