The mathematical model for nanomaterial convection through a complex geometry in presence of Kelvin force has been reported in this article. To involve the feature of nanomaterial, single phase model was selected which has nice accuracy for low concentration of iron oxide. Impose of magnetic source next to inner hot wall generates the new force which helps the nanofluid migration. The mathematical equations were solved via CVFEM. The accuracy of method was checked with comparing results against old publication. The styles of flow and isotherms with change of Ra, MnF were examined in results. Augment of Kelvin force converts the sole vortex to two eddies with opposite directions in low Ra and thermal plume appears inside the domain. Rise of buoyancy makes the strength of eddy to augment and Kelvin force makes the streamline values to increase. Nu enhances about 179. 36% with rise of Kelvin forces when Ra = 1e5. Nu augments about 11.13% with dispersing nanoparticles in to H₂O. Rise of Ra makes Nu to grow about 119.97% when MnF = 4000.

本文报道了在存在开尔文力的情况下通过复杂几何形状进行纳米材料对流的数学模型。考虑到纳米材料的特性，选择了单相模型，该模型对于低浓度的氧化铁具有很好的精度。靠近内部热壁施加磁源会产生新的力，有助于纳米流体迁移。数学方程通过 CVFEM 求解。通过将结果与旧出版物进行比较来检查方法的准确性。在结果中检查了随着 Ra、MnF 变化的流动和等温线的样式。开尔文力的增强将唯一的涡旋转换为两个方向相反的低 Ra 涡旋，并且热羽流出现在域内。浮力的增加使涡流强度增加，开尔文力使流线值增加。当 Ra = 1e5 时，Nu 会随着开尔文力的增加而增强约 179. 36%。通过将纳米粒子分散到 H 中，Nu 增加了约 11.13%₂ O. 当 MnF = 4000 时，Ra 的上升使 Nu 增长约 119.97%。