In the present paper, unsteady natural convective heat transfer flow inside a square enclosure filled with nanofluids containing magnetic nanoparticles using nonhomogeneous dynamic model is investigated numerically. The horizontal top wall of the enclosure is considered a colder wall and the bottom wall is maintained at uniform temperature whereas two other vertical walls of the cavity are thermally insulated. The Galerkin weighted residual finite element method has been used to solve the governing non-dimensional partial differential equations. In numerical simulations, four types of nanoparticles such as magnetite (Fe₃O₄), cobalt ferrite (CoFe₂O₄), Mn-Zn ferrite (Mn-ZnFe₂O₄), and silicon dioxide (SiO₂), and three types of base fluids such as water (H₂O), engine oil (EO) and kerosene (Ke) have been considered. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various model parameters such as thermal Rayleigh number, nanoparticles volume fraction and nanoparticles shape factor are studied. The results show that the average Nusselt number increases as the thermal Rayleigh number and nanoparticles volume fraction intensify. The results indicate that the average Nusselt numbers are higher for the blade shape of nanoparticles. Kerosene-based nanofluids exhibit higher heat transfer rate. Mn-ZnFe₂O₄-kerosene nanofluid has a higher average Nusselt number than that of other 11 types of nanofluids which are studied in the present analysis.

在本文中，使用非均匀动力学模型，对填充有包含磁性纳米颗粒的纳米流体的方形外壳内部的非稳态自然对流传热进行了数值研究。外壳的水平顶壁被认为是较冷的壁，并且底壁被保持在均匀的温度，而空腔的另外两个垂直壁被热绝缘。Galerkin加权残差有限元方法已用于求解控制的无量纲偏微分方程。在数值模拟中，四种类型的纳米粒子，例如磁铁矿（Fe ₃ O ₄），铁氧体钴（CoFe ₂ O ₄），锰锌铁氧体（Mn-ZnFe ₂ O _4）），二氧化硅（SiO ₂）以及三种基础流体，例如水（H ₂ O），机油（EO）和煤油（Ke）。与以前发表的作品进行了比较，并获得了很好的一致性。研究了各种模型参数（如热瑞利数，纳米颗粒体积分数和纳米颗粒形状因子）的影响。结果表明，随着热瑞利数和纳米颗粒体积分数的增加，平均努塞尔数增加。结果表明，纳米颗粒叶片形状的平均努塞尔数更高。煤油基纳米流体表现出更高的传热速率。锰锌铁₂ O ₄-煤油纳米流体的平均Nusselt数高于本分析中研究的其他11种纳米流体的平均Nusselt数。