Abstract The time-dependent ferrofluid flow in a square enclosure that includes an open circular pipe has been studied. A variable magnetic field resulting from a magnetic source that is located at a specific point outside the enclosure is taken into account and different thermal conditions are assumed for the inner circular pipe. The mixture consists of water as a based ferrofluid and Fe3O4 as nanoparticles. In addition, basics of the magnetohydrodynamics (MHD) and the ferrohydrodynamics (FHD) are considered during the mathematical formulations of the current physical model. The novel Incompressible Smoothed Particles Hydrodynamics (ISPH) method is applied to solve the dimensionless governing equations. The controlling parameters for this situation are the Hartmann number, magnetic number, solid volume fraction and different locations of the heated part on the inner circular pipe. It is found that maximum values of the stream function are reduced by 74.3% when the Hartmann number Ha is increased from 0 to 30. In addition, insertion the heated part at the bottom right part of the inner pipe gives a best rate of the heat transfer compared to other thermal conditions.

中文翻译：

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封闭空间中铁磁流体的可变磁对流的 ISPH 模拟包括开放的圆形管道

摘要 研究了包含开放圆形管道的方形外壳中随时间变化的铁磁流体流动。考虑到由位于外壳外部特定点的磁源产生的可变磁场，并为内部圆形管道假设不同的热条件。该混合物由作为基铁磁流体的水和作为纳米颗粒的 Fe3O4 组成。此外，在当前物理模型的数学公式中还考虑了磁流体力学 (MHD) 和铁流体力学 (FHD) 的基础知识。新的不可压缩平滑粒子流体动力学 (ISPH) 方法用于求解无量纲控制方程。这种情况的控制参数是哈特曼数、磁数、内圆管上受热部分的固体体积分数和不同位置。发现当哈特曼数Ha从0增加到30时，流函数的最大值减少了74.3%。此外，将加热部分插入内管的右下部分给出了最佳的热率转移与其他热条件相比。