Abstract In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form by suitable transformations. Due to the complex non-linear partial differential equations, the numerical solution is calculated by using an implicit finite difference scheme. The impact of involved parameters, namely, magnetic parameter, nanoparticle volume fraction parameter, the amplitude of the wavy surface, and the Grashof number, on Nusselt and average Nusselt numbers are studied through graphs and tables. The results show that for large values of the magnetic parameter, both the Nusselt number and the average Nusselt number decrease in ferrofluid flow. The value of the Nusselt number in the Darcy model is higher than the value of the Nusselt number in the non-Darcy model.

中文翻译：

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非达西多孔介质中饱和波状表面钴铁粒子热物理性质的数值检验

摘要 在这项研究中，研究了磁场对不可压缩铁磁流体沿多孔介质中饱和的垂直波浪表面流动的影响。铁磁流体是通过将磁性颗粒（在这种情况下是钴）以纳米级水平加入基础流体中制成的。对于多孔介质的研究，使用了两个著名的模型，即达西模型和非达西模型。建立了基于力学守恒定律的偏微分方程控制数学模型，并通过适当的变换将该模型转化为无量纲形式。由于非线性偏微分方程复杂，数值解采用隐式有限差分格式计算。所涉及参数的影响，即磁参数，通过图表和表格研究了纳米粒子体积分数参数、波状表面的振幅和格拉肖夫数、努塞尔特数和平均努塞尔特数。结果表明，对于较大的磁参数值，铁磁流体流动中的努塞尔数和平均努塞尔数均减小。Darcy 模型中 Nusselt 数的值高于非 Darcy 模型中 Nusselt 数的值。