Purpose

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

Design/methodology/approach

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

Findings

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

Originality/value

The obtained results are new and presented for the first time in the literature.

中文翻译：

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使用 Darcy-Brinkman-Forchheimer 模型的三级流体的电磁流体动力学流动和热传递

目的

本文的目的是检查三级非牛顿流体的电磁流体动力学行为，在存在电场和磁场的情况下，在一对平行板之间流动。板之间的流动介质是多孔的。本研究研究了焦耳热和粘性能量耗散的影响。

设计/方法/方法

半解析/数值方法，即微分变换方法，用于获得非线性微分控制方程组的解。这种求解技术是有效的，可以适用于解决简单几何中的各种非线性问题，正如通过使用这种方法的结果与完全数值方案的结果之间的比较所证实的那样。

发现

计算结果表明 Darcy-Brinkman-Forchheimer 参数和三级流体模型参数延迟，而由于粘性耗散增加，这两个参数对温度分布具有相反的影响。磁场的存在也增强了两块板之间的温度分布，但会延迟速度分布，因为它会产生相反的洛伦兹力。与先前发表的结果的图形比较也作为本研究的一个特例提供。

原创性/价值

获得的结果是新的，并首次在文献中提出。