Purpose

The purpose of study is to examine the dual nature of the branches for the problem of Darcy–Forchheimer porous medium flow of rotating nanofluid on a linearly stretching/shrinking surface under the field of magnetic influence. The dual nature of the branches confronts the uniqueness and existence theorem, moreover, mathematically it is a great achievement. For engineering purposes, this study applied a linear stability test on the multiple branches to determine which solution is physically reliable (stable).

Design/methodology/approach

Nanofluid model has been developed with the help of Buongiorno model. The partial differential equations in space coordinates for the law of conservation of mass, momentum and energy have been transformed into ordinary differential equations by introducing the similarity variables. Two numerical techniques, namely, the shooting method in Maple software and the three-stage Lobatto IIIA method in Matlab software, have been used to find multiple branches and to accomplish stability analysis, respectively.

Findings

The parametric investigation has been executed to find the multiple branches and explore the effects on skin friction, Sherwood number, Nusselt number, concentration and temperature profiles. The findings exhibited the presence of dual branches only in the case of a shrinking sheet.

Originality/value

The originality of work is a determination of multiple branches and the performance of the stability analysis of the branches. It has also been confirmed that such a study has not yet been considered in the previous literature.

中文翻译：

---

线性收缩/拉伸片上旋转纳米流体的 MHD Darcy-Forchheimer 多孔介质流动的对偶性和稳定性：Buongiorno 模型

目的

研究的目的是研究分支的双重性质，以解决磁场影响下线性拉伸/收缩表面上旋转纳米流体的 Darcy-Forchheimer 多孔介质流动问题。分支的双重性与唯一性和存在性定理对立，而且在数学上是一个了不起的成就。出于工程目的，本研究对多个分支应用了线性稳定性测试，以确定哪种解决方案在物理上可靠（稳定）。

设计/方法/方法

纳米流体模型是在 Buongiorno 模型的帮助下开发的。通过引入相似变量，将质量、动量和能量守恒定律的空间坐标偏微分方程转化为常微分方程。分别采用Maple软件中的射击法和Matlab软件中的三阶段Lobatto IIIA法两种数值技术来寻找多个分支并完成稳定性分析。

发现

已执行参数调查以找到多个分支并探索对皮肤摩擦、舍伍德数、努塞尔数、浓度和温度曲线的影响。研究结果表明仅在收缩片材的情况下存在双分支。

原创性/价值

工作的独创性是多个分支的确定和分支稳定性分析的表现。还证实，以前的文献中还没有考虑过这样的研究。