Purpose

This study aims to explore the stagnation flow over a shrinking surface in a hybrid nanofluid consists of Al₂O₃ and Cu nanoparticles. Here, the flow is subjected to the magnetohydrodynamic (MHD) and the melting phenomenon effects.

Design/methodology/approach

The similarity variables are used to gain the similarity equations. These equations are solved via the bvp4c solver. The effects of several physical parameters on the flow and the thermal characteristics of the hybrid nanofluid are analysed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves.

Findings

Results show that two solutions are found for the limited range of the stretching/shrinking parameter λ, and then these solutions are terminated at λ=λc. The rise of the melting parameter Me from 0 to 2 contributes to enhance 109.63% of the local Nusselt number Rex-1/2Nux and 3.30% of the skin friction coefficient Rex1/2Cf. Contrarily, the values of Rex-1/2Nux and Rex1/2Cf decline by 25.04% and 5.58%, respectively, as the magnetic parameter Mg increases from 0 to 0.3. Additionally, Al₂O₃-Cu/water has the highest values of Rex1/2Cf and the lowest values of Rex-1/2Nux. Lastly, it is found that the first solution is physically stable as time evolves.

Originality/value

This paper considers the MHD stagnation point flow of a hybrid nanofluid over a shrinking surface with the melting phenomenon effects. Most importantly, it is shown that there exist dual solutions within a specific range of the physical parameters. Besides, the temporal stability of the solutions is also reported in this study. The finding can contribute to foresee the flow and thermal behaviours in industrial applications. Also, the suitable values of parameters can be determined to avoid misjudgement in flow and heat transfer analysis.

中文翻译：

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具有混合纳米颗粒和熔化现象效应的收缩表面上的 MHD 驻点流动

目的

本研究旨在探索由 Al ₂ O ₃和 Cu 纳米颗粒组成的混合纳米流体中收缩表面上的停滞流动。在这里，流动受到磁流体动力学（MHD）和熔化现象的影响。

设计/方法/方法

相似性变量用于获得相似性方程。这些方程通过 bvp4c 求解器求解。分析讨论了几种物理参数对混合纳米流体流动和热特性的影响。后来，时间稳定性分析用于确定随着时间的推移获得的对偶解的稳定性。

发现

结果表明，对于拉伸/收缩参数的有限范围，找到了两种解决方案 λ，然后这些解决方案终止于 λ=λC. 熔化参数的上升 米e从 0 到 2 有助于提高本地努塞尔数的 109.63% 关于X-1/2ñ你X和3.30%的皮肤摩擦系数 关于X1/2CF. 相反，值 关于X-1/2ñ你X和 关于X1/2CF分别下降 25.04% 和 5.58%，作为磁参数 米G从 0 增加到 0.3。此外，Al ₂ O ₃ -Cu/水具有最高的 ReX1/2CF和最低值 ReX-1/2ñ你X. 最后，发现第一个解决方案随着时间的推移在物理上是稳定的。

原创性/价值

本文考虑了混合纳米流体在具有熔化现象效应的收缩表面上的 MHD 驻点流动。最重要的是，表明在特定物理参数范围内存在双重解。此外，本研究还报告了溶液的时间稳定性。这一发现有助于预测工业应用中的流动和热行为。此外，可以确定合适的参数值，以避免在流动和传热分析中的误判。