Purpose

This paper aims to examine the hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects.

Design/methodology/approach

Here, the authors consider copper (Cu) and alumina (Al₂O₃) as hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions.

Findings

The authors found that the heat transfer rate is greater for Al₂O₃-Cu/water hybrid nanofluid if compared to Cu/water nanofluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. The authors also notice that the bifurcation of the solutions occurs in the downward buoyant force and the shrinking regions. In addition, the first solution of the skin friction and heat transfer coefficients increase with the added hybrid nanoparticles and the mixed convection parameter. The temporal stability analysis shows that one of the solutions is stable as time evolves.

Originality/value

The present work is dealing with the problem of a mixed convection flow of a hybrid nanofluid towards a stagnation point on an exponentially stretching/shrinking vertical sheet, with the buoyancy effects is taken into consideration. The authors show that two solutions are obtained for a single value of parameter for both stretching and shrinking cases, as well as for both buoyancy aiding and opposing flows. A temporal stability analysis then shows that only one of the solutions is stable and physically reliable as time evolves.

中文翻译：

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混合纳米流体流向指数级拉伸/收缩垂直片上的停滞点，并产生浮力

目的

本文旨在研究混合纳米流体流向具有浮力效应的指数拉伸/收缩垂直板的停滞点。

设计/方法/方法

在这里，作者认为铜（Cu）和氧化铝（Al ₂ O ₃）是杂化纳米粒子，而水是基础流体。使用相似变换将控制方程简化为相似方程。通过bvp4c求解器在Matlab软件中对所得方程进行编程，以获得其解。

发现

作者发现，与Cu /水纳米流体相比，Al ₂ O ₃ -Cu /水混合纳米流体的传热速率更高。此外，对于某些物理参数，观察到溶液的非唯一性。作者还注意到，溶液的分叉发生在向下的浮力和收缩区域中。此外，皮肤摩擦和传热系数的第一个解决方案随添加的杂化纳米颗粒和混合对流参数的增加而增加。时间稳定性分析表明，随着时间的流逝，解决方案之一是稳定的。

创意/价值

目前的工作是处理杂化纳米流体向指数拉伸/收缩垂直片上的停滞点的混合对流的问题，并考虑了浮力效应。作者表明，对于拉伸和收缩情况，以及对浮力辅助和反向流动，参数的单个值都获得了两种解决方案。然后，时间稳定性分析表明，随着时间的流逝，只有一种解决方案是稳定的并且在物理上是可靠的。