Purpose

This paper aims to examine the effect of Dufour and Soret diffusions on Al₂O₃-water nanofluid flow over a moving thin needle by using the Tiwari and Das model.

Design/methodology/approach

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. The features of the skin friction, heat transfer and mass transfer coefficients, as well as the velocity, temperature and concentration profiles for different values of the physical parameters, are analysed and discussed.

Findings

The non-uniqueness of the solutions is observed for a certain range of the physical parameters. The authors also notice that the bifurcation of the solutions occurs in which the needle moves toward the origin (λ < 0). It is discovered that the first branch solutions of the skin friction coefficient and the heat transfer coefficients increase, but the mass transfer coefficient decreases in the presence of nanoparticle. Additionally, the simultaneous effect of Dufour and Soret diffusions tends to enhance the heat transfer coefficient; however, dual behaviours are observed for the mass transfer coefficient. Further analysis shows that between the two solutions, only one of them is stable and thus physically reliable in the long run.

Originality/value

The problem of Al₂O₃-water nanofluid flow over a moving thin needle with Dufour and Soret effects are the important originality of the present study. Besides, the temporal stability of the dual solutions is examined for time.

中文翻译：

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Dufour和Soret对移动细针上Al2O3-水纳米流体流动的影响：Tiwari和Das模型

目的

本文旨在检验对Al杜福尔和索瑞扩散的效果₂ Ó ₃ -水通过使用蒂瓦里和DAS模型纳米流体流过一个运动薄针。

设计/方法/方法

使用相似性变换将控制方程式简化为相似性方程式。通过bvp4c解算器在Matlab软件中对所得方程进行编程，以获得其解。分析并讨论了皮肤摩擦，传热和传质系数的特征，以及不同物理参数值的速度，温度和浓度曲线。

发现

对于一定范围的物理参数，观察到溶液的非唯一性。作者还注意到，溶液的分叉发生在针向原点移动的地方（λ<0）。发现皮肤摩擦系数和热传递系数的第一分支溶液增加，但是在存在纳米粒子的情况下，传质系数降低。另外，Dufour和Soret扩散的同时作用往往会提高传热系数。然而，传质系数观察到双重行为。进一步的分析表明，在两种解决方案之间，只有其中一种是稳定的，因此从长远来看在物理上是可靠的。

创意/价值

具有Dufour和Soret效应的活动细针上的Al ₂ O _3-水纳米流体流动问题是本研究的重要创意。此外，检查双重解的时间稳定性。