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Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface

Cu-C6H9NaO7 和 Ag-C6H9NaO7 纳米流体在非线性收缩表面流动的多重解

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Abstract

Model of Casson nanofluid flow over a nonlinear shrinking surface is considered. Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver. The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations. The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order. In order to determine the stability of the dual solutions obtained, stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable). Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.

摘要

本文研究了Casson 纳米流体在一类非线性收缩表面的流动模型。将 Tiwari 和 Das 模型应用于 含铜、银的海藻酸钠纳米流体中, 通过适当的相似变换, 将考虑黏性耗散影响的控制非线性方程组转 化为常微分方程的边界值问题(BVPS)。将所得方程用打靶法转化为初值问题, 再用四阶 Runge-Kutta 法求解。为了确定所得到的对偶解的稳定性, 对第一(第二)解进行了稳定性分析, 发现第一(第二)解 是稳定的(不稳定的)和物理可实现的(不可实现的)。在第二解中, 随着 Casson 参数(β)的增加, 热边界 层的厚度增加, 温度也会升高。

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Acknowledgement

The authors would like to thank Universiti Utara Malaysia (UUM) for the moral and financial support in conducting this research.

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Authors and Affiliations

  1. School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Sintok, Kedah, Malaysia

    Zurni Omar & Sumera Dero

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ilyas Khan

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  1. Liaquat Ali Lund
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  2. Zurni Omar
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Correspondence to Ilyas Khan.

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Lund, L.A., Omar, Z., Khan, I. et al. Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface. J. Cent. South Univ. 26, 1283–1293 (2019). https://doi.org/10.1007/s11771-019-4087-6

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