Purpose

In recent times, ternary hybrid nanofluid has garnered attention from scientist and researchers due to its improved thermal efficiency. This study aims to delve into the examination of ternary hybrid nanofluid (Al₂O₃–Cu–TiO₂/water), particularly concerning axisymmetric flow over a nonlinearly permeable stretching/shrinking disk. In addition, the investigation of convective boundary conditions and thermal radiation effects is also considered within the context of the described flow problem.

Design/methodology/approach

Mathematical formulations representing this problem are reduced into a set of ordinary differential equations (ODEs) using similarity transformation. The MATLAB boundary value problem solver is then used to solve the obtained set of ODEs. The impact of considered physical parameters such as suction parameter, radiation parameter, nonlinear parameter, nanoparticle volumetric concentration and Biot number on the flow profiles as well as the physical quantities is illustrated in graphical form.

Findings

The findings revealed the thermal flux for the nonlinearly shrinking disk is approximately 1.33%, significantly higher when compared to the linearly shrinking disk. Moreover, the existence of dual solutions attributed to the nonlinear stretching/shrinking disk is unveiled, with the first solution being identified as the stable and reliable solution through temporal stability analysis.

Practical implications

Understanding ternary hybrid nanofluid behavior and flow has applications in engineering, energy systems and materials research. This study may help develop and optimize nanofluid systems like heat exchangers and cooling systems.

Originality/value

The study of flow dynamics across nonlinear stretching/shrinking disk gains less attention compared to linear stretching/shrinking geometries. Many natural and industrial processes involve nonlinear changes in boundary shapes or sizes. Understanding flow dynamics over nonlinear shrinking/stretching disks is therefore essential for applications in various fields such as materials processing, biomedical engineering and environmental sciences. Hence, this study highlights the axisymmetric flow over a nonlinear stretching/shrinking disk using ternary hybrid nanofluid composed of alumina (Al₂O₃), copper (Cu) and titania (TiO₂). Besides, this study tackles a complex problem involving multiple factors such as suction, radiation and convective boundary conditions. Analyzing such complex systems can provide valuable insights into real-world phenomena where multiple factors interact.

中文翻译：

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非线性渗透拉伸/收缩盘上对流边界条件的轴对称三元杂化纳米流体流动的辐射影响

 目的

近年来，三元杂化纳米流体因其改进的热效率而受到科学家和研究人员的关注。本研究旨在深入研究三元杂化纳米流体 （Al₂O₃–Cu–TiO₂/water） 的检查，特别是关于非线性可渗透拉伸/收缩盘上的轴对称流。此外，在所描述的流动问题的背景下，还考虑了对流边界条件和热辐射效应的研究。

设计/方法/方法

表示此问题的数学公式使用相似性变换简化为一组常微分方程 （ODE）。然后使用 MATLAB 边界值问题求解器求解获得的 ODE 集。以图形形式说明了所考虑的物理参数（如吸力参数、辐射参数、非线性参数、纳米颗粒体积浓度和 Biot 数）对流向剖面和物理量的影响。

 发现

研究结果显示，非线性收缩盘的热通量约为 1.33%，与线性收缩盘相比，热通量明显更高。此外，揭示了归因于非线性拉伸/收缩盘的对偶解的存在，第一个解通过时间稳定性分析被确定为稳定可靠的解。

 实际意义

了解三元杂化纳米流体的行为和流动在工程、能源系统和材料研究中具有应用。这项研究可能有助于开发和优化纳米流体系统，如热交换器和冷却系统。

 原创性/价值

与线性拉伸/收缩几何结构相比，非线性拉伸/收缩盘的流动动力学研究受到的关注较少。许多自然和工业过程都涉及边界形状或大小的非线性变化。因此，了解非线性收缩/拉伸盘的流动动力学对于材料加工、生物医学工程和环境科学等各个领域的应用至关重要。因此，本研究强调了使用由氧化铝 （Al₂O₃）、铜 （Cu） 和二氧化钛 （TiO₂） 组成的三元杂化纳米流体在非线性拉伸/收缩盘上的轴对称流动。此外，本研究还解决了一个涉及吸力、辐射和对流边界条件等多种因素的复杂问题。分析此类复杂系统可以为多个因素相互作用的现实世界现象提供有价值的见解。