Purpose

This paper aims to study the stagnation point flow of Al₂O₃–Cu/H₂O hybrid nanofluid over a radially shrinking disk with the imposition of the magnetic field, viscous-Ohmic dissipation and convective boundary condition.

Design/methodology/approach

Similarity variables are introduced and used in reducing the governing partial differential equations into a system of ordinary differential equations. A built-in bvp4c solver in MATLAB is then used in the computation of the numerical solutions for equations (7) and (8) subject to the boundary conditions (9). Then, the behavior of the flow and thermal fields of the hybrid nanofluid, with various values of controlling parameters, are analyzed.

Findings

The steady flow problem resulted in multiple (dual) solutions. A stability analysis performed to identify the stable solution applicable in practice revealed that the first solution is stable while the second solution is unstable. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than the Al₂O₃–H₂O nanofluid. Thus, the hybrid nanofluid has a better heat transfer performance than the nanofluid. Besides that, the presence of the magnetic field, suction, convective boundary condition and the enhancement of nanoparticle volume fraction of Cu augments the skin friction coefficient and Nusselt number of the hybrid nanofluid. Meanwhile, the presence of viscous-Ohmic dissipation reduces the heat transfer performance of the fluid.

Originality/value

To the best of the authors’ knowledge, the present results are original and new for the study of the flow and heat transfer of Al₂O₃–Cu/H₂O hybrid nanofluid past a permeable radially shrinking disk. Considerable efforts have been directed toward the study of the boundary layer flow and heat transfer over stretching/shrinking surfaces and disks because of its numerous industrial applications, such as electronic, power, manufacturing, aerospace and transportation industries. Common heat transfer fluids such as water, alumina, cuprum and engine oil have limited heat transfer capabilities due to their low heat transfer properties. In contrast, metals have higher thermal conductivities than these fluids. Therefore, it is desirable to combine the two substances to produce a heat transfer medium that behaves like a fluid but has higher heat transfer properties.

中文翻译：

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由于具有对流边界条件的径向收缩盘，MHD 混合纳米流体驻点流的双重解决方案

目的

_{本文旨在研究 Al 2} O ₃ –Cu/H ₂ O 混合纳米流体在施加磁场、粘性欧姆耗散和对流边界条件的径向收缩盘上的驻点流动。

设计/方法/途径

引入相似变量并将其用于将控制偏微分方程简化为常微分方程组。然后使用 MATLAB 中的内置 bvp4c 求解器计算受边界条件 (9) 约束的方程 (7) 和 (8) 的数值解。然后，分析了具有不同控制参数值的混合纳米流体的流动和热场行为。

发现

稳流问题导致了多个（对偶）解决方案。为确定适用于实践的稳定解决方案而进行的稳定性分析表明，第一个解决方案是稳定的，而第二个解决方案是不稳定的。发现混合纳米流体的表面摩擦系数和努塞尔数大于 Al ₂ O ₃ –H ₂O纳米流体。因此，混合纳米流体具有比纳米流体更好的传热性能。除此之外，磁场、吸力、对流边界条件的存在和铜纳米粒子体积分数的增加增加了混合纳米流体的表面摩擦系数和努塞尔数。同时，粘性欧姆耗散的存在降低了流体的传热性能。

原创性/价值

_{据作者所知，目前的结果对于研究 Al 2} O ₃ –Cu/H ₂的流动和传热是原创的和新的O 混合纳米流体通过可渗透的径向收缩盘。由于其众多的工业应用，如电子、电力、制造、航空航天和运输行业，人们对拉伸/收缩表面和圆盘上的边界层流动和传热的研究付出了相当大的努力。水、氧化铝、铜和机油等常见的传热流体由于传热性能低，传热能力有限。相反，金属比这些流体具有更高的热导率。因此，希望将这两种物质结合起来产生一种行为类似于流体但具有更高传热性能的传热介质。