Purpose

The purpose of this paper is to numerically investigate the hybrid nanofluid flow with the imposition of magnetohydrodynamic (MHD) and radiation effects alongside the convective boundary conditions over a permeable stretching/shrinking surface.

Design/methodology/approach

The mathematical model is formulated in the form of partial differential equations (PDEs) and are then transformed into the form of ordinary differential equations (ODEs) by using the similarity variables. The deriving ODEs are solved numerically by using the bvp4c solver in MATLAB software. Stability analysis also has been performed to determine the stable solution among the dual solutions obtain. For method validation purposes, a comparison of numerical results has been made with the previous studies.

Findings

The flow and the heat transfer of the fluid at the boundary layer are described through the plot of the velocity profile, temperature profile, skin friction coefficient and local Nusselt number that are presented graphically. Dual solutions are obtained, but only the first solution is stable. For the realizable solution at the shrinking surface, the proliferation of nanoparticle volume fraction (copper) and magnetic (magnetohydrodynamics) parameters can impede the boundary layer separation. Also, Biot number could enhance the temperature profile and the heat transfer rate at the shrinking surface region. The incrementation of 0.1% of Biot number has enhanced the heat transfer rate by approximately 0.1% and the incrementation of 0.5% volume fraction for copper has reduced the heat transfer rate by approximately 0.17%.

Originality/value

The presented model and numerical results are original and new. It can be used as a future reference for further investigation and related practical application. The main contribution of this investigation includes giving the initial prediction and providing the numerical data for the other researchers for their future reference regarding the impacts of nanoparticles volumetric concentration towards the main physical quantities of interest in the presence of magnetic and radiation parameters with the convective boundary conditions.

中文翻译：

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MHD 混合纳米流体在具有辐射的可渗透拉伸/收缩表面上具有对流热传递

目的

本文的目的是对具有磁流体动力学 (MHD) 和辐射效应以及对流边界条件的可渗透拉伸/收缩表面上的混合纳米流体流动进行数值研究。

设计/方法/方法

数学模型以偏微分方程（PDE）的形式表示，然后利用相似变量转化为常微分方程（ODE）的形式。使用 MATLAB 软件中的 bvp4c 求解器对导出的 ODE 进行数值求解。还进行了稳定性分析以确定获得的对偶解中的稳定解。出于方法验证的目的，已将数值结果与以前的研究进行了比较。

发现

边界层流体的流动和传热通过速度曲线、温度曲线、表面摩擦系数和局部努塞尔数以图形方式描述。得到了对偶解，但只有第一个解是稳定的。对于收缩表面的可实现解决方案，纳米粒子体积分数（铜）和磁性（磁流体动力学）参数的扩散会阻碍边界层分离。此外，毕奥数可以提高收缩表面区域的温度分布和传热率。Biot 数每增加 0.1%，传热率提高了约 0.1%，而铜体积分数每增加 0.5%，传热率降低了约 0.17%。

原创性/价值

提出的模型和数值结果是原始的和新的。可作为今后进一步研究和相关实际应用的参考。本研究的主要贡献包括给出初步预测并为其他研究人员提供数值数据，以供他们将来参考在存在对流边界的磁和辐射参数的情况下，纳米粒子体积浓度对感兴趣的主要物理量的影响条件。