Purpose

This paper aims to model and analyze Jeffery Hamel’s channel flow with the magnetohydrodynamics second-grade hybrid nanofluid. Considering the importance of studying the velocity slip and temperature jump in the boundary conditions of the flow, which leads to results close to reality, this paper intends to analyze the mentioned topic in the convergent and divergent channels that have significant applications.

Design/methodology/approach

The examination is conducted on a EG-H_2 O <30%–70%> base fluid that contains hybrid nanoparticles (i.e. SWCNT-MWCNT). To ensure comprehensive results, this study also considers the effects of thermal radiation, thermal sink/source, rotating convergent-divergent channels and magnetic fields. Initially, the governing equations are formulated in cylindrical coordinates and then simplified to ordinary differential equations through appropriate transformations. These equations are solved using the Explicit Runge–Kutta numerical method, and the results are compared with previous studies for validation.

Findings

After the validation, the effect of the governing parameters on the temperature and velocity of the second-grade hybrid nanofluid has been investigated by means of various and comprehensive contours. In the following, the issue of entropy generation and its related graphical results for this problem is presented. The mentioned contours and graphs accurately display the influence of problem parameters, including velocity slip and temperature jump. Besides, when thermal radiation is introduced (Rd = +0.1 and Rd = +0.2), entropy generation in convergent-divergent channels decreases by 7% and 14%, respectively, compared to conditions without thermal radiation (Rd = 0). Conversely, increasing the thermal sink/source from 0 to 4 leads to an 8% increase in entropy generation at Q = 2 and a 17% increase at Q = 4 in both types of channels. The details of the analysis of contours and the entropy generation results are fully mentioned in the body of the paper.

Originality/value

There are many studies on convergent and divergent channels, but this study comprehensively investigates the effects of velocity slip and temperature jump and certainly, this geometry with the specifications presented in this paper has not been explored before. Among the other distinctive features of this paper compared to previous works, the authors can mention the presentation of velocity and temperature results in the form of contours, which makes the physical analysis of the problem simpler.

中文翻译：

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Jeffery-Hamel 流中速度滑移和温度跳跃对 MHD 二级混合纳米流体熵产生的影响

 目的

本文旨在利用磁流体动力学二级混合纳米流体对 Jeffery Hamel 通道流进行建模和分析。考虑到研究流动边界条件中的速度滑移和温度跃变的重要性，其结果接近现实，本文打算分析在收敛和发散通道中具有重要应用的上述主题。

设计/方法论/途径

该检查是在含有混合纳米颗粒（即 SWCNT-MWCNT）的 EG-H_2 O <30%–70%> 基础液上进行的。为了确保结果全面，本研究还考虑了热辐射、热沉/热源、旋转会聚-发散通道和磁场的影响。最初，控制方程在柱坐标系中表达，然后通过适当的变换简化为常微分方程。使用显式龙格-库塔数值方法求解这些方程，并将结果与​​以前的研究进行比较以进行验证。

 发现

经过验证后，通过多种综合等值线研究了控制参数对二级混合纳米流体温度和速度的影响。下面介绍熵生成问题及其相关的图形结果。上述等值线和图表准确地显示了问题参数的影响，包括速度滑移和温度跳跃。此外，当引入热辐射时（Rd = +0.1和Rd = +0.2），与没有热辐射的情况（Rd = 0）相比，会聚-发散通道中的熵产生分别减少了7%和14%。相反，在两种类型的通道中，将散热器/热源从 0 增加到 4 会导致 Q = 2 时熵产生增加 8%，Q = 4 时熵产生增加 17%。论文正文中充分提到了轮廓分析和熵生成结果的细节。

 原创性/价值

关于收敛和发散通道的研究有很多，但这项研究全面研究了速度滑移和温度跳跃的影响，当然，这种具有本文提出的规格的几何形状以前从未被探索过。与之前的作品相比，本文的其他显着特征之一是作者可以以等值线的形式呈现速度和温度结果，这使得问题的物理分析更加简单。