The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid (n=0.7) and dilatant fluid (n=1.2) are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid (n=1.2) gives higher values of Cfx,Cfz,Nux and Shx compared to the pseudoplastic fluid (n=0.7).

中文翻译：

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Cattaneo-Christov热通量和自由流存在下霍尔电流对非牛顿幂律纳米流体流动和传热的影响

纳米流体是纳米技术领域最近的一项具有挑战性的任务，用于基础流体的传热增强。本研究的主要目的是检查霍尔电流对指数延伸表面上的非牛顿幂律纳米流体的影响。在 Cattaneo-Christov 热通量和自由流中执行以分析热弛豫特征。研究了对流过程中的熵生成评估和 Bejan 数。Runge-Kutta-Fehlberg 方法用于求解变换后的控制非线性方程。图中讨论了关键物理因素对初级和次级速度、温度和熵产生剖面的影响。局部皮肤摩擦系数，在关键物理参数的影响下，努塞尔特和舍伍德数以表格形式显示。两种不同类型的幂律指标，包括假塑性流体(n=0.7)和膨胀液(n=1.2)进行。结果表明，与假塑性流体相比，膨胀流体的流动速度由于粘度较高而降低。增加霍尔电流参数为轴向和次级速度曲线提供动力。热泳参数为温度曲线、纳米颗粒体积分数和局部熵生成提供动力。膨胀液(n=1.2)给出更高的值CFX,CFz,怒X和嘘X与假塑性流体相比(n=0.7).