The proposed study demonstrates the flow phenomenon and thermo-variation of a magnetized stretching sheet induced-radiative nanofluid flow. By incorporating the response surface methodology, the heat transfer rate of the thermally convective flow of nanofluid is optimized. The graphene nanomaterial is used in the water-based nanofluid. A dynamic magnetic field, thermal radiation, and the Cattaneo–Christov heat flux model have used to represent the thermal behavior of the nanofluid. The simulation utilizes experimentally estimated values for the nanomaterial’s thermal conductivity and viscosity. To further reveal the thermal enhancement of the flow, the impact of nanoparticle diameter and the solid-liquid interfacial layer is proposed at the molecular level. The response surface methodology and the sensitivity analysis has used to examine the effects of the nanoparticle volume fraction, Biot number, and magnetic parameter on the rate of heat transfer statistically. A set of equations is formed from the governing partial differential equations by implementing suitable similarity transformations. The bvp4c approach is used to solve the problem numerically. The effect of various parameters has displayed through tables, graphs, and surface plots on heat transfer, mass transfer, and the local Nusselt number. It is discovered that as the Biot number increases, so does the concentration and temperature profile. An excellent accord between the present and previously existing solutions is establishing the validity of the achieved results.

中文翻译：

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通过拉伸片影响纳米粒子直径和纳米层对热对流微极化纳米流体流动的传热优化：敏感性分析方法

所提出的研究证明了磁化拉伸片诱导辐射纳米流体流动的流动现象和热变化。通过结合响应面方法，优化了纳米流体热对流的传热速率。石墨烯纳米材料用于水基纳米流体。动态磁场、热辐射和 Cattaneo–Christov 热通量模型已用于表示纳米流体的热行为。该模拟利用纳米材料的热导率和粘度的实验估计值。为了进一步揭示流动的热增强，在分子水平上提出了纳米颗粒直径和固液界面层的影响。响应面法和敏感性分析已用于检验纳米颗粒体积分数、毕奥数和磁参数对传热速率的影响。通过实施合适的相似性变换，由控制偏微分方程形成一组方程。bvp4c 方法用于数值求解该问题。各种参数的影响已通过表格、图表和曲面图显示在传热、传质和局部努塞尔数上。发现随着毕奥数增加，浓度和温度分布也增加。当前和以前存在的解决方案之间的极好一致性正在确定所取得结果的有效性。和磁参数对传热速率的统计。通过实施合适的相似性变换，由控制偏微分方程形成一组方程。bvp4c 方法用于数值求解该问题。各种参数的影响已通过表格、图表和曲面图显示在传热、传质和局部努塞尔数上。发现随着毕奥数增加，浓度和温度分布也增加。当前和以前存在的解决方案之间的极好一致性正在确定所取得结果的有效性。和磁参数对传热速率的统计。通过实施合适的相似性变换，由控制偏微分方程形成一组方程。bvp4c 方法用于数值求解该问题。各种参数的影响已通过表格、图表和曲面图显示在传热、传质和局部努塞尔数上。发现随着毕奥数增加，浓度和温度分布也增加。当前和以前存在的解决方案之间的极好一致性正在确定所取得结果的有效性。bvp4c 方法用于数值求解该问题。各种参数的影响已通过表格、图表和曲面图显示在传热、传质和局部努塞尔数上。发现随着毕奥数增加，浓度和温度分布也增加。当前和以前存在的解决方案之间的极好一致性正在确定所取得结果的有效性。bvp4c 方法用于数值求解该问题。各种参数的影响已通过表格、图表和曲面图显示在传热、传质和局部努塞尔数上。发现随着毕奥数增加，浓度和温度分布也增加。当前和以前存在的解决方案之间的极好一致性正在确定所取得结果的有效性。