In the current research, the effect of thermophoretic motion combined with temperature-dependent thermal conductivity on natural convection flow around the surface of a sphere at several circumferential locations has been presented. The modeled nonlinear governing partial differential has been transformed into a dimensionless form with the help of appropriate non-dimensional variables. Later, the finite difference method is applied to solve the proposed model. The effect of controlling parameters, such as thermal conductivity variation parameter $\gamma$, Prandtl number Pr, Schmidt number Sc, thermophoretic coefficient $k$, and thermophoresis parameter $N_t$ on the velocity field, temperature distribution, mass concentration, skin friction, rate of heat transfer, and rate of mass transfer has been highlighted. The estimations of the emerging parameters on the physical properties are displayed in graphical and in tabular forms. It has been predicted that the rise in $\gamma$, $N_t$, $Sc$, Pr, and $k$ increases the velocity distribution, but the reverse behavior has been seen in the temperature field. The enhancement in $N_t$, $Sc$, Pr, and $k$ boosts up the curves of mass concentration, and the rise in $\gamma$ suppresses the concentration function. It has been observed that an increase in $\gamma$ reduces the skin friction and the rate of mass transfer but opposite behavior of the rate of heat transfer occurs. Furthermore, increasing values of Sc cause the skin friction to lose the dominance in the rate of heat and mass transfer. It has been also noticed that increasing values of $N_t$ strengthen the skin friction and rate of heat transfer, and attenuation occurs in the case of the rate of mass transfer.

中文翻译：

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热泳运动和可变热导率对自由对流换热影响的数值模拟

在当前的研究中，已提出了热泳运动与温度相关的热导率相结合对几个圆周位置处球体表面周围自然对流流动的影响。借助适当的无量纲变量，已将建模的非线性控制偏微分转换为无量纲形式。后来，应用有限差分法对提出的模型进行求解。控制参数的影响，例如热导率变化参数$\gamma$，Prandtl数Pr，Schmidt数Sc，热泳系数 $ķ$和热泳参数 ${ñ}_{Ť}$在速度场上，突出了温度分布，质量浓度，皮肤摩擦，热传递速率和质量传递速率。物理属性上新兴参数的估计以图形和表格形式显示。据预测，$\gamma$， ${ñ}_{Ť}$， $\mathrm{小号}C$，Pr和 $ķ$增加了速度分布，但是在温度场中却看到了相反的行为。增强${ñ}_{Ť}$， $\mathrm{小号}C$，Pr和 $ķ$ 提高了质量浓度曲线，并且增加了 $\gamma$抑制集中功能。据观察，$\gamma$减少了皮肤摩擦和传质速率，但是传热速率却发生了相反的行为。此外，Sc值的增加会导致皮肤摩擦失去传热和传质的优势。还已经注意到，${ñ}_{Ť}$ 增强皮肤的摩擦力和热传递率，而在质量传递率的情况下衰减会发生。