Non-Newtonian fluids within heterogeneous porous media may give rise to complex spatial energy and mass distributions owing to non-local mechanisms, the modeling of which remains unclear. This study investigates the natural convection heat and mass transfer of non-Newtonian fluids in porous media, considering the Soret and Dufour effects. A strongly coupled model is developed to quantify the coupled transport of energy and reactive pollutants with the non-Newtonian fluid. The constitutive equation for the non-Newtonian fluid is described by a two-sided Caputo type space fractional velocity gradient. The governing equation, with a symmetric diffusion term, is effectively solved using a stable and convergent shifted Grünwald–Letnikov formula. The influences of three important parameters, which are the average skin friction coefficient, the average Nusselt number, and the Sherwood number, on fluid heat and mass transfer are calculated and analyzed. Numerical results reveal a significant interaction between the fractional derivative and the buoyancy ratio number, both of which affect the average skin friction coefficient. Furthermore, the average Nusselt number increases with the Dufour number while decreasing with the average Sherwood number. These findings enhance our understandings of the dynamics of energy and mass co-transport in non-Newtonian fluids, particularly in relation to their constitutive equation featuring spatial non-local properties.

中文翻译：

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使用两侧空间分数阶导数模型进行具有 Soret 和 Dufour 效应的多孔介质中非牛顿流体的对流传热和传质


由于非局部机制，非均质多孔介质内的非牛顿流体可能会产生复杂的空间能量和质量分布，其建模仍不清楚。本研究研究了多孔介质中非牛顿流体的自然对流传热传质，考虑了索雷效应和杜福尔效应。开发了一个强耦合模型来量化能量和活性污染物与非牛顿流体的耦合传输。非牛顿流体的本构方程由两侧 Caputo 型空间分数速度梯度来描述。使用稳定且收敛的平移 Grünwald-Letnikov 公式可以有效求解具有对称扩散项的控制方程。计算分析了平均表面摩擦系数、平均努塞尔数和舍伍德数三个重要参数对流体传热传质的影响。数值结果表明分数阶导数和浮力比数之间存在显着的相互作用，两者都会影响平均表面摩擦系数。此外，平均努塞尔数随着杜福尔数的增加而增加，而随着平均舍伍德数的增加而减少。这些发现增强了我们对非牛顿流体中能量和质量共输动力学的理解，特别是与其具有空间非局域特性的本构方程有关。