Thermophoresis and Brownian motion simultaneously occur in numerous industrial processes and have significance from an engineering point of view. The modeling of such processes provides mathematical models. The solutions of these models are used to investigate the dynamics of thermophoresis and Brownian motion in the fluid subjected to Ohmic and viscous dissipation and thermal radiation in the presence of a magnetic field. The cross-rheological model is used for modelling. Numerical solutions to the problems are computed using the finite element method (FEM). Numerical modeling through FEM is easier for complex geometries and shapes. Further, adaptability, accuracy and convergence are its key features. The grid-independent analysis is performed, accuracy is ensured and convergence is studied. Thermophoresis effects have increasing effects on the concentration profile. The strongest thermophoresis effects in mono-nano-cross-fluid are found in comparison to hybrid and ternary nanofluids. The Brownian motion parameter has a decreasing impact on the concentration profile. The strongest impact of the Brownian motion parameter in the case of ternary nanofluid is noted. Moreover, Brownian motion plays a significant role in controlling the thickness of the concentration boundary layer. Heat generation causes an increase in the thermal boundary layer region. The ternary nanofluid generates the heat. Therefore, it is recommended that fluid should not be heat generative as it impacts the efficiencies of fluid adversely. Hence, for maximum transportation of heat, ternary nanofluid should not be heat generative. The destructive chemical reaction, an enhancement in wall mass flux is noted. However, wall mass flux decreases as the strength of the generative chemical reaction increases.

热泳和布朗运动同时发生在许多工业过程中，从工程角度来看具有重要意义。此类过程的建模提供了数学模型。这些模型的解决方案用于研究在存在磁场的情况下遭受欧姆和粘性耗散以及热辐射的流体中的热泳和布朗运动的动力学。交叉流变模型用于建模。使用有限元法 (FEM) 计算问题的数值解。对于复杂的几何形状和形状，通过 FEM 进行数值建模更容易。此外，适应性、准确性和收敛性是其关键特征。进行了与网格无关的分析，保证了精度并研究了收敛性。热泳效应对浓度分布的影响越来越大。与混合和三元纳米流体相比，单纳米交叉流体中的热泳效应最强。布朗运动参数对浓度分布的影响逐渐减小。在三元纳米流体的情况下，布朗运动参数的影响最强。此外，布朗运动在控制浓度边界层的厚度方面起着重要作用。热量的产生导致热边界层区域的增加。三元纳米流体产生热量。因此，建议流体不应产生热量，因为它会对流体的效率产生不利影响。因此，为了最大限度地传输热量，三元纳米流体不应产生热量。注意到破坏性化学反应，壁质量通量的增强。然而，壁质量通量随着生成化学反应强度的增加而减少。