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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.