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This paper analyzed the influence of the Brownian motion and thermophoresis on the behavior of microrotation, linear velocity profile, heat transfer, mass diffusion upon a mixed convective flow of two non-miscible nanofluids in a vertical channel in the presence of a transverse magnetic field and temperature gradient. In the OY axis direction, the modified and coupled Navier-Stokes and nanoparticle volume fraction equations are solved using similarity variables. The solution is carried out and highlights non-dimensional numbers and parameters such as Hartmann number (Ha), Prandtl number (Pr), Eckert number (Ec), Reynolds number (Re), and non-analogous Grashof number (Grc) used in cases of mass transfer caused by natural convection and a concentration gradient. Additionally, the Grashof number (Gr) of heat transfer is used as a function of temperature gradients. The material parameter (K), thermophoresis parameter (MT), Brownian motion parameter (MB), etc. are considered. The algorithm of the final equations is plotted using the bvp4c function in @Matlab software, providing insightful graphs that demonstrate motivating effects on nanofluid flow behavior. The ascending and descending curves of velocity profiles are positively influenced by Lorentz force, thermophoretic phenomenon, and Brownian movement, thereby enhancing heat transfer. The results are thoroughly discussed and compared to previous studies.
Tetbirt et al. (Wed,) studied this question.