Thermal study of magnetohydrodynamic nanofluid flow and brownian motion between parallel sheets

This research paper has inspected the phenomena related to heat and mass transfer within a balanced, stable nanofluid flow confined between two parallel sheets. Our investigation focuses on a uniform magnetic field as a contributing factor. The nanofluid model incorporates the significance of thermophoresis and Brownian motion. We have opted for the Akbari Ganji Method)AGM(Python and Homotopy Perturbation Method)HPM(Python to solve the ruling equations because of their significant accuracy, high speed, and lower input volume. Utilizing these two approaches also requires activating the SymPy library. We have juxtaposed the obtained findings with those derived from a numerical approach, specifically the 4th-order Runge-Kutta, to validate the precision and accuracy of AGM and HPM. The analysis comprehensively evaluates various critical parameters, including the magnetic parameter, viscosity coefficient, thermophoretic parameter, and Brownian parameter. The findings reveal as the thermophoretic and Brownian parameters increase, there is a decline in the Nusselt number, while conversely, a contrasting current is exhibited in the viscosity coefficient. Furthermore, as the Brownian motion rises, the nanofluid concentration and Nusselt number decline. Any increase in magnetic parameters reduces the viscosity and concentration profile while heat transfer increases. An increase in the Schmidt number results in a decline in both concentration and the Nusstlet number.