Modeling of the Magnetohydrodynamic Flow of the Nanofluid Confined Between Two Parallel Plates

Squeezing flow between parallel plates is very applicable in many industrial and biomedical applications. In light of this fact, this research presents an analytical study of unsteady squeezing nanofluid flow and heat transfer between two parallel plates under the effect of a variable magnetic field using the two-phase Buongiorno model. The nonlinear differential equations governing the problem are solved by the Homotopy perturbation method (HPM). The key parameters addressed in this analysis are the Hartmann number, squeeze number, Eckert number, Brownian motion parameter, thermophoresis parameter, and Schmidt number. To demonstrate the high accuracy of the results, the obtained results were compared to the direct numerical solutions (NM) which show good agreement. Then, for each parameter, a graphical analysis is proposed to examine in detail the flow and heat transfer characteristics. The results show that the improvement of the thermophoresis parameter increased the temperature profile while decreasing the concentration profile. Furthermore, the results show that raising the Brownian motion parameter increases the concentration profile while having no influence on the temperature profile.