With the advance of microfluidic platforms and due to the need to solve different implications that still exist on the transport of electrically conducting fluids, the analysis on strategies in micropumps that involve a simplicity in its structure, absence of mechanical moving parts, flow reversibility and low power requirement is current. Therefore, the present investigation contributes with the analysis of the combined magnetohydrodynamic/pressure driven flow of multilayer immiscible fluids in a microchannel formed by two parallel flat plates. The mathematical model is based in a steady fully developed flow and the pumped fluids follow the power law model to describe the pseudoplastic fluids rheology, while magnetic effects on the flow are given from the Lorentz forces. The velocity profiles and flow rate are obtained in the limit of small Hartmann numbers by solving analytically a closed system of ordinary differential equations, together to the corresponding boundary conditions at the solid-liquid interfaces in the channel walls and at the liquid-liquid interfaces between the fluid layers. The results show that the flow field is controlled by the dimensionless parameters that arise from the mathematical modeling being a parameter that indicates the competition between pressure to the magnetic forces, magnetic parameters related to Hartmann numbers, viscosities ratios between the fluids, flow behavior indexes and the dimensionless position of the liquid-liquid interfaces.

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