Electromagnetic flow for two-layer immiscible fluids

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This article aims to analyze the electromagnetic flow for two-layer of immiscible fluids in an inclined channel. Thermal conductivity and viscosity are considered as functions of temperature. The channel contains two regions one of them full of permeable matrix soaked in a Newtonian fluid and the second region has pure fluid. Due to the nonlinearity of the mathematical model, we will apply the homotopy analysis method (HAM) to get the solutions for the current problem and the obtained results are compared with the numerical solution. The results show that the electric field boosts the velocity profile in both regions. While the velocity decelerates with increasing the magnetic field due to the Lorentz force.