analytical solution of mhd flow and heat transfer over a permeable nonlinearly stretching sheet in a porous medium filled by a nanofluid

in this paper, the differential transform method and padé approximation (dtm-padé) is applied to obtain the approximate analytical solutions of the mhd flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. the similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved by dtm-padé and validity of our solutions is verified by the numerical results (fourth-order runge-kutta scheme with the shooting method). the stretching velocity of sheet is assumed to have a power-law variation with the horizontal distance along the plate. it was shown that the differential transform method (dtm) solutions are only valid for small values of independent variable but the obtained results by the dtm-padé are valid for the whole solution domain with high accuracy. finally, the analytical solutions of the problem for different values of the fixed parameters are shown and discussed. furthermore, it is found that permeability parameter of medium has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.