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 di erential transform method and Pad e approximation DTM-Pad e is applied to obtain the approximate analytical solutions of the MHD ow and heat transfer of a nano uid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial di erential equa- tions to a set of nonlinear ordinary di erential equations which are then solved by DTM-Pad e and validity of our solutions is veri ed 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 di erential transform method (DTM) solutions are only valid for small values of independent variable but the obtained results by the DTM-Pad e are valid for the whole solution domain with high accuracy. Finally, the analytical solutions of the problem for di erent values of the xed parameters are shown and discussed. Furthermore, it is found that permeability parameter of medium has a greater e ect on the ow and heat transfer of a nano uid than the magnetic parameter.