ANALYTICAL APPROXIMATIO AND NUMERICAL SOLUTION OF ELECTRICALLY CONDUCTING FLUID FLOW OVER A STRETCHED WITH THE NONLINEAR VELOCITY IN A POROUS MEDIUM FILLED BY A NANOFLUID

摘要

The semi-analytical solution, differential transform method with Pade approximation (DTM-Pade) is used to investigate the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous in present work. The set of nonlinear ordinary differential equations that obtained by similarity solution are solved by DTM-Pade and validity of our solutions is verified by the numerical results by fourth-order Runge-Kutta scheme with the shooting method. 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-Pade 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.