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This book is intended for use as a textbook in analysis of magnetic filed on the state of non Newtonian fluidfor undergraduate searchers in the applied mathematics and physicsThe objectives of this text are:1-,(HAM) is employed to find the velocity ,heat transfer of non- Newtonian fluid of second order by assumption:a-Steady flow of incompressible fluidb-Two -dimensional and laminar fluid flow c- Constant fluid properties i,e C p, k,µ all remain constants. d- Only conductive and convective energies in the flow areconsidered. e-. Heat generation on account of fluid friction (known as viscouswork) being small (as the flow velocities are moderate) .finally, the results and discussions are given the effects of the various parameters of interest for the velocity and heat transfer .