- - - Mathematics department, faculty of science, South Valley University, qena, Egypt

This article is concerned with study of the steady and incompressible three-dimensional flow of magnetohydrodynamic couple stress nanofluids over a stretching sheet through a porous medium under influence of, non-linear thermal radiation and heat generation/absorption, taking into account effects of both Brownian motion coefficient and thermophoresis coefficient. On the other hand, the system of nonlinear partial differential equations governing the flow process has been transformed into a system of nonlinear ordinary differential equations using similarity transformations and dimensionless variables, knowing that the numerical method used to solve the new system of differential equations is the fourth-order Runge-Kutta method with the shooting technique in the code of MATLAB program. The effects of all physical parameters resulting from this study on the distributions of velocity, temperature and concentration of nanoparticles within the base fluid were studied by means of graphs that were made by the MATLAB program. Finally, some of the results of the current study showed that the effects of the magnetic field parameter and Darcy number on the velocity distribution were negative, while their effect on the concentration of nanoparticle distribution was positive.

Couple stress fluid, Nanofluid, thermal radiation, Magnetohydrodynamic (MHD), Porous media