In this contribution, the magnetohydrodynamic non-Newtonian nanofluid flow through a porous medium in eccentric annuli with peristalsis is investigated. This has been done under the combined effect of viscous dissipation and radiation. The inner annulus is rigid and at rest, while the outer annulus has a sinusoidal wave traveling down its wall. The fundamental equations are modulated under the long wave length assumptions, and a closed form of solution is obtained for the axial velocity. While, homotopy perturbation solution is obtained, which satisfies the energy and nanoparticles equations. Numerical results for the axial velocity, temperature, and nanoparticles phenomena distributions as well as the reduced Nusselt and Sherwood numbers are obtained and tabulated for various parametric conditions.