Paramount idea of this article is to model peristaltic flow of copper-water for spherical and cylindrical shape magneto-nanoparticles in a curved channel. The nanomaterial saturates a non-uniform permeable medium in which the porosity of the medium fluctuate with the distance from the channel boundaries. H-C model is considered to predict the effective thermal conductivity of the nanomaterial. Effects of radial magnetic field, variable viscosity and mixed convection are also accounted. The boundary conditions yield the second order velocity and thermal slip effects. Assumptions of small Reynolds number and large wavelength approximation are utilized to simplify the governing equations. Final form of the system of equations are solved numerically through NDSolved command in Mathematica 8 software. Influence of embedded parameters on velocity, temperature and heat transfer rate of the nanomaterial at upper wall of the channel are physically interpreted. Comparison between the spherical and cylindrical shapes magneto-nanoparticles is also presented. Graphical results shows that pressure gradient and pressure rise are enhanced for both radial magnetic field parameter and nanoparticle volume fraction. Velocity of the nanomaterial increases when variable viscosity parameter is enhanced. (C) 2016 Elsevier Ltd. All rights reserved.