This paper's aim is to discuss the influence of nanoparticles and porous media, and magnetic field on the peristaltic flow transport of a couple of stress fluids in an asymmetric channel with different waveforms of non-Newtonian fluid. Initially, Mathematical modelling of the 2-D and two directional flows of a couple of stress fluids with a nanofluid is first given and then simplified beneath the hypothesis of long wavelength and low Reynolds number approximation. After making these approximations, we will obtain associated nonlinear differential equations. Then the exact solutions of the temperature distribution, nanoparticle concentration, velocity, stream function, and pressure gradient will be calculated. Finally, the results that we obtained illustrate graphically.