Mathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic motion within vertical asymmetric channels filled with magnetic third grade nanofluid model under the influences of rheological characteristics. Various configurations of the outer boundaries are considered, namely, square wave, multi-sinusoidal wave, trapezoidal wave, and triangular wave. An inclined magnetic f ield together with nanoparticles and mass concentrations as well as viscous dissipation are con sidered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND-Solve). The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multi-sinusoidal wave gives periodic behaviors of dp/dx. Also, it is better to maximize the variable viscosity coefficient to enhance the rate of heat transfer while, the rate of heat transfer is diminished by the growth in the thermo-diffusion effects as well as variable thermal conductivity coefficient.