This article presents a computational study for the peristaltic pumping within vertical irregular divergence channels filled with magnetic six-constant Jeffrey nanofluids. Various configurations of the outer boundaries are considered, namely, square wave, trapezoidal wave, multisinusoidal wave, and triangular wave. An induced magnetic field together with nanoparticles and mass concentration are considered. Influences of the Dufour and Soret numbers are examined, and the cases of long wavelength and low Reynolds number are applied. All the computations are obtained numerically via MATHEMATICA symbolical software (built-in command ND-Solve), and the obtained results are presented in terms of the axial velocity u, current density Jz, the function of magnetic force U, axially induced magnetic field hx, nanoparticle fraction profile X, concentration profile c, temperature profile h, extra stress tensor Sxy, pressure gradient dp dx , pressure rise Dpk, and stream function w: The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multisinusoidal wave gives periodic behaviors of dp dx : Also, higher axial-induced magnetic fields are given at the higher values of the magnetic Reynolds number.