This paper presents a computational study for the peristaltic pumping within vertical irregular divergence channels filled with magnetic Johnson—Segalman nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi-sinusoidal wave, trapezoidal wave, and triangular wave. An inclined magnetic field together with nanoparticles and mass concentrations is considered.InfluencesoftheDufourandSoretnumbersareexamined, and the cases of low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND-Solve), and the obtained results are presented in terms of the axial velocity 𝑢,heattransferrate𝑍, nanoparticle fraction profile Ω, concentration profile 𝛾, temperature profile 𝜃, extra stress tensor 𝑆𝑥𝑦, pressure gradient 𝑑𝑝/𝑑𝑥, pressure rise Δ𝑝𝜆, and stream function 𝜓. 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, the maximizing in thermophoresis parameter is better to obtain a higher rate of heat transfer while the increase in thermo-diffusion and diffusion thermo effects causes a reduction in the rate of heat transfer. The discipline of biological and medical engineering, particularly for nanofluid peristaltic pumps, can benefit from the practical uses of such a model,whichcanbeusedtosimulatethesmallvessel transport of particles in hemodynamics.