Here, we communicate the peristalsis of single- and multi-walled CNTs through nonlinear porous, non-uniform propagating channel boundaries. Non-uniform channel boundaries are of asymmetric characteristics. Flow equations are modeled by taking variable viscosity, linear and nonlinear porous medium (i.e., Darcy and Darcy–Forchheimer), nonlinear thermal radiation, mixed convection, heat generation and absorption aspects. Convective heat transfer aspects are at the convectively heated surface. The entropy generation rate is modeled via the second law of thermodynamics. Modeled equations are simplified with the help of long wavelength assumption. Dimensionless system of equations with respective boundary conditions is solved numerically via built-in shooting algorithm in Mathematica 8 software. Further, these numerical results are directly received in the form of curves. Such curves are made for velocity, temperature, pressure gradient, trapping, entropy rate and Bejan number. Heat transfer rate at lower and upper walls is achieved through bar charts.