This article presents the peristaltic transport of an incompressible Williamson nanofluid through the asymmetric inclined annular channel. Our present model is determined for blood flow containing nanoparticles in a gap between two coaxial tubes. Further, this study carried out a novel approach of single and discrete phase model of gold nanoparticles. The effects of magnetic field, thermophoresis, and Brownian force are taken into consideration to develop the model. Exact solutions for temperature distribution and nanoparticles concentration are evaluated, whereas Homotopy Perturbation Method (HPM) is used to determine the approximate analytical solution for the velocity distribution. The outcomes are discussed through figures against different pertinent flow parameters. The graphical discussion of trapping phenomena and the distribution of nanoparticles are disclosed elaborately. The results of the present study will provide characteristic knowledge of nanoparticles for deposition and intended distribution of drugs in the presence of a catheter. © 2021 Informa UK Limited, trading as Taylor & Francis Group.