Inside a permeable flexible circular pipe, a power-law fluid flows with variable cross-section is examined under the presumptions of a long wave length and a low Reynolds number. An unending series of peristaltic waves propagate beside the wall. The solution is obtained in a wave frame of reference, and the pumping characteristics are discovered in detail for various physical parameters. It has been found that raising the Darcy number improves the velocity and pressure gradient in the tube of variable cross section. The temperature distribution and concentration distribution are also determined and analyzed for Darcy number and slip parameter. The results are further should for new relationships on shear thickening and thinning. All figures are plotted using MATHEMATICA software.