Numerical analysis of nanofluid flow conveying nanoparticles through expanding and contracting gaps between permeable walls

In this study, the problem of nanofluid flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved using Least Square Method. The concept of this method is briefly introduced, and it's application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. Graphical results are presented to investigate the influence of the volume fraction of nanoparticle, non-dimensional wall dilation rate and permeation Reynolds number on the velocity, normal pressure distribution and wall shear stress. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels. The results indicate that velocity boundary layer thickness near the walls decreases with increase of Reynolds number and nanoparticle volume friction and it increases as non-dimensional wall dilation rate increases.