Series solution of slip flow of Al2O3and Fe3O4nanoparticles in a horizontal channel with a porous medium by using least square and Galerkin methods

Abstract

This study theoretically investigates the effects of slip on the two-dimensional flow of nano liquid in a semi-porous channel, which is designed by two long rectangular plates having porous media. One of the channel walls is porous and the other rigid and slippery. A transverse magnetic field characterized by homogeneous strength was applied to the flow direction. Magnetic nanoparticles (Fe3O4) and non-magnetic nanoparticles (Al2O3) were considered with Ethylene Glycol (EG) and water as Base Fluids (BFs). Least Square Method (LSM) and Galerkin Method (GM) were adopted to solve those equations that were transformed from partial Differential Equations (DEs) to ordinary ones by Berman's similarity transformations. The obtained results of the two analytical methods were compared with those of the fourth-order Runge-Kutta Numerical Method (NM). Based on a comparison of GM and LSM, although the variation in velocity profiles was quite insignificant, the accuracy of GM was higher than LSM. The contributions of various flow parameters were depicted in graphs. Results showed a decrement in the fluid velocity with an increase in the slip and porosity parameters. The fluid boundary layer decreased as the Reynolds number increased. Flow field for magnetic nanoparticles is less than that for nonmagnetic particles.