Magnetohydrodynamic stagnation point flow toward stretching/shrinking permeable plate in porous medium filled with a nanofluid

Abstract

In this article, the magnetohydrodynamic stagnation point flow and heat transfer of an incompressible viscous nanofluid over a shrinking/stretching permeable sheet is investigated theoretically and analytically. The ambient fluid velocity, stretching/shrinking velocity of sheet and the wall temperature are assumed to vary linearly with the distance from the stagnation point. The similarity solution is used to reduce the governing system of partial differential equations to a set of highly non-linear ordinary differential equations which are then solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in series form and graphical results are presented to investigate the influence of various pertinent parameters. Here, three different types of nanoparticles, namely copper $\text{Cu}$ , alumina ${\text{Al}}_2{\text{O}}_3$ and titania ${\text{TiO}}_2$ with water as the base fluid are considered. It is observed that, for all three nanoparticles, the magnitude of the skin friction coefficient and local Nusselt number increases with the nanoparticle volume fraction Φ. The highest values of the skin friction coefficient and the local Nusselt number were obtained for the $\text{Cu}$ nanoparticles compared to ${\text{Al}}_2{\text{O}}_3$ and ${\text{TiO}}_2$ .