An exact solution for two-dimensional laminar boundary layer flows in porous media under stretching/shrinking boundary with power-law velocity

Abstract

Background: The boundary layer flow past stretching/shrinking sheet is widely discussed due to their significance in chemical and engineering applications. A class of laminar boundary layer flows driven by a permeable stretching/shrinking boundary with power-law velocities is under investigation as well as in the presence of mass transpiration and Darcy-Brinkman porous media. Problem section: The fluid flow modelled into coupled highly non-linear partial differential equations and these are mapped into nonlinear ordinary differential equations via similarity transformations, which as a consequence are analytically solved. Significant findings: The domain of solution so derived is a function of mass transpiration, stretching/shrinking boundary, Brinkman viscosity ratio and power-law index. The associated nonlinear equations exhibit lower-and upper-branch solutions that reveal very interesting axial and transverse profiles for various physical parameters under different cases of power-law indices. The boundary-layer effect of various power-law indices over the moving surface is thoroughly revisited in the present study to include the influence of mass transpiration and porous media. In the mass suction case, velocity is a monotonically decreasing function and highest velocity happens at the wall. In the mass injection case, the highest velocity does happen in the fluid region.