MHD boundary layer flow of viscoelastic fluid over a wedge in porous medium

The two-dimensional laminar boundary layer flow of viscoelastic fluid over a moving/static wedge, in the porous matrix, subjected to a uniformly applied magnetic field is studied to investigate the interplay of viscoelastic fluid and moving wedge. The viscoelastic fluid in the boundary layer is modelled using Walters' liquid B fluid which describes the gradually fading memory. The wedge is allowed to move in the same/or opposite direction to that of mainstream flow, and the fluid flow vertically through the wedge is also taken into account. The resultant governing equation, obtained with the help of appropriate similarity transformations, is analysed numerically using the Keller-box method. The general features of the investigated physical solutions are the continuation of a Newtonian fluid, the effect of Walters' liquid B fluid and the pressure gradient to enhance the velocity and decrease the thickness of the boundary layer. Analysis of the boundary layer flow of viscoelastic fluid along with the magnetic field and porous medium unveils single and double solution structures. We noticed an additional solution in the boundary layer for the same set of parameters. Naturally, there exists a critical point beyond which even a single solution does not exist. As the combination of magnetic and permeability parameters is increased, both solutions coalesce into one, thereby yielding a single solution to the model. The linear stability analysis is also performed on the dual solutions, and it reveals that the first solution is always practically realizable. Further, when the velocity ratio parameter is taken sufficiently large, the present model reduces to the flow situation in which the boundary layer forms due to a stretching sheet in a still fluid, and the corresponding equation is solved using an exponentially decaying series solution. Both results are shown to be compared well with each other and existing results in the literature. The interesting flow phenomena are discussed in detail.