Linear stability on transpiration effect of self-similar boundary layer flow for non-Newtonian fluids over a moving wedge

The two-dimensional boundary layer flow of non-Newtonian fluid over a wedge is numerically studied, in which the wedge is considered to be permeable and moving opposite or in the direction of the mainstream. The non-Newtonian fluid model is described by the power law and Carreau fluid. The equations governing fluid flow are nonlinear partial differential equations, which are then converted into ordinary differential equations for each fluid upon imposing suitable similarity transformations and assuming both wedge and mainstream velocity are expected to obey the power of distance. The Chebyshev collocation and shooting methods are utilized for the solutions to the boundary layer problem. Numerical results have shown that for a certain range of parameters, the solutions are not unique and do not exist to the model, leading to double solutions that are seen to satisfy the boundary conditions. This prompts us to assess the stability of the solutions as to which of these is practically encountered. The linear stability analysis applied on these double solutions shows that the first solution is always stable and hence practically realizable. The various physical reasons behind these results are discussed in some detail.