Unsteady linear viscoelastic fluid model over a stretching/shrinking sheet in the region of stagnation point flows

In this paper, a mathematical model for the unsteady stagnation point flow of a linear viscoelastic fluid bounded by a stretching/shrinking sheet is presented. The developed equations are used to discuss the problem of two-dimensional and axisymmetric flows in the region of the stagnation point over a stretching/shrinking sheet and an axisymmetric shrinking sheet. The nonlinear partial differential equations are transformed to ordinary differential equations, first taking boundary layer approximations into account and then using similarity transformations. The resulting nonlinear problems are solved by a homotopy analysis approach. The significant features of the obtained series solutions are discussed by graphs. To the best of our knowledge, the homotopy analysis method solution for unsteady linear viscoelastic fluid over a stretching/shrinking sheet with stagnation point flow is presented for the first time in the literature.