Unsteady separated stagnation-point flow over a permeable surface

Abstract

In this paper, we have investigated numerically the unsteady separated stagnation-point flow of an incompressible viscous fluid over a porous flat plate subjected to continuous suction or blowing. The analysis covers the complete range of the suction/blowing parameter d, including $$d = 0$$ and $$d \rightarrow \pm \infty $$ , in conjunction with the flow strength parameter $$a (> 0)$$ and the unsteadiness parameter $$\beta $$ . Two types of solutions, namely attached flow solution (AFS) and reverse flow solution (RFS), have been found for a negative value of $$\beta $$ . A novel result that emerges from our analysis is the characteristic features of the boundary layer flows which firmly depend on the sum values of $$(a + \beta )$$ in case of massive blowing $$(d \ll 0)$$ given at the wall. In fact, a negative value of $$(a + \beta )$$ opposes the flow like an adverse pressure gradient and the solution domain ends off with a RFS. On the other hand, a positive value of $$(a + \beta )$$ assists the flow like a favourable pressure gradient for which the solution continues with an AFS. An interesting result of this analysis is that after a certain negative value of $$(a + \beta )$$ , dependent on a and $$\beta $$ , the solution of this flow problem does not exist for blowing, and this trend persists even for suction $$(d>0)$$ . On the other hand, for large positive values of $$(a + \beta )$$ , the attached flow solution exists in case of both strong suction and massive blowing, whereas for small positive values of $$(a + \beta )$$ and especially in case of hard blowing, the solution of the governing boundary layer equation does not appear to have the boundary layer character. Furthermore, when $$(a + \beta ) = 0$$ , the velocity gradient at the wall is zero for both AFS and RFS flows, and ultimately, the governing boundary layer equation produces a trivial solution which does not satisfy the outer boundary condition.