Unsteady stagnation-point boundary layer flows of power-law fluids over a porous flat plate

Abstract

The problem of unsteady stagnation-point flows of power-law fluids over a porous flat plate with mass transfer is considered with a view to examine the rheological behaviors of the fluids. This study is completely based on the four physical parameters, namely, flow strength parameter a, mass transfer parameter d, unsteadiness parameter $$\beta$$ and non-Newtonian power-law index n. For $$d=0$$ , the numerical results of this analysis reveal the existence of two types of solutions - one is attached flow solution (AFS) and the other is reverse flow solution (RFS) in a definite range of n ( $$0< n \le 2$$ ) when (a, $$\beta )= (1, - 1)$$ . The present analysis confirms that the velocity profile for any dilatant fluid $$(n > 1)$$ matches smoothly with the free stream velocity for a suitable amount of blowing $$d(< 0)$$ depending upon the values of n. We will also discuss the asymptotic behaviors of the boundary layer flows for large values of d, i.e., for $$d \rightarrow \pm \infty$$ . The asymptotic analysis ensures the existence of the above two solutions for large values of suction $$d>0$$ , whereas the boundary layer solution is terminated after a certain value of blowing $$d<0$$ , dependent on the values of $$\beta (< 0)$$ and n. Below this critical value of blowing d, this unsteady flow problem also provides us with a solution which does not appear to have a boundary layer character.