A note on the stagnation-point flow over a permeable shrinking sheet with slip effects

Abstract

A detailed study of the problem of the boundary-layer flow on a shrinking permeable surface near a forward stagnation point with an outer flow u∞∝ xm, a tangential wall velocity uw ∝ xm, and velocity slip on the surface considered previously by Fauzi et al. [1] for m=1 (stagnation point flow) is presented. Further numerical results are obtained and the asymptotic behaviour of the flow under various conditions of the governing parameters is described. Four cases of the problem are considered, namely an impermeable fixed wall, an impermeable moving wall, a permeable fixed wall and a permeable moving wall. For the case of an impermeable fixed wall, it is found that there is a critical value βc of β=2m/(m+1) dependent on the velocity slip parameter A, and that this critical value approaches a finite limit as A increases. For the case of impermeable moving wall, the critical value is negative, decreasing as A is increased. Asymptotic solutions for both strong suction and strong blowing are obtained for the permeable fixed wall. For the case of permeable moving wall, the critical values λc of the parameter λ, the ratio of the wall velocity to the outer flow, found by Fauzi et al. [1] are completed and plotted against the governing suction parameter S. It is seen that λc becomes large as suction is increased.