On the duality of unsteady stretching surface flow: the sheet and disk cases

Abstract

This communication is a continuation of our previously published works on the duality of solution of stretching/shrinking surface flows. In this regard, a huge volume of literature is already available advocating that the duality of the solution is a salient feature of the shrinking surface flows, only. It is believed that for a shrinking surface flow the solution does not exist; requires sufficient wall suction for its existence; and is non-unique whenever it exists. On this basis, the shrinking surface flow is believed to be richer in physics by exhibiting more non-linear phenomena. Because of such facts, the available literature has developed a significant miSunderstanding about the shrinking surface flows. It has been established that the shrinking surface flows constitute a superior class of viscous flows instigated by the motion of a continuous surface. However, we think that there is nothing special with the shrinking surface flows, at all. All the fascinations attributed to the shrinking surface flows can be seen for the stretching surface flows, too. The reason behind the appearance of such fascinating features is the retarded nature of the ongoing boundary-layer flow. A retarded boundary-layer can be assisted in a variety of ways; and an assisted, retarded, boundary-layer exhibits a non-unique behavior. In this study, the duality of the solution has been discussed for unsteady stretching surface flow by considering two-dimensional planner and axisymmetric cases corresponding to flat sheet and disk geometries. It is shown that in a stretching surface flow, it is possible to observe the duality of the solution not only in the presence of wall suction but also in the presence of wall injection velocity.