Viscous flow due to a shrinking sheet

Abstract

Abstract. The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier–Stokes equations

“…The exact solution in this work provides a general formulation for both the stretching sheet (Crane problem [2]) and the shrinking sheet (Miklavčič and Wang problem [25]). In addition, the current results extend the sheet velocity from a pure linear velocity to a more general condition with a constant wall translating velocity.…”

“…This new type of shrinking sheet flow is essentially a backward flow as discussed by Goldstein [26]. Physically, there are two conditions that the flow towards the shrinking sheet is likely to exist: whether an adequate suction on the boundary is imposed (Miklavčič and Wang [25]) suction is required to maintain the flow over a shrinking sheet. Problems of boundary layer flow over shrinking sheets with mass transfer have been studied by Fang [27], Fang et al [28], Fang and Zhang [29] and Fang et al [30,31].…”

“…Miklavčič and Wang [25] studied the flow over a shrinking sheet with mass flux (suction or injection), which is an exact solution of the Navier-Stokes equations. It has been shown that mass suction is required to maintain the flow over a shrinking sheet.…”

Three-dimensional MHD boundary layer flow due to an axisymmetric shrinking sheet with radiation, viscous dissipation and heat source/sink

“…Wang [5] first pointed out the flow over a shrinking sheet when he was working on the flow of a liquid film over an unsteady stretching sheet. The existence and uniqueness of steady viscous flow due to a shrinking sheet was established by Miklavcic and Wang [6] and they concluded that for some specific value of suction at the sheet, dual solutions exist and also in certain range of value of suction, no boundary layer solution exists. Fang and Zhang [7] recently investigated the heat transfer characteristics of the shrinking sheet problem with a linear velocity.…”

Unsteady boundary layer separated stagnation-point flow towards a permeable shrinking sheet

“…The flow due to a shrinking sheet has its important applications in industries such as manufacturing of polymer sheets, filaments and wires. The shrinking sheet phenomenon with a suction effect was first investigated by Miklav i and Wang [3]. Since then, there have been quite a number of studies which are related to permeable shrinking flow, either in different fluid media or different boundary conditions.…”