Stagnation flow towards a shrinking sheet
TL;DR: In this paper, a similarity transform was used to reduce the Navier-Stokes equations to a set of non-linear ordinary differential equations, which are then integrated numerically.
Abstract: The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier–Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.
Citations
More filters
TL;DR: In this article, the effect of magnetic field on stagnation point flow and heat transfer due to nanofluid towards a stretching sheet was analyzed using Runge-Kutta fourth order method with shooting technique.
258 citations
TL;DR: In this paper, the steady two-dimensional stagnation point flow of a micropolar fluid over a shrinking sheet in its own plane was analyzed and the features of the flow characteristics were analyzed and discussed.
Abstract: An analysis is carried out to study the steady two-dimensional stagnation-point flow of a micropolar fluid over a shrinking sheet in its own plane. The shrinking velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. The features of the flow characteristics are analyzed and discussed. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are nonunique.
234 citations
Cites background or methods or result from "Stagnation flow towards a shrinking..."
...Very recently, Wang (2008) investigated the stagnation flow towards a shrinking sheet in a viscous fluid....
[...]
...The numerical results obtained are then compared with those reported by Wang (2008) for a viscous fluid....
[...]
...This observation is in agreement with the results reported by Wang (2008) for a viscous fluid....
[...]
...These solutions are also exact solutions of the Navier-Stokes equations (Wang, 2008)....
[...]
TL;DR: In this paper, an exact solution of the unsteady Navier-Stokes equations is obtained through the application of similarity transformation techniques, and numerical techniques are used to solve the similarity equations for different values of the mass suction parameters and the unstraininess parameters.
Abstract: The unsteady viscous flow over a continuously shrinking surface with mass suction is studied. The solution is fortunately an exact solution of the unsteady Navier–Stokes equations. Similarity equations are obtained through the application of similarity transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the mass suction parameters and the unsteadiness parameters. Results show that multiple solutions exist for a certain range of mass suction and unsteadiness parameters. Quite different flow behaviour is observed for an unsteady shrinking sheet from an unsteady stretching sheet.
232 citations
TL;DR: In this article, the authors investigated the heat transfer of a viscous fluid flow over a stretching/shrinking sheet with a convective boundary condition, and the authors proposed the exact solutions of the momentum equations, which are valid for the whole Navier-Stokes equations.
228 citations
TL;DR: In this paper, the effects of partial slip on steady boundary layer stagnation-point flow of an incompressible fluid and heat transfer towards a shrinking sheet were analyzed using similarity transformation technique and then the self-similar equations were solved numerically using shooting method.
223 citations
References
More filters
TL;DR: In this paper, a plastischem material fliesst aus einem Spalt with einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist.
Abstract: Eine Platte aus plastischem Material fliesst aus einem Spalt mit einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist. Eine exakte Losung der Grenzschichtgleichungen fur die von der Platte erzeugte Luftbewegung wird gegeben. Oberflachenreibung und Warmeleitungskoeffizient werden berechnet.
3,317 citations
Book•
01 Jan 1911
811 citations
TL;DR: In this paper, a two-dimensional stagnation point flow of an incompressible viscous fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation point, and it is shown that for a fluid of small kinematic viscosity, a boundary layer is formed when the stretching velocity is less than the free stream velocity.
Abstract: Steady two-dimensional stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that for a fluid of small kinematic viscosity, a boundary layer is formed when the stretching velocity is less than the free stream velocity and an inverted boundary layer is formed when the stretching velocity exceeds the free stream velocity. Temperature distribution in the boundary layer is found when the surface is held at constant temperature and surface heat flux is determined.
574 citations
TL;DR: An exact similarity solution of the Navier-Stokes equations is found in this article, where the solution represents the three-dimensional fluid motion caused by the stretching of a flat boundary.
Abstract: An exact similarity solution of the Navier–Stokes equations is found. The solution represents the three‐dimensional fluid motion caused by the stretching of a flat boundary.
563 citations
521 citations