The unsteady MHD boundary-layer flow on a shrinking sheet

Abstract The unsteady boundary-layer flow on a shrinking surface in an electrically conducting fluid is considered as it develops from rest. The nature of the solution is shown to depend on a dimensionless magnetic parameter M . For M > 1 a steady state is reached at large times, when M = 1 there is also a boundary-layer flow for all times but now with a thickness growing at a rate proportional to t (dimensionless time). However, for M 1 the solution breaks down at a finite time t s with the boundary-layer thickness and maximum velocity becoming large as t approaches t s , though with the skin friction remaining finite.

[1]  J. Merkin,et al.  Free convection boundary layers on a vertical surface in a heat-generating porous medium , 2007 .

[2]  K. Stewartson.  ON GOLDSTEIN'S THEORY OF LAMINAR SEPARATION , 1958 .

[3]  Ian Proudman,et al.  Boundary-layer growth near a rear stagnation point , 1962, Journal of Fluid Mechanics.

[4]  Eugen Magyari,et al.  Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities , 2010 .

[5]  S. Liao.  An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate , 2006 .

[6]  I. Pop,et al.  Transition of MHD boundary layer flow past a stretching sheet , 2010 .

[7]  I. Pop,et al.  MHD boundary-layer flow due to a moving extensible surface , 2008 .

[8]  P. S. Gupta,et al.  Heat and mass transfer on a stretching sheet with suction or blowing , 1977 .

[9]  K. Vajravelu,et al.  MHD flow past a stretching permeable sheet , 2009, Appl. Math. Comput..

[10]  Ioan Pop,et al.  Unsteady flow past a stretching sheet , 1996 .

[11]  K. Stewartson.  On Asymptotic Expansions in the Theory of Boundary Layers , 1957 .

[12]  L. Crane.  Flow past a stretching plate , 1970 .

[13]  Tiegang Fang,et al.  Thermal boundary layers over a shrinking sheet: an analytical solution , 2010 .

[14]  N. Riley,et al.  Unsteady heat transfer for flow over a flat plate , 1963, Journal of Fluid Mechanics.

[15]  V. Kumaran,et al.  A note on the flow over a stretching sheet , 1996 .

[16]  J. Merkin.  Natural-convection boundary-layer flow on a vertical surface with Newtonian heating , 1994 .

[17]  I. Pop,et al.  Transient boundary-layer heat transfer from a flat plate subjected to a sudden change in heat flux , 2001 .

[18]  John H. Merkin,et al.  Free convection near a stagnation point in a porous medium resulting from an oscillatory wall temperature , 2000 .

[19]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[20]  Z. Ji,et al.  Viscous Flow over an Unsteady Shrinking Sheet with Mass Transfer , 2009 .

[21]  C. Wang,et al.  Stagnation flow towards a shrinking sheet , 2008 .

[22]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[23]  Ioan Pop,et al.  Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet , 2004 .

[24]  Tiegang Fang,et al.  Closed-form exact solutions of MHD viscous flow over a shrinking sheet , 2009 .

[25]  C. Wang,et al.  Viscous flow due to a shrinking sheet , 2006 .

[26]  H. Kuiken.  On boundary layers in fluid mechanics that decay algebraically along stretches of wall that are not vanishingly small , 1981 .

[27]  J. Merkin,et al.  Convective Flows on Reactive Surfaces in Porous Media , 1998 .