The unsteady MHD boundary-layer flow on a shrinking sheet

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, with the boundary-layer thickness and maximum velocity becoming large as t approaches t(s), though with the skin friction remaining finite. (C) 2010 Elsevier Masson SAS. All rights reserved.