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 MM. For M>1M>1 a steady state is reached at large times, when M=1M=1 there is also a boundary-layer flow for all times but now with a thickness growing at a rate proportional to tt (dimensionless time). However, for M<1M<1 the solution breaks down at a finite time tsts with the boundary-layer thickness and maximum velocity becoming large as tt approaches tsts, though with the skin friction remaining finite.