Unsteady hydromagnetic pipe flow at small Hartmann number

Summary In this paper we have studied the problem of the unsteady flow of an electrically conducting incompressible viscous fluid through a circular pipe under the influence of a uniform applied transverse magnetic field when the walls are non-conducting. It has been assumed that the velocity vanishes on the non-conducting walls and initially the fluid is at rest. The velocity field and the induced magnetic field are calculated by an iteration procedure and have been found up to second order terms inM (Hartmann number) which is taken to be small. We have also neglected the term involving (= 4/) the self inductance of the fluid, which is valid for small values ofM.Since the pressure gradient is not necessarily a constant in unsteady flow, we have assumed it to be an arbitrary function of time. A particular case when the pressure gradient is an exponential function of time has also been investigated in detail. For a constant pressure gradient the curves for the velocity field and the induced magnetic field have been drawn (at different values of Hartmann number and time). It has been found that for small values of time the fluid is accelerated near the centre in contrast to the case of a non-conducting fluid.