  Recently, we have proposed a model for the screening of the magnetic field of
an accreting neutron star by the accreted material flowing from the polar
regions towards the equator and sinking there underneath the surface (Choudhuri
& Konar). In this model it was assumed that the flow pattern remained
stationary over time. However, as the surface magnetic field weakens, the
accretion takes place over a wider region around the pole, making the flow more
radial and isotropic. In the present work, we extend this two-dimensional model
to include the time-dependence of the flow of the accreted material. The final
radial flow is found to be less efficient in screening the magnetic field
compared to the initial tangential flow. After an initial phase of rapid decay,
the magnetic field slowly reaches an asymptotic value when the accretion
becomes nearly isotropic and radial. Assuming the initial extent of the polar
cap to be $\sim 5^0$--$10^0$, a simple geometric argument suggests that the
magnetic field should decay by 3-4 orders of magnitude before stabilizing to an
asymptotic value, consistent with the magnetic fields observed in millisecond
pulsars.
