  Hadronic to quark matter phase transition may occur inside neutron stars (NS)
having central densities of the order of 3-10 times normal nuclear matter
saturation density ($n_0$). The transition is expected to be a two-step
process; transition from hadronic to 2-flavour matter and two-flavour to
$\beta$ equilibrated charge neutral three-flavour matter. In this paper we
concentrate on the first step process and solve the relativistic hydrodynamic
equations for the conversion front in presence of high magnetic field. Lorentz
force due to magnetic field is included in the energy momentum tensor by
averaging over the polar angles. We find that for an initial dipole
configuration of the magnetic field with a sufficiently high value at the
surface, velocity of the front increases considerably.
