Solving relativistic hydrodynamic equation in presence of magnetic field for phase transition in a neutron star

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.