  We present here the solutions of magnetized accretion flows on to a compact
object with hard surface such as neutron stars. The magnetic field of the
central star is assumed dipolar and the magnetic axis is assumed to be aligned
with the rotation axis of the star. We have used an equation of state for the
accreting fluid in which the adiabatic index is dependent on temperature and
composition of the flow. We have also included cooling processes like
bremsstrahlung and cyclotron processes in the accretion flow. We found all
possible accretion solutions. All accretion solutions terminate with a shock
very near to the star surface and the height of this primary shock do not vary
much with either the spin period or the Bernoulli parameter of the flow,
although the strength of the shock may vary with the period. For moderately
rotating central star there are possible formation of multiple sonic points in
the flow and therefore, a second shock far away from the star surface may also
form. However, the second shock is much weaker than the primary one near the
surface. We found that if rotation period is below a certain value $(\pmin)$,
then multiple critical points or multiple shocks are not possible and $\pmin$
depends upon the composition of the flow. We also found that cooling effect
dominates after the shock and that the cyclotron and the bremsstrahlung cooling
processes should be considered to obtain a consistent accretion solution.
