  Mass transfer in close binaries is often non-conservative and the modeling of
this kind of mass transfer is mathematically challenging as in this case due to
the loss of mass as well as angular momentum the governing system gets
complicated and uncertain. In the present work a new mathematical model has
been prescribed for the non-conservative mass transfer in a close binary system
taking in to account the gradually decreasing profile of the mass accretion
rate by the accreting star with respect to time as well as with respect to the
increase in mass of the accreting star. The process of mass transfer is
understood to occur up to a critical mass limit of the accreting star beyond
which this process may cease to work.
