  Calculation of the mass transfer (MT) rate $\dot{M}_\text{d}$ of a Roche lobe
overflowing star is a fundamental task in binary star evolution theory. Most of
the existing MT prescriptions are based on a common set of assumptions that
combine optically-thick and optically-thin regimes with different flow
geometries. In this work, we develop a new model of MT based on the assumption
that the Roche potential sets up a nozzle converging on the inner Lagrangian
point and that the gas flows mostly along the axis connecting both stars. We
derive a set of 1D hydrodynamic equations governing the gas flow with
$\dot{M}_\text{d}$ determined as the eigenvalue of the system. The inner
boundary condition directly relates our model to the structure of the donor
obtained from 1D stellar evolution codes. We obtain algebraic solution for the
polytropic equation of state (EOS), which gives $\dot{M}_\text{d}$ within a
factor of 0.9 to 1.0 of existing optically-thick prescriptions and which
reduces to the existing optically-thin prescription for isothermal gas. For a
realistic EOS, we find that $\dot{M}_\text{d}$ differs by up to a factor of 4
from existing models. We illustrate the effects of our new MT model on
$30\,M_\odot$ low-metallicity star undergoing intensive thermal time-scale MT
and find that it is more likely to become unstable to L2 overflow and
common-envelope evolution than for existing MT prescriptions. Our model
provides a framework for including additional physics such as radiation or
magnetic fields.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena