  One possible fate of an accreting white dwarf is explosion in a type Ia
supernova. However, the route to the thermonuclear runaway has always been
uncertain owing to the lack of a convective model consistent with the Urca
process.
  We derive a formalism for convective motions involving two radial flows. This
formalism provides a framework for convective models that guarantees
self-consistency for chemistry and energy budget, allows time-dependence and
describes the interaction of convective motions with the global contraction or
expansion of the star. In the one-stream limit, we reproduce several already
existing convective models and allow them to treat chemistry. We also suggest
as a model easy to implement in a stellar evolution code.
  We apply this formalism to convective Urca cores in Chandrasekhar mass white
dwarfs. We stress that in degenerate matter, nuclear reactions that change the
number of electrons strongly influence the convective velocities. We point out
the sensitivity of the energy budget on the mixing. We illustrate our model by
computing {\it stationary} convective cores with Urca nuclei. We show that even
a very small mass fraction of Urca nuclei ($10^{-8}$) strongly influences the
convective velocities.
  Finally, we present preliminary computations of the late evolution of a close
to Chandrasekhar mass C+O white dwarf including the convective Urca process.
