We derive a new formalism for convective motions involving two radial flows .
This formalism provides a framework for convective models that guarantees consistency for the chemistry and the energy budget in the flows , allows time-dependence and accounts for the interaction of the convective motions with the global contraction or expansion of the star .
In the one-stream limit the formalism reproduces several existing convective models and allows them to treat the chemistry in the flows .
We suggest a version of the formalism that can be implemented easily in a stellar evolution code .

We then apply the formalism to convective Urca cores in Chandrasekhar mass white dwarfs and compare it to previous studies .
We demonstrate that , in degenerate matter , nuclear reactions that change the number of electrons strongly influence the convective velocities and we show that the net energy budget is sensitive to the mixing .
We illustrate our model by computing stationary convective cores with Urca nuclei .
Even a very small mass fraction of Urca nuclei ( as little as 10 ^ { -8 } ) strongly influences the convective velocities .
We conclude that the proper modelling of the Urca process is essential for determining the ignition conditions for the thermonuclear runaway in Chandrasekhar-mass white dwarfs .