I review the two main aspects of convection modeling important for the stellar structure: i) the determination of the temperature gradient in the stellar interior, and in particular in the superadiabatic part of the envelope, which plays a key role for the determination of the stellar Teff; ii) the description of chemical mixing –mainly in the presence of nuclear burning. I discuss these two aspects in general, and their importance for low and very low mass stars and brown dwarfs structures.

In particular, I discuss the uncertainty (of ∼ 200K) in the Teff of masses M ≲ 0.1 M⊙ in the phase of Deuterium burning, and the role of mixing in the problem of Lithium burning in very low masses. For this latter problem, I show that the relation between the age of a cluster and the luminosity of the lithium depletion edge is not only independent of the mixing timescale, but also independent of the metallicity, in the population I range, so that the Lithium test can be safely used as an age indicator.

Modeling convection: MLT and FST models

A convection model for general use in stellar structure relies on the computation of two main quantities: the fluxes and the scale length ∧. As the models presently available are all local, one can not expect that the description be unique, so there will be also one or more tuning parameters.