The mixing length theory (MLT) used to compute the temperature gradient in superadiabatic layers of stellar (interior and atmosphere) models contains in its standard form 4 free parameters. Three parameters are fixed a priori (and define what we denote as the MLT flavour) whereas one (the so-called mixing length) is calibrated by reproducing observational constraints. The classical Bohm-Vitense flavour is used in all modern MLT-based stellar model computations and, despite its crude approximations, the resulting $T_{eff}$ scale appears -- perhaps surprisingly -- remarkably realistic, once the mixing length parameter is calibrated with a solar model. Model atmosphere computations employ parameter choices different from what is used in stellar interior modelling, raising the question of whether a single MLT flavour and mixing length value can be used to compute interiors and atmospheres of stars of all types. As a first step towards addressing this issue, we study whether the MLT flavour (the so-called ML2) and mixing length choice that have been proven adequate to model white dwarf atmospheres, is able to provide, when used in stellar models, results at least comparable to the use of the classical Bohm-Vitense flavour. We have computed solar models and evolutionary tracks for both low- and intermediate-mass Population I and II stars, adopting both solar calibrated Bohm-Vitense and ML2 flavours of the MLT in our stellar evolution code, and state-of-the-art input physics. The two sets of models provide consistent results, with only minor differences. Both calibrations reproduce also the $T_{eff}$ of red giants in a sample of Galactic globular clusters.
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