Context. HD 181231 and HD 175869 are two late rapidly rotating Be stars, which have been observed using high-precision photometry with the CoRoT satellite during about five consecutive months and 27 consecutive days, respectively. An analysis of their light curves, by Neiner and collaborators and Gutiérrez-Soto and collaborators respectively, showed that several independent pulsation g-modes are present in these stars. Fundamental parameters have also been determined by these authors using spectroscopy. Aims. We aim to model these results to infer seismic properties of HD 181231 and HD 175869, and constrain internal transport processes of rapidly rotating massive stars. Methods. We used an adiabatic (NRO) and a non-adiabatic (Tohoku) oscillation code that accounts for the combined action of Coriolis and centrifugal accelerations on stellar pulsations as needed for rapid rotator modelling. We coupled these codes with a 2D (ROTORC) stellar structure model to take the rotational deformation of the star into account. The action of transport processes was parametrised with the mixing parameter α ov, which represents the "non-standard" extension of the convective core, and determined by matching observed pulsation frequencies assuming a single star evolution scenario. In a second step, we used (Geneva) evolution models to evaluate the contribution of the secular rotational transport and mixing processes in the radiative envelope. A Monte Carlo analysis of spectropolarimetric data was also performed to examine the role of a potential fossil magnetic field. Finally, based on state-of-the-art modelling of penetrative convection and internal waves, we unravelled their respective contribution to the needed "non-standard" mixing. Results. We find that extra mixing of α ov = 0.3-0.35H p is needed in HD 181231 and HD 175869 to match the observed frequencies with those of prograde sectoral g-modes. We also detect the possible presence of r-modes. We investigated the respective contributions of several transport processes to this mixing: the hydrodynamical processes in particular the meridional circulation and shear-induced turbulence caused by the radiative envelope differential rotation, the possible magnetic field, the penetrative convection at the top of the convective core, and the transport by internal waves. Conclusions. We showed that the extension of the convective core needed to match observations and models may be explained by mixing induced by the penetrative movements at the bottom of the radiative envelope and by the secular hydrodynamical transport processes induced by the rotation in the envelope. We showed how asteroseismology opens a new door to probe transport processes in stellar interiors.
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