  Stellar evolution models of B-type stars are still uncertain in terms of
internal mixing properties, notably in the area between the convective core and
the radiative envelope. This impacts age determination of such stars in
addition to the computation of chemical yields produced at the end of their
life. We investigated the thermal and chemical structure and rotation rate in
the near-core boundary layer of the double-lined B-type binary KIC4930889 from
its four-year Kepler light curve, ground-based spectroscopy, and Gaia
astrometry. We computed grids of 1D stellar structure and evolution models for
different mixing profiles and prescriptions of the temperature gradient in the
near-core region. We examined the preferred prescription and the near-core
rotation rate using 22 prograde dipole modes detected by Kepler photometry. We
employed a Mahalanobis distance merit function and considered various nested
stellar model grids, rewarding goodness of fit but penalising model complexity.
Furthermore, we found a preference for either an exponentially decaying mixing
profile in the near-core region or absence of additional near-core mixing, but
found no preference for the temperature gradient in this region. The frequency
(co)variances of our theoretical predictions are much larger than the errors on
the observed frequencies. This forms the main limitation on further
constraining the individual parameters of our models. Additionally,
non-adiabatic pulsation computations of our best models indicate a need for
opacity enhancements to accurately reproduce the observed mode excitation. The
eccentric close binary system KIC4930889 proves to be a promising target to
investigate additional physics in close binaries by developing new modelling
methods with the capacity to include the effect of tidal interactions for full
exploitation of all detected oscillation modes.
