In the quantum field theory framework, both flavour mixing and Unruh effect have been shown to arise from Bogoliubov transformations connecting inequivalent Hilbert spaces. In the present work, we study how these transformations combine when field mixing for an accelerated observer (Rindler observer) is considered. In particular, a simplified two–flavour model involving Dirac neutrino fields is analyzed. In spite of such basic setting, we find that the spectrum of Unruh radiation gets significantly modified, losing its characteristic thermal behaviour. Exploiting this result, the possibility of fixing new constraints on the neutrino squared mass differences is investigated