  The recent claim by the NANOGrav collaboration of a possible detection of an
isotropic gravitational wave background stimulated a series of investigations
searching for the origin of such a signal. The QCD phase transition appears as
a natural candidate and in this paper the gravitational spectrum generated
during the conversion of quarks into hadrons is calculated. Here, contrary to
recent studies, equations of state for the quark-gluon plasma issued from the
lattice approach were adopted. The duration of the transition, an important
parameter affecting the amplitude of the gravitational wave spectrum, was
estimated self-consistently with the dynamics of the universe controlled by the
Einstein equations. The gravitational signal generated during the transition
peaks around 0,28 \mu Hz, being unable to explain the claimed NANOGrav signal.
However, the expected QCD gravitational wave background could be detected by
the planned spatial interferometer Big Bang Observer in its advanced version
for frequencies above 1.0 mHz. This possible detection assumes that algorithms
recently proposed will be able to disentangle the cosmological signal from that
expected for the astrophysical background generated by black hole binaries.
