  The specific shear viscosity, $\eta/s$, of the quark-gluon plasma formed in
ultrarelativistic heavy-ion collisions at RHIC and LHC is estimated based on
the progressive longitudinal broadening of transverse momentum two-particle
correlators, $G_2$, reported as a function of collision centrality by the STAR
and ALICE experiments. Estimates are computed as a function of collision
centrality using the Gavin ansatz which relates the $G_2$ longitudinal
broadening to the specific shear viscosity. Freeze out times required for the
use of the ansatz are computed using a linear fit of freeze out times reported
as a function of the cubic root of the charged particle pseudorapidity density
(${\rm d}N_{\rm ch}$/d$\eta)^{1/3}$. Estimates of $\eta/s$ based on ALICE data
exhibit little to no dependence on collision centrality at LHC energy, while
estimates obtained from STAR data hint that $\eta/s$ might be a function of
collision centrality at top RHIC energy.
