  We explore the viability of a bulk viscous matter-dominated Universe to
explain the present accelerated expansion of the Universe. The model is
composed by a pressureless fluid with bulk viscosity of the form \zeta =
\zeta_0 + \zeta_1 * H where \zeta_0 and \zeta_1 are constants and H is the
Hubble parameter. The pressureless fluid characterizes both the baryon and dark
matter components. We study the behavior of the Universe according to this
model analyzing the scale factor as well as some curvature scalars and the
matter density. On the other hand, we compute the best estimated values of
\zeta_0 and \zeta_1 using the type Ia Supernovae (SNe Ia) probe. We find that
from all the possible scenarios for the Universe, the preferred one by the best
estimated values of (\zeta_0, \zeta_1) is that of an expanding Universe
beginning with a Big- Bang, followed by a decelerated expansion at early times,
and with a smooth transition in recent times to an accelerated expansion epoch
that is going to continue forever. The predicted age of the Universe is a
little smaller than the mean value of the observational constraint coming from
the oldest globular clusters but it is still inside of the confidence interval
of this constraint. A drawback of the model is the violation of the local
second law of thermodynamics in redshifts z >= 1. However, when we assume
\zeta_1 = 0, the simple model \zeta = \zeta_0 evaluated at the best estimated
value for \zeta_0 satisfies the local second law of thermodynamics, the age of
the Universe is in perfect agreement with the constraint of globular clusters,
and it also has a Big-Bang, followed by a decelerated expansion with the smooth
transition to an accelerated expansion epoch in late times, that is going to
continue forever.
