  We present and constrain a cosmological model which component is a
pressureless fluid with bulk viscosity as an explanation for the present
accelerated expansion of the universe. We study the particular model of a
constant bulk viscosity coefficient \zeta_m. The possible values of \zeta_m are
constrained using the cosmological tests of SNe Ia Gold 2006 sample, the CMB
shift parameter R from the three-year WMAP observations, the Baryon Acoustic
Oscillation (BAO) peak A from the Sloan Digital Sky Survey (SDSS) and the
Second Law of Thermodynamics (SLT). It was found that this model is in
agreement with the SLT using only the SNe Ia test. However when the model is
submitted to the three cosmological tests together (SNe+CMB+BAO) the results
are: 1.- the model violates the SLT, 2.- predicts a value of H_0 \approx 53 km
sec^{-1} Mpc^{-1} for the Hubble constant, and 3.- we obtain a bad fit to data
with a \chi^2_{min} \approx 400 (\chi^2_{d.o.f.} \approx 2.2). These results
indicate that this model is ruled out by the observations.
