  In this paper we study the consistency of a cosmological model representing a
universe filled with a one-component dissipative dark matter fluid, in the
framework of the causal Israel-Stewart theory, where a general expression
arising from perturbation analysis for the relaxation time $\tau$ is used. This
model is described by an exact analytic solution recently found in [N. Cruz, E.
Gonz\'alez and G. Palma, Gen. Rel. Grav. \textbf{52}, 62 (2020), which depends
on several model parameters as well as integration constants, allowing the use
of Type Ia Supernovae and Observational Hubble data to perform an astringent
observational test. The constraint regions found for the parameters of the
solution allow the existence of an accelerated expansion of the universe at
late times, after the domination era of the viscous pressure, which holds
without the need of including a cosmological constant. Nevertheless, the fitted
parameter values lead to drawbacks as a very large non-adiabatic contribution
to the speed of sound, and some inconsistencies, not totally conclusive, with
the description of the dissipative dark matter as a fluid, which is
nevertheless a common feature of these kind of models.
