  Relativistic transport phenomena are important from both theoretical and
practical point of view. Accordingly, hydrodynamics of relativistic gas has
been extensively studied theoretically. Here, we introduce a three-dimensional
canonical model of hard-sphere relativistic gas which allows us to impose
appropriate temperature gradient along a given direction maintaining the system
in a non-equilibrium steady state. We use such a numerical laboratory to study
the appropriateness of the so-called first order (Chapman-Enskog) relativistic
hydrodynamics by calculating various transport coefficients. Our numerical
results are consistent with predictions of such a theory for a wide range of
temperatures. Our results are somewhat surprising since such linear theories
are not consistent with the fundamental assumption of the special theory of
relativity ($v\leq c$). We therefore seek to explain such results by studying
the appropriateness of diffusive transport in the relativistic gas, comparing
our results with that of a classical gas. We find that the relativistic
correction (constraint) in the hydrodynamic limit amounts to small negligible
corrections, thus indicating the validity of the linear approximation in near
equilibrium transport phenomena.
