Maxwellian iteration of a causal relativistic model of polyatomic gases and evaluation of bulk, shear viscosity and heat conductivity

In the present paper, we give the parabolic limit of the field equations of a recent hyperbolic model of relativistic polyatomic gas in the framework of Rational Extended Thermodynamics (RET) theory. We obtain in this way the corresponding constitutive equations of the Thermodynamics of Irreversible Processes (TIP) obtained first in the context of relativity by Eckart. The limit is reached via the Maxwellian iteration procedure to make a connection between the phenomenological coefficients (shear, bulk viscosity, and heat conductivity) and the relaxation times. The classical and ultrarelativistic limit of these coefficients are also obtained finding that, in the case of classical limit, they coincide with the ones known in the literature. As a particular case, we study the monatomic gas and we can plot the dimensionless coefficients associated with bulk, shear, and heat conductivity. In contrast to a monatomic gas in which the bulk viscosity is very small and tends to the classical regime of the order of magnitude of O(1/c4) the bulk viscosity and the dynamical pressure for polyatomic gases, due to the rotation and vibration of internal modes, are of the order of unit (except in the ultrarelativistic limit), and this might open new perspectives in cosmology.