Nonlinear Extended Thermodynamics of a Non-Viscous Fluid in the Presence of Heat Flux

In this paper we build up, in a complete way, an Extended Thermodynamic theory of a nonviscous fluid in the presence of heat flux. The theory chooses as fundamental fields the density, the velocity, the energy density and the heat flux. The relations which constrain the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. These relations are exact, because no approximation has been used for their determination, and maintain their validity also for processes far from equilibrium. In the paper it is shown that the constitutive theory is determined by the choice of only four scalar functions of the intrinsic Lagrange multipliers. The complete nonequilibrium expressions of the chemical potential and of the entropy flux are determined: in these equations additional nonlinear terms appear, which are proportional to the Lagrange multiplier of a vector field related to the heat flux. The theory developed furnishes a nonlinear monofluid model of liquid helium II, in an inertial frame, in the complete absence of viscous phenomena. Nonlinear field equations for liquid helium II are written, a nonlinear boundary condition is formulated, two vector fields, which can be regarded as the velocities of the normal and the superfluid components of the two fluid model, are introduced.