Galilean relativistic fluid mechanics

Single-component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances are derived, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given. The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time- and spacelike components of the third-order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived. It is proved that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production, is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow. A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.