Abstract We formulate a thermodynamically consistent continuum theory for compressible, viscous, heat-conducting fluids in which the velocity entering the balance of mass is distinguished from the specific linear momentum entering the balances of linear momentum and energy. Starting from balances of mass, linear momentum, angular momentum, and internal energy, together with a power identity and the Clausius–Duhem inequality, we derive the mechanical and thermodynamic consequences of allowing these fields to differ. From local angular-momentum balance, we show that the Cauchy stress need not be symmetric and we determine its skew part. From the dissipation inequality, we obtain an admissible internal-energy flux and a closure in which the relative transport between mass and linear momentum is proportional to the pressure gradient rather than to the mass-density gradient. We also derive a free-enthalpy imbalance across shocks and a reduced wall dissipation inequality for rigid, impermeable walls undergoing prescribed rigid motion, together with simple admissible wall laws for temperature-controlled and heat-flow-controlled settings. For ideal gases, we write the governing equations in conservative dimensionless form, recover the classical compressible Navier–Stokes–Fourier theory when relative transport vanishes, and identify a distinguished low-Mach regime in which mass transport and linear-momentum transport remain distinct at leading order.
Espath et al. (Mon,) studied this question.