  We derive the pressure tensor and the heat flux to accompany the new
macroscopic conservation equations that we developed previously in a
volume-based kinetic framework for gas flows. This kinetic description allows
for expansion or compression of a fluid element, and is characterized by a flux
of volume that conventional modelling does not account for. A new convective
form of transport arises from this new approach, which is due purely to
macroscopic expansion or compression. It supplements the conventional transport
processes, which are transport due purely to mass motion (classical convective
transport) and transport due purely to random motion (diffusive transport). In
addition, we show that the thermodynamic parameters of the fluid (temperature
and pressure) appear with new non-equilibrium contributions that depend on
density variations in the gas. Our new model may be useful for describing gas
flows that display non-local-thermodynamic-equilibrium (rarefied gas flows),
flows with relatively large variations of macroscopic properties, and/or highly
compressible fluids and flows.
