  In the above paper by Bechtel, Cai, Rooney and Wang, Physics of Fluids, 2004,
16, 3955-3974 six different theories of a Newtonian viscous fluid are
investigated and compared, namely, the theory of a compressible Newtonian
fluid, and five constitutive limits of this theory: the incompressible theory,
the limit where density changes only due to changes in temperature, the limit
where density changes only with changes in entropy, the limit where pressure is
a function only of temperature, and the limit of pressure a function only of
entropy. The six theories are compared through their ability to model two test
problems: (i) steady flow between moving parallel isothermal planes separated
by a fixed distance with no pressure gradient in the flow direction (Couette
flow), and (ii) steady flow between stationary isothermal parallel planes with
a pressure gradient (Poiseuille flow). The authors found, among other, that the
incompressible theory admits solutions to these problems of the plane
Couette/Poiseuille flow form: a single nonzero velocity component in a
direction parallel to the bounding planes, and velocity and temperature varying
only in the direction perpendicular to the planes.
