Quasi-1D boundary-layer flow with wall transpiration under the Green–Naghdi extension of classical, incompressible viscous fluid flow theory

Employing only analytical methodologies, we investigate Green–Naghdi's 1996 theory of incompressible viscous flow in the context of boundary-layer flow over a permeable flat wall at which transpiration is possible. We determine and discuss exact, physically plausible, solutions, for both the constant and periodic transpiration velocity cases, to the fourth order equation of motion derived from Green–Naghdi's formulation. We also compare/contrast our findings with/to those predicted by Navier–Stokes theory, as well as point out connections to both the theory of dipolar fluids and the Navier–Stokes-α model. It is shown that unlike Navier–Stokes theory, Green–Naghdi's theory can yield a wide range of physically plausible solution profiles, even when the transpiration velocity is constant-valued and positive.