Analytical solution of boundary layer equations for a nonlinearly viscous dilatant fluid on a flat plate in the case with mass transfer

An analytical (exact) solution of equations of a two-dimensional boundary layer of a non-Newtonian viscous fluid in the case with mass transfer is obtained with the use of the Ostwald–Reiner power-law model in a particular case with $n=2$ (dilatant fluid). It is noted that the apparent viscosity in this case is described by an expression that coincides with the equation for turbulent viscosity of a Newtonian fluid derived by the Prandtl mixing length model. For the particular case under consideration, it is found that there is an analogy between the flows of a non-Newtonian fluid and a Newtonian fluid with turbulent viscosity.