Poiseuille Flow of Carreau-Yasuda Fluid at Variable Pressure Gradient

The unsteady Poiseuille flow of Carreau-Yasuda fluid in a pipe, caused by a variable pressure gradient, is studied theoretically. In a particular case, the steady flow is considered separately. It is proved that at some values of the viscosity model parameters, the problem has a generalized solution, while at others - classical solution. For the latter, a necessary and sufficient condition is found, which depends on the maximum pressure gradient and on the Carreau-Yasuda model parameters.