UNSTEADY POISEUILLE FLOW OF CARREAU-YASUDA FLUID IN A PIPE. SOLUTION EXISTENCE

A BSTRACT : The Poiseuille flows of non-Newtonian fluids may have complicated structures depending on the rheological characteristics of the fluid. The Carreau-Yasuda viscosity model is often used to describe the behaviour of many complex fluids. The Poiseuille flow of such fluids has many applications and occurs as a fundamental problem from a practical and theoretical point of view. At high shear rates, the flow may become unstable, then the Poiseuille flow problem may have no solution. In this paper, we prove the condition for the existence of its classical solution.