Existence and Stability of Solutions for Steady Flows of Fibre Suspension Flows

Abstract

We establish existence, uniqueness, convergence and stability of solutions to the equations of steady flows of fibre suspension flows. The existence of a unique steady solution is proven by using an iterative scheme. One of the restrictions imposed on the data confirms a well known fact proven in Galdi and Reddy (J Non-Newtonian Fluid Mech 83:205–230, 1999), Munganga and Reddy (Math Models Methods Appl Sci 12:1177–1203, 2002) and Munganga et al. (J Non-Newtonian fluid Mech 92:135–150, 2000) that the particle number N p must be less than 35/2. Exact solutions are calculated for Couette and Poiseuille flows. Solutions of Poiseuille flows are shown to be more accurate than those of Couette flow when a time perturbation is considered.