Existence and Stability of Solutions for Steady Flows of Fibre Suspension Flows - Munganga, J. M. W. (Journal of mathematical fluid mechanics, 2013)
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.