Abstract
The present paper is devoted to the analysis of a nonlinear system modeling unsteady flows of an incompressible non-Newtonian fluid mixed with a reactant. We are interested on generalized second grade fluids, which are chemically reacting and whose viscosity depends both on the shear-rate and the concentration. We prove existence and uniqueness of strong-weak solution for a flow filling in the plane R2 and subject to space periodic boundary conditions. This result is established under the fulfillment of some assumptions on the viscosity stress tensor and the flux vector of the diffusion-convection equation reflecting the chemical reaction. Copyright (c) 2016 John Wiley & Sons, Ltd.