Analysis of non-Newtonian flow with reacting species in a channel filled with a saturated porous medium

•Non-Newtonian fluid flow is a model problem in petroleum engineering in processes.•We investigate the parameter dependence of flow quantities in a typical such flow.•We observe transient increase in velocity (W) & transient decrease in concentration (ϕ).•In steady state, W and ϕ both increase or both decrease together.•Parameters that increase/decrease the source terms would increase/decrease both W & ϕ.

This article examines the unsteady, pressure driven flow of a non-Newtonian fluid with reacting species in a parallel plate channel filled with a homogeneous, isotropic and saturated porous medium. A differential type third grade constitute equation is employed to model the non-Newtonian character of the fluid. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and discussed qualitatively and quantitatively with respect to various parameters embedded in the problem.