Viscoelastic flow and species transfer in a Darcian high-permeability channel

We study the two-dimensional steady, laminar flow of an incompressible, viscoelastic fluid with species diffusion in a parallel plate channel with porous walls containing a homogenous, isotropic porous medium with high permeability. The Darcy model is employed to simulate bulk drag effects on the flow due to the porous matrix. The upper convected Maxwell model is implemented due to its accuracy in simulating highly elastic fluid flows at high Deborah numbers. The conservation equations are transformed into a pair of couple nonlinear ordinary differential equations which are solved numerically using efficient 6th order Runge–Kutta shooting quadrature in the computer algebra package system MAPLE. The effects of Darcy number (Da), Deborah number (De), Schmidt number (Sc) and transpiration Reynolds number (ReT) on velocity and species concentration distributions and also wall shear stress and concentration gradients are examined in detail. The study finds applications in petroleum filtration dynamics, hydrocarbon fluid flow in geosystems, oil spill contamination in soils and also chemical engineering technologies.

Research Highlights
► A well-posed mathematical model is non-dimensionalized and solved numerically.
► Comprehensive graphs of velocity and concentration distributions.
► Interpretation of the numerical results with applications in geo-fluid dynamics.
► A comprehensive literature review of key developments in the field.