Influence of anisotropic permeability on Brinkman–Darcy–Forchheimer flow through curved channels

Abstract

The analysis of fluid motion in curved channels embedded with porous structures is important for understanding transport phenomena in complex geometries. The study examines the steady, laminar flow of an incompressible fluid through a curved channel saturated with an anisotropic porous medium, highlighting the combined effects of channel curvature and directional permeability. The flow is generated by an azimuthal pressure gradient. The Brinkman–extended Darcy–Forchheimer model, which accounts for viscous shear, Darcy resistance, and inertial Forchheimer effects, is used to formulate the governing equations, which are solved numerically by using the spectral quasilinearization method (SQLM). An internal MATLAB program was employed to generate velocity and temperature profiles for various physical parameters. The analysis shows that increasing the anisotropic permeability ratio from $K = 0.5$ to $K = 2$ reduces peak velocity by 33% and raises central temperature by 28%. Similarly, as the channel transitions from a highly curved state from $\kappa = 1.25$ to $\kappa \to \infty$, peak velocity decreases by 70% and central temperature increases by 16%, reflecting the reduced influence of centrifugal forces. Unlike isotropic models, this work quantifies how anisotropy and non-Darcy effects interact with curvature, offering predictive insights for porous flow systems, biomedical devices, and heat exchangers.