This investigation is motivated by the dynamics of blood flow, particularly its interaction with clots and drug carriers within vessels. The study focuses on the magnetohydrodynamic Brinkman flow of a Rivlin–Ericksen viscoelastic fluid through a porous microchannel embedded with an array of cylindrical obstacles. The governing equations are expressed in a stream function-vorticity formulation, where viscoelasticity is incorporated through the first-order Rivlin–Ericksen tensor and magnetic influences are represented by a Lorentz force term. The modified vorticity transport equation includes nonlinear contributions associated with the Deborah number (De) to account for elastic effects, the Hartmann number (Ha) to capture magnetic field strength, and porous resistance defined by the Darcy number (Da) and slip length (ls). A Beavers–Joseph condition is imposed at the porous-fluid interface to describe interfacial momentum transfer. The Dual Reciprocity Boundary Element Method (DRBEM) is employed for solving the resulting boundary integral equations, enabling efficiency in complex geometries. Numerical experiments reveal that increasing Ha suppresses vortical motion, whereas higher De enhances it, underscoring the competing effects of magnetic damping and viscoelastic amplification. The framework provides valuable insights for microfluidic design, artificial organs, and biomedical applications.
C. et al. (2026) studied this question.