This work presents a computational investigation of the steady, incompressible flow of a viscoelastic fluid through a porous microchannel embedded with multiple cylindrical obstacles. The fluid motion is governed by the Maxwell–Brinkman model, wherein the Maxwell constitutive relation captures viscoelastic behavior, while the Brinkman term accounts for the resistance due to the porous matrix. The Dual Reciprocity Boundary Element Method (DRBEM) is employed to solve the governing equations, formulated in terms of streamfunction and vorticity. A distinctive feature of the model is the incorporation of the Beavers–Joseph boundary condition, which permits partial slip at the interface between the free fluid and the porous region along the flow direction. The study systematically explores the effects of obstacle size, interfacial slip length, and fluid elasticity on the velocity distribution and wall shear stress. Additionally, streamline and vorticity patterns are analyzed to elucidate key characteristics of the flow structure. The results offer insights that are pertinent to the optimization of microfluidic devices and have potential applications in biomedical engineering and MEMS technologies.
C. et al. (Tue,) studied this question.