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<p>This study presents an analytical examination of steady, axisymmetric creeping flow of a non-Newtonian couple stress fluid through a porous cylinder surrounded by an infinite porous medium in the presence of a transverse magnetic field. The mathematical model is formulated using the Brinkman-extended Darcy approach, and a stream function representation is employed to satisfy all boundary and interface continuity conditions along with the far-field flow requirement. Exact closed form solutions, expressed using modified Bessel functions, are obtained for velocity components, pressure distribution, vorticity, couple stress effects, and the corresponding normal and tangential stresses. These solutions further enable the precise evaluation of the dimensionless drag coefficient, providing physical insight into the hydrodynamic resistance of magnetically influenced porous structures. A systematic parametric study demonstrates the combined influence of permeability, couple stress length scale, and Hartmann number on the velocity field, streamline pattern, and drag behavior. The two-region configuration also serves as a conceptual representation of a coated drug-eluting stent embedded within biological tissue, allowing interpretation of near-wall transport characteristics without implying clinical application.The derived analytical results serve as reliable benchmark solutions for validating numerical simulations and contribute to the understanding and design of layered porous and magnetohydrodynamic flow systems encountered in engineering and biofluid applications.</p>

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Analytical investigation of drag force dynamics in hydromagnetically influenced flow of a non-Newtonian couple stress fluid through a biporous medium

  • 期刊论文

  • 发表日期：

    2026年3月20日

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  • Sobia Jayaraman,
  • Pankaj Shukla

摘要

This study presents an analytical examination of steady, axisymmetric creeping flow of a non-Newtonian couple stress fluid through a porous cylinder surrounded by an infinite porous medium in the presence of a transverse magnetic field. The mathematical model is formulated using the Brinkman-extended Darcy approach, and a stream function representation is employed to satisfy all boundary and interface continuity conditions along with the far-field flow requirement. Exact closed form solutions, expressed using modified Bessel functions, are obtained for velocity components, pressure distribution, vorticity, couple stress effects, and the corresponding normal and tangential stresses. These solutions further enable the precise evaluation of the dimensionless drag coefficient, providing physical insight into the hydrodynamic resistance of magnetically influenced porous structures. A systematic parametric study demonstrates the combined influence of permeability, couple stress length scale, and Hartmann number on the velocity field, streamline pattern, and drag behavior. The two-region configuration also serves as a conceptual representation of a coated drug-eluting stent embedded within biological tissue, allowing interpretation of near-wall transport characteristics without implying clinical application.The derived analytical results serve as reliable benchmark solutions for validating numerical simulations and contribute to the understanding and design of layered porous and magnetohydrodynamic flow systems encountered in engineering and biofluid applications.