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<p>Magnetorheological (MR) fluids are widely used in adaptive damping systems, smart lubrication devices, microfluidic control systems, and magnetically regulated valves because their flow behaviour can be rapidly controlled using external magnetic fields. Accurate prediction of MR fluid transport in porous channels is therefore important for improving the efficiency and stability of such smart engineering systems. However, limited studies have simultaneously incorporated magnetic-field-dependent rheology, porous resistance, and wall slip effects within a unified mathematical framework. The present study aims to develop a mathematical model for steady incompressible MR fluid flow through a porous channel formed by parallel plates under the influence of a transverse magnetic field. The formulation incorporates a power-law-based equivalent viscosity model together with Darcy–Forchheimer porous resistance and velocity-slip boundary conditions. The governing nonlinear equations are transformed into dimensionless form using similarity transformations and solved numerically using the MATLAB boundary-value solver <i>bvp4c</i>. Additionally, numerical accuracy is validated using a fourth-order Runge–Kutta (RK4) shooting method. The results demonstrate that increasing the Hartmann number from 1 to 15 reduces the axial velocity from 1.27337 to 1.06740 due to enhanced Lorentz forces opposing the flow. Similarly, increasing the Forchheimer parameter from 0 to 3 decreases the velocity near the channel walls from 1.54182 to 1.31603 because of stronger inertial resistance within the porous medium. Furthermore, increasing the rheological parameter from 2 to 2.8 raises the shear stress from 3.13838 to 3.62397, indicating enhanced non-Newtonian resistance, whereas increasing the slip parameter from 0 to 0.5 reduces the velocity from 1.19049 to 1.04308 by weakening wall-fluid interaction. The proposed model successfully captures the coupled influence of magnetic damping, porous resistance, rheological effects, and wall slip behaviour, providing useful theoretical insight for the design and optimisation of MR-based smart flow-control and adaptive engineering systems.</p>

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Mathematical modelling of magnetorheological fluid flow through a porous channel with slip and Darcy–Forchheimer effects

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月7日

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  • B. Netravati,
  • Ashwini Bhat,
  • Nagaraj N. Katagi,
  • Manjunath Shettar

摘要

Magnetorheological (MR) fluids are widely used in adaptive damping systems, smart lubrication devices, microfluidic control systems, and magnetically regulated valves because their flow behaviour can be rapidly controlled using external magnetic fields. Accurate prediction of MR fluid transport in porous channels is therefore important for improving the efficiency and stability of such smart engineering systems. However, limited studies have simultaneously incorporated magnetic-field-dependent rheology, porous resistance, and wall slip effects within a unified mathematical framework. The present study aims to develop a mathematical model for steady incompressible MR fluid flow through a porous channel formed by parallel plates under the influence of a transverse magnetic field. The formulation incorporates a power-law-based equivalent viscosity model together with Darcy–Forchheimer porous resistance and velocity-slip boundary conditions. The governing nonlinear equations are transformed into dimensionless form using similarity transformations and solved numerically using the MATLAB boundary-value solver bvp4c. Additionally, numerical accuracy is validated using a fourth-order Runge–Kutta (RK4) shooting method. The results demonstrate that increasing the Hartmann number from 1 to 15 reduces the axial velocity from 1.27337 to 1.06740 due to enhanced Lorentz forces opposing the flow. Similarly, increasing the Forchheimer parameter from 0 to 3 decreases the velocity near the channel walls from 1.54182 to 1.31603 because of stronger inertial resistance within the porous medium. Furthermore, increasing the rheological parameter from 2 to 2.8 raises the shear stress from 3.13838 to 3.62397, indicating enhanced non-Newtonian resistance, whereas increasing the slip parameter from 0 to 0.5 reduces the velocity from 1.19049 to 1.04308 by weakening wall-fluid interaction. The proposed model successfully captures the coupled influence of magnetic damping, porous resistance, rheological effects, and wall slip behaviour, providing useful theoretical insight for the design and optimisation of MR-based smart flow-control and adaptive engineering systems.