Published Paper Details:

This study presents a comprehensive analytical investigation of magnetohydrodynamic (MHD) flows in porous channels incorporating velocity slip boundary conditions, suction/injection effects, and time-dependent forcing mechanisms. The research addresses a critical gap in contemporary fluid mechanics literature where the combined effects of magnetic fields, porous media resistance, and wall slip phenomena have received limited theoretical treatment, despite their fundamental importance in emerging technological applications ranging from microfluidics to biomedical engineering systems. The mathematical framework developed herein provides exact analytical solutions for the governing dimensionless equations describing both oscillatory and pulsating flow regimes through vertical parallel-plate channels filled with saturated porous media. The analysis incorporates transverse magnetic fields, generalized slip boundary conditions, wall transpiration mechanisms, and harmonically varying pressure gradients using advanced mathematical techniques including separation of variables, eigenfunction expansions, and complex variable methods. The derived solutions enable systematic parametric investigations of velocity profiles, temperature distributions, skin friction coefficients, and heat transfer rates across the complete parameter space. Key findings reveal that velocity slip significantly modifies classical flow patterns, with the slip parameter ? acting as a primary control mechanism that can enhance flow rates by up to 19-fold for superhydrophobic surfaces. The study demonstrates that increased injection at heated surfaces substantially enhances skin friction coefficients on both channel plates, while the Hartmann number Ha provides effective flow control through magnetic damping effects. The Darcy number Da emerges as a critical parameter governing the transition between different flow regimes, with porous media resistance creating quasi-steady behavior in highly resistive systems. Temperature-dependent slip effects and oscillatory flow characteristics exhibit complex interactions that depend on the Strouhal number St and Womersley parameter ?w, revealing optimal frequency ranges for various applications. The analytical approach provides exact benchmarks for numerical validation and offers unprecedented theoretical insights into the complex coupling between electromagnetic forces, porous media physics, and interfacial slip phenomena. These solutions address fundamental questions in modern fluid mechanics while enabling precise engineering design for applications including lab-on-chip devices, magnetofluidic systems, enhanced oil recovery, fusion reactor blanket cooling, and biological flow modeling. The unified analytical treatment of oscillatory and pulsating flows under combined MHD-slip-porous conditions represents a significant theoretical advancement over previous studies that typically addressed only subsets of these phenomena or relied on restrictive assumptions. The research outcomes establish a new theoretical foundation for understanding and predicting flow behavior in next-generation microfluidic devices, biomedical applications involving blood flow through permeable vessels, and industrial processes requiring precise flow control under electromagnetic fields. The exact analytical solutions serve as essential validation tools for computational fluid dynamics codes and provide design guidelines for optimizing system performance across diverse engineering applications. Furthermore, the mathematical framework developed can be extended to investigate non-Newtonian fluids, anisotropic porous media, and multiphase systems, opening new avenues for future research in advanced fluid mechanics and transport phenomena.