Impact of Rectified Sine Pulses on the Motion of Fractionalized MHD Oldroyd-B Fluid with Second Order Slip

Abstract

Precise prediction of viscoelastic fluid behavior under oscillatory forcing is serious in polymer dispensation, porous media transport, and biomedical systems. This study investigates the influence of first- and second-order slip conditions on the magnetohydrodynamic (MHD) flow of a fractionalized Oldroyd-B fluid over a porous plate impelled by rectified sine pulses. Using fractional calculus and Laplace transforms, analytical solutions for the velocity field and shear stress are derived in terms of generalized M-functions. The solutions recover several subclasses of fluids, including classical/non-fractional Oldroyd-B, Maxwell, second-grade, and Newtonian fluids. Graphical analyses expose that increasing slip coefficients decreases velocity up to 25-35 \%\, while fractional parameters $\psi$ and $\phi$ significantly modify relaxation and retardation effects associated with the classical case. The relaxation time $\mathcal{R}_{1}$ is found to have a dominant influence on both velocity and shear stress associated with other parameters. The results highlight that second-order slip produces stronger damping than first-order slip, mostly at longer oscillation periods. The novelty of this work lies in being the first analytical treatment of fractionalized Oldroyd-B MHD flow with second-order slip under rectified sine pulses, providing standard solutions that can guide numerical and experimental validation. Potential applications include polymer extrusion, porous media flow control, and microfluidic design.