Computational investigation of oscillatory turbulent regime flow, viscous dissipation and Darcy-Forchheimer effects in magnetohydrodynamic Williamson fluids over porous stretched surface

This study investigates the oscillatory behavior and heat transfer characteristics of magnetohydrodynamic (MHD) Williamson nanofluids over a porous stretchable surface. Emphasis is placed on the effects of viscous dissipation, Brownian motion, and porous drag under varying flow regimes. The similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs). The numerical solutions of the governing ODEs are derived through the Keller-box method, and outcomes of various parameters are illustrated graphically and in tabular form. By utilizing various computational techniques, the study provides valuable insights for optimizing energy efficiency in microfluidic and engineering systems. The heat-mass transfer characteristics are analyzed under multiple influencing factors, including convective boundary conditions, porosity, viscous dissipation (Ec), and magnetic effects (ξ). The results demonstrate that the fluid velocity and concentration levels are more pronounced near the surface. The analysis also reveals that skin friction (−f″0) rate exhibits higher values on the sheet, with the Nusselt number (−θ′(0) rate follows a similar trend. Interestingly, skin friction rate reduces by increasing certain parameters. Factors such as the magnetic field ((ξ)), inclination angle (γ), Biot number (Bi), Darcy-Forchheimer parameter (Ω), and Eckert number (Ec) enhance the heat transfer rate. The observed reduction in skin friction rate with increasing λ benefits industrial coating processes by decreasing resistance on stretching surfaces. An improved heat transfer rate, influenced by magnetic field strength and the Biot number, enhances the cooling performance of thermal management systems. At Ec = 0.5, viscous dissipation has increased the near-wall temperatures by 18.7 %, while higher Nt = 0.3 has reduced thermal gradients by 22.4 % through enhanced nanoparticle migration. The Pr = 7.0 condition has improved the heat transfer efficiency by 31.2 % compared to Pr = 0.7, demonstrating optimal thermal management potential for high-viscosity applications. The impacts of Darcy-Forchheimer and viscous dissipation effects play a critical role in optimizing heat exchangers and porous media applications.