Mathematical modelling of Darcy–Forchheimer MHD Williamson nanofluid flow above a stretching/shrinking surface with slip conditions

Abstract The purpose of this research work is to develop a detailed mathematical model that incorporates the Darcy–Forchheimer model, magnetohydrodynamics, slip conditions, and viscous dissipation effects to describe the flow of Williamson carbon nanotube (CNT) nanofluid over a stretching/shrinking surface. For an accurate description of the flow behaviour of nanofluids, the non-linear drag force inside a porous medium must be captured by the Darcy–Forchheimer model. For applications in engineering and industrial processes, the magnetohydrodynamics aspect takes into account the impact of an applied magnetic field on the electrically conducting fluid. CNTs, which are recognized for their remarkable mechanical and thermal capabilities, are present in the nanofluid, and their non-Newtonian behaviour is characterized using the Williamson fluid model. The inclusion of slip conditions at the boundary takes into consideration the fluid’s partial adherence to the surface, an important consideration in applications involving micro- and nanoscale processes. To give a more accurate account of the energy balance in the system, viscous dissipation effects that symbolize the transformation of kinetic energy into thermal energy are also included. Similarity transformations are used to convert a non-linear ordinary differential equation. After that, these equations are seminumerically solved using the homotopy analysis method. The velocity and temperature profiles are examined in order to determine the influence of different factors, including the Forchheimer number, magnetic parameter, Williamson parameter, slip parameter, and viscous dissipation. The results demonstrate how these parameters have a major impact on the flow and heat transfer properties of the nanofluid, offering guidance for improving complex flow conditions and nanofluid-related industrial and technical processes.