Purpose This study develops a mathematical framework to investigate the steady, two-dimensional flow and heat transfer of a Carreau–Yasuda nanofluid across a stretched cylinder, taking into account complex physical phenomena including variable thermophysical properties and porous media. The surface of the stretching cylinder is assumed to be velocity slip. The Darcy–Forchheimer model is used to represent flow through a porous medium, accounting for both linear drag and inertial effects; however, the magnetic field provides a Lorentz force that changes the flow dynamics. The thermal absorption, enthalpy change, Brownian motion, thermophoresis motion effects and variable thermal conductivity variations have an impression on the distribution of temperature and heat transfer. Design/methodology/approach The governing nonlinear coupled partial differential equations switched to nonlinear ordinary differential equations by using suitable similarity transformations. These boundary value problems (BVPs) are then converted into initial value problems (IVPs) and numerically solved using the shooting technique and the fifth-order Runge-Kutta (RK-5th) approach. Graphical findings show how significant dimensionless parameters affect velocity, temperature and nanoparticle concentration, indicating their considerable impact on the nanofluid’s flow behavior and heat transfer characteristics. This approach gives a thorough description of nanofluid flow along a cylinder, providing important insights into the interactions between fluid mechanics, heat transfer, magnetic fields and mass diffusion in nanofluid systems. Findings The Forchheimer number, Weissenberg number and magnetic fields reduce fluid flow velocity. The increment in the thermal region is observed due to the thermophoretic and Brownian motion of nanoparticles. The concentration region declines due to Brownian motion of nanoparticles and rises due to thermophoretic motion. The curvature parameter is the source of decrement in the velocity region, whereas the incrementing behavior of thermal and solutal field is observed due to curvature coefficient. The temperature reliant viscosity coefficient and the fluid parameter (Weissenberg number) enhances the thermal profile. The Damkohler number upturns the temperature profile while the activation energy and heat absorption coefficient drops the thermal region. The declining behavior of concentration profile is observed by rising the activation energy and Damkohler number. Research limitations/implications In this work, shear thinning characteristics of the Carreau–Yasuda fluid are analyzed. To observe the shear thinning characteristics, we have to consider the values of power law index n 1. The limitation of the current work is we cannot consider the values n 1. The analysis of unstable, turbulent or transitional flow regimes frequently found in real-world applications is not included in this work as it assumes steady-state and laminar flow. Practical implications In summary, this work provides important insights into how numerous physical factors, such as magnetic fields, chemical reaction rates and thermophoresis, influence the flow, thermal and mass transfer properties of non-Newtonian nanofluids. These findings establish a framework for improving nanofluid applications in porous and magnetically affected environments, with applications including heat transfer systems, chemical processing and energy-efficient cooling technologies. Originality/value Although numerous studies have been conducted on Carreau–Yasuda fluids and nanofluids under the impacts of magnetic and porous media, the majority of the these studies are restricted to Darcy-type porous resistance, stretching sheets, constant thermophysical characteristics and no-slip boundary conditions. In Carreau–Yasuda nanofluid flow, the combined effects of Darcy–Forchheimer inertial drag, temperature dependent viscosity, velocity slip and stretched cylindrical shape still remain largely unexplored.
Awais et al. (Sat,) studied this question.