Numerical Analysis of Buoyancy‐Driven Darcy–Forchheimer Sutterby Fluid With Variable Transport Properties

ABSTRACT Non‐Newtonian flow materials exhibit complicated rheological characteristics that play an important role in industrial and engineering transport processes. However, the coupled influence of Sutterby fluid rheology, porous‐medium resistance, buoyancy, thermal radiation, heat generation, and Arrhenius energy on flow and thermal/solutal transport over deformable cylindrical surfaces remains insufficiently explored. To address this gap, the present study develops a mathematical model for magnetized Sutterby fluid flow over a stretching/shrinking cylinder embedded in a porous medium, incorporating variable fluid properties, Darcy–Forchheimer formulation, and mixed convection effects. Heat generation, Arrhenius energy, and nonlinear thermal radiation are included to provide a more comprehensive description of energy and species transport. The findings provide a mathematical framework for understanding coupled mass, momentum, and heat transport in non‐Newtonian flows. The governing PDEs are transformed into a coupled system of ODEs through suitable similarity transformations and solved numerically utilizing the MATLAB BVP4C solver and the three‐stage Labatto III‐A method. The effects of the governing parameters on the flow behavior, thermal energy, and concentration distributions, together with the skin friction coefficient, thermal, and solutal transfer rates, are systematically examined for shrinking configurations. The results demonstrate that increasing the suction parameter enhances the thermal transport rate and friction drag in both flow regimes. In contrast, the friction drag coefficient decreases over the shrinking cylinder with growing material and Reynolds number parameters. Furthermore, thermal radiation, the temperature‐ratio parameter, thermal conductivity parameter, activation parameter, variable mass diffusivity, temperature difference, and the heat generation parameter substantially modify the thermal and solutal profile characteristics of the Sutterby fluid. The authenticity of the current numerical analysis is demonstrated by the present findings, which are in good agreement with the results presented in the existing literature.