Computational study of thermal risk mitigation via fractional MHD nanofluid modeling

This article presents a comprehensive investigation of the unsteady magnetohydrodynamic (MHD) flow of a fractional-order Carreau nanofluid over an oscillatory stretching surface embedded in a Darcy–Forchheimer porous medium. The formulation incorporates the combined effects of Joule heating, internal heat generation/absorption, Brownian diffusion, thermophoresis, chemical reaction, and Arrhenius activation energy. The Carreau model is adopted to capture the shear-dependent viscosity characteristic of polymeric and lubricating fluids, while the Caputo time-fractional derivative accounts for memory and non-local relaxation, offering a more realistic representation of viscoelastic nanofluid behavior than classical models. The resulting nonlinear fractional system is nondimensionalized and solved numerically with an explicit finite-difference scheme, whose accuracy is verified using the Method of Manufactured Solutions and grid-independence tests. Results reveal that the fractional order and oscillation frequency strongly influence the boundary-layer thickness and transport phenomena. Joule heating and exothermic effects elevate the fluid temperature, whereas Brownian motion and thermophoresis enhance nanoparticle dispersion, thereby improving mass transfer. Compared with its classical counterpart, the fractional Carreau model exhibits systematic gains in the Nusselt and Sherwood numbers across realistic ranges of W e , N b , and N t , reflecting history-dependent stress relaxation and memory-driven diffusion. The study provides fundamental insights into how fractional memory, activation energy, and oscillatory motion synergistically enhance thermal and mass transfer efficiency, offering practical implications for thermal risk mitigation, high-performance cooling systems, and reactive transport processes in industrial and energy applications.