Modeling and optimization of heat transfer and flow dynamics of non-Newtonian Carreau nanofluids in differentially heated enclosed domains: coupled effects of rheology, geometry, and external forces

• A comparative analysis was conducted on Carreau and power-law models for shear-thinning nanofluids in heated enclosures. • Identification of critical thresholds of the parameters where nanoparticle effects switch from enhancement to deterioration. • Introduction of enhancement maps in the (Ra, n) plane for fixed A, Pe, and φ that identify enhancement zones. • Geometry, external forces, and rheology effects interact with each other to expand or shrink enhancement zones. This study presents a novel and comprehensive examination of heat transfer enhancement of non-Newtonian nanofluids in differentially heated domains with particular emphasis on the coupling effects between fluid rheology, geometry, and external forces. In contrast to earlier investigations, which more or less restrict the problem either to Newtonian simplifications or simple-governing parameters variations, this study examines more general and realistic configurations under thermal fluxes through employing different models to capture the shear-thinning behavior (Carreau and power-law models). The Navier-Stokes and energy equations are adjusted to consider the nanofluid altered properties using experimental models. The in-house code is validated experimentally and numerically with previous studies in different cases. The obtained results showed that while higher nanoparticle loading improves thermal conductivity, it may cause viscosity-induced heat deterioration, especially for horizontal cavities and high Rayleigh number. This deterioration is reversed by imposing intense external driving forces (high Pe ). Additionally, the study also determines critical values of each governing parameter, as a function of the remaining ones, beyond which the nanofluid benefits exceed viscous costs. A key contribution is the construction of enhancement maps in the ( Ra, n ) plane for fixed A and Pe that identify operating conditions for heat transfer enhancement. This provides useful information for optimal design of engineering applications incorporating nanofluids, hence higher thermal performances in next-generation heat transfer technologies in energy, electronics cooling, and process engineering.