Time-Fractional Free Convection of Maxwell, Williamson, and Micropolar Nanofluids over a Vertical Plate in Saturated Porous Media

Abstract

This study develops a unified time-fractional framework to investigate free convection of Maxwell, Williamson, and micropolar nanofluids in porous media under the combined effects of magnetic field, thermal radiation, and internal heat generation. The governing fractional-order equations are transformed using similarity variables and solved numerically with Maple 24. Un-
like earlier studies that treated individual models, the present work simultaneously incorporates elasticity, shear-thinning, and microrotation mechanisms, enabling direct comparisons of heat and mass transfer characteristics across these non-Newtonian nanofluids. Results show that Williamson nanofluids outperform Maxwell and micropolar fluids, yielding Nusselt numbers up to 18 − 22% higher and Sherwood numbers up to 15 − 20% higher due to their shear-thinning behavior. Internal heat generation is found to increase fluid motion by approximately 12% in terms of velocity magnitude. Still, it reduces surface heat transfer rates by about 10 − 14%, reflecting a trade-off between buoyancy enhancement and thermal resistance. The influence of fractional order is significant: reducing the order from α = 1.0 to α = 0.7 decreases wall heat flux by nearly 17%, confirming the memory-dependent damping effect of fractional dynamics. These quantitative insights guide the selection and optimization of non-Newtonian nanofluids in applications such as magnetic refrigeration, porous heat exchangers, and advanced thermal energy systems.