The purpose of this study is to develop an integrated analytical-machine learning framework for optimizing heat transfer in unsteady squeezing nanofluid flow between parallel plates. The research employs a higher-order Akbari–Ganji method (AGM) coupled with random forest regression to quantify the effects of squeeze number \(S\) ( \(S<0\) : squeezing; \(S>0\) : expansion), Eckert squeeze number (S), Eckert number (Ec), and nanoparticle volume fraction (ϕ) on thermal performance. Four nanoparticles (TiO2, Al2O3, Ag, Cu) dispersed in water were analyzed. The key findings demonstrate that: (1) The higher-order AGM achieved exceptional accuracy with maximum deviations of 3 × 10⁻⁷ for temperature and 5 × 10−8 for velocity profiles compared to numerical solutions; (2) machine learning analysis revealed Eckert number as the dominant parameter with 75.7% influence on Nusselt number, followed by volume fraction (12.3%) and squeeze number (12.0%); (3) increasing Ec from 0.5 to 2.0 resulted in 300% enhancement in Nusselt number; (4) silver nanoparticles provided 35% higher heat transfer rate compared to Al₂O₃ at ϕ = 0.05, though with 28% increase in friction factor; (5) optimal operating conditions were identified as Ec = 1.5–2.0, ϕ = 0.05–0.06, and S = − 1.0 to − 0.3, achieving maximum Nusselt number of 15.13. The integrated framework offers practical design guidelines for thermal management systems in microelectronics cooling, photovoltaic systems, and microfluidic heat exchangers, with potential for 40–50% improvement in heat transfer efficiency compared to conventional approaches.
