Computational investigation of Tangent-Hyperbolic Ternary-Hybrid nanofluid flow with Coriolis forces in Darcy–Forchheimer porous media

Purpose This study aims to investigate the thermal and flow behavior of a tangent ternary hybrid nanofluid (HNF) (Cu–TiO2–SiO2/H2O) in a Darcy–Forchheimer porous medium under the influence of Coriolis forces. The primary objective is to analyze how nanoparticle shape factors and rotational effects enhance heat transfer and modify velocity profiles. A comprehensive numerical approach is applied to quantify skin friction and Nusselt number variations. The results provide insights into optimizing ternary HNF configurations for improved thermal management in rotating porous systems, offering both theoretical and practical relevance to advanced energy and industrial cooling applications. Design/methodology/approach The governing nonlinear partial differential equations describing the tangent ternary HNF flow (Cu–TiO2–SiO2/H2O) in a Darcy–Forchheimer porous medium with Coriolis forces are transformed into dimensionless ordinary differential equations. The effects of nanoparticle shape, rotation and porous medium resistance on velocity and temperature profiles are analyzed. A numerical shooting method is used to solve the resulting boundary value problem, enabling precise evaluation of skin friction, Nusselt number and thermal enhancement characteristics. Parametric studies systematically explore the influence of physical and geometric parameters on the flow and heat transfer behavior. Findings The results demonstrate that Coriolis forces significantly alter velocity distributions, inducing rotational flow patterns that enhance heat transfer. Nanoparticle shape strongly influences thermal performance, with platelet and cylindrical particles providing higher Nusselt numbers compared to spherical shapes. The presence of the Darcy–Forchheimer porous medium increases flow resistance, raising skin friction while moderating thermal enhancement. Overall, the synergistic effects of rotational dynamics, ternary nanoparticle dispersion and particle geometry yield substantial heat transfer improvement. These insights provide practical guidance for optimizing HNF configurations in rotating porous systems and advanced thermal management applications. Originality/value This work presents a novel investigation of a tangent ternary HNF (Cu–TiO2–SiO2/H2O) under the combined influence of Coriolis forces, nanoparticle shape and Darcy–Forchheimer porous medium effects. Unlike previous studies, it systematically analyzes the impact of particle geometry on thermal enhancement in rotating porous systems. The study uses a numerical shooting method for precise evaluation of flow and heat transfer characteristics. The findings offer valuable insights for the design and optimization of hybrid nanofluid-based thermal systems, with potential applications in rotating machinery, geothermal energy and advanced cooling technologies.