Computational analysis of heat transfer in Darcy Forchheimer magneto hydrodynamic Casson ternary hybrid nanofluid flow through convergent/divergent channel

This study investigates the Darcy–Forchheimer magneto-hydrodynamic (MHD) flow of a ternary nanofluid through a convergent/divergent channel with stretching and shrinking walls. The fluid is assumed to be viscous, incompressible, and electrically conducting, allowing the Lorentz force to significantly influence the flow characteristics. Although related Jeffery-Hamel nanofluid models have previously been analyzed using numerical techniques such as RKF-45, ND Solve, bvp4c and other computational methods, the novelty of the present work lies in the incorporation of a Darcy–Forchheimer porous medium, ternary nanoparticles (Ag–Al 2 O 3 –TiO 2 ), stretching/shrinking wall effects, and the application of the Improved Residual Power Series Method (IRPSM) to obtained accurate semi-analytic solutions. The governing nonlinear equations are derived through similarity transformations and solved using (IRPSM). The accuracy of the obtained solutions is verified through comparison with available results in the literature, showing excellent agreement. The effects of pertinent physical parameters on the velocity and temperature distributions are analyzed graphically, while the skin-friction coefficient and Nusselt number are also evaluated. The result reveals that the stretching/shrinking parameter and Reynold number produce similar effects on the velocity field in both converging/diverging channels. Increasing the magnetic parameter and channel opening angle suppresses the velocity profile, where the temperature profile is enhanced by stronger magnetic effects. The Darcy and Forchheimer parameters provide additional resistance to the flow and significantly influence the thermal behavior of the fluid. Furthermore, increasing the Reynold number reduces the temperature distribution. Compared with conventional numerical solvers, IRPSM offers an accurate semi-analytical framework that avoids discretization errors, fast convergence, and produces highly reliable solutions for strongly nonlinear flow and heat transfer problems. The ternary nanofluid exhibits superior heat transfer characteristic compared with conventional and hybrid nanofluids, demonstrating its potential for advanced thermal management and engineering applications involving porous MHD flows.