Numerical and semi-analytical approaches for heat transfer analysis of ternary hybrid nanofluid flow: A comparative study

This study presents a meticulous investigation into the intricate dynamics of a Fe3O4(25%)–Al2O3(50%)–ZnO(25%)/water ternary hybrid nanofluid within the framework of the Darcy–Forchheimer model, inclusive of heat source and suction/injection phenomena on two stretching surfaces. The governing partial differential equations are transformed into ordinary differential equations by strategically applying similarity variables. These equations are then solved using the efficient analytical approach of the Homotopy Analysis Method (HAM) and numerically using the implicit finite difference-based Keller Box Method (KBM). We further compare the solutions obtained through HAM with the numerical results from the KBM approach. The inquiry discerns those pivotal parameters such as porosity (Pm) and magnetic (M) amplifying the velocity profile (g), while parameters including Reynolds number (Re), inertia coefficient (Fr), rotational (Ro), and stretching (α) manifest diminishing effects. Furthermore, the study reveals a direct correlation between temperature escalation and the amplification of Eckert number (Ec), magnetic (M), radiation (R), heat source (Q), and stretching (α) parameters. In the case of suction applied to the lower and upper surfaces, the velocity profiles f′ and g, decrease whereas for injection, the opposite trend is observed. When there is suction at the upper surface the temperature profile decreases, but for suction at the upper surface the same increases. However, when there is injection, a reverse pattern is observed. Compared to water, suspension of nanoparticles with a 5% volume fraction of spheres, cylinders, platelets, and blades achieves 13%, 23%, 27%, and 36% heat transfer rates, respectively. This research provides crucial insights into nanofluid flow and heat transfer, with significant implications for various technological applications.