Three-stage Lobatto analysis on thermally magnetized radiative flow and heat transportation in (Cu-TiO2/H2O) hybrid nanofluid engrained with spherical shaped nanoparticle

Despite extensive research on hybrid nanofluids (HNF), the role of nanoparticle shapes particularly the performance of spherical particles remains underexplored. The purpose of the current study is to investigate the thermal applications of magnetically responsive hybrid nanofluid flow and heat transfer with a focus on the impact of distinct nanoparticle shapes. In this work, a hybrid nanofluid composed of copper (Cu), titanium dioxide (TiO 2 ), and water (H 2 O) as the base fluid is considered, using spherical-shaped particles (n = 3), and its behavior is examined under rotational effects. Radiative effects are incorporated into the analysis to provide deeper insight into heat transfer characteristics. Current study addresses the transport dynamics of spherical nanoparticles under convective thermal conditions, incorporating the advanced thermophysical properties of hybrid nanomaterials. The modeled momentum and energy equations are transformed into simplified forms using appropriate scaling parameters and are then solved numerically using the three stage Lobatto scheme with the aid of MATLAB. The key findings show that the (x)-component of the velocity profile decreases with increasing values of the rotation and magnetic parameters, whereas the (y)-component exhibits the opposite trend and increases as these parameters grow. Furthermore, the Nusselt number of the hybrid nanofluid improves with increasing the values of rotational parameter ( λ ), radiation parameter (Rd), and magnetic parameter ( M ). The tabulated results for the friction factor and Nusselt number are validated with previously available studies, and the findings are in close agreement with the existing literature. In addition, the rate of heat transfer growths by 36.60% as the mass flux/suction parameter ( ) rises from 0.2 to 0.4.