Shifted Legendre polynomial collocation technique for heat transfer analysis using mass-based nanofluid flow in counter and co-rotating cone disk apparatus

Purpose The purpose of this paper is to examine the heat transfer characteristics of Casson hybrid nanofluid (HNF) in the conical space between a cone and disk, considering variable thermal conductivity and a nonuniform heat source/sink. This study presents a comparative evaluation of conventional HNF and mass-based HNF models for different cone-disk rotational configurations. Design/methodology/approach The governing nonlinear partial differential equations are converted into coupled ordinary differential equations by using similarity transformations and solved numerically by the shifted Legendre polynomial collocation method (SLPCM). Also, response surface methodology (RSM) and a Levenberg-Marquardt artificial neural network (LM-ANN) methods are employed to explore heat transfer. Findings Variable thermal conductivity increases the energy diffusion in the fluid, which increases the temperature and thickness of the thermal boundary layer. Similarly, nonuniform heat generation acts as an internal energy source and enhances the temperature profile in the conical gap. The mass-based HNF model predicts better heat transfer performance than the conventional model. The co-rotating cone-disk case exhibits the strongest streamline structures among the rotational modes considered, while the stationary-cone/rotating-disk case yields the weakest flow circulation. The predictions using LM-ANN are in very good agreement with the numerical results. Practical implications The findings offer valuable insights for the design of rotating thermal systems, lubrication devices, rheometers, polymer-processing equipment and advanced cooling technologies involving non-Newtonian HNFs. Originality/value The study covers a comparative analysis of conventional and mass-based HNF models in rotating cone-disk systems and combines SLPCM, RSM and LM-ANN techniques in a single framework for heat transfer analysis and prediction.