This study investigates the transportation of mass and heat in the 3D flow of hybrid nanofluids over a rotating disk in the presence of uniform magnetic field acting along the transverse direction to the flow. Water is being used as a base fluid mixed with nanoparticles of aluminum oxide and copper. The mathematical model of the nano-fluidic problem in terms of partial differential equations (PDEs) is formulated by considering the velocity slip at the boundary and heat transport mechanism due to thermal convection and radiation effects. Suitable similarity transformations are being used to transform the governing system of PDEs into a system of nonlinear ordinary differential equations. The transformed model is then analyzed by employing the competency of the Lobatto IIIA technique. Numerical and graphical illustrations are presented for the analysis of different flow parameters by varying velocities and temperature profiles. The behavior of heat transfer rate and coefficient skin friction is also studied numerically for the presented flow model.

The objective of this study is to explore the flow features and heat transfer properties of an MHD hybrid nanofluid between two parallel plates under the effects of joule heating and heat absorption/generation (MHD-HFRHT) by utilizing the computational strength of Levenberg–Marquardt Supervised Neural Networks (LM-SNNs). Similarity equations are utilized to reduce the governing PDEs into non-linear ODEs. A reference solution in the form of data sets for MHD-HFRHT flow is obtained by creating different scenarios by varying involved governing parameters such as the Hartman number, rotation parameter, Reynolds number, velocity slip parameter, thermal slip parameter and Prandtl number. These reference data sets for all scenarios are placed for training, validation and testing through LM-SNNs and the obtained results are then compared with reference output to validate the accuracy of the proposed solution methodology. AI-based computational strength with the applicability of LM-SNNs provides an accurate and reliable source for the analysis of the presented fluid-flow system, which has been tested and incorporated for the first time. The stability, performance and convergence of the proposed solution methodology are validated through the numerical and graphical results presented, based on mean square error, error histogram, regression plots and an error-correlation measurement. MSE values of up to the accuracy level of 1 × 10⁻¹¹ established the worth and reliability of the computational technique. Due to an increase in the Hartmann number, a resistance was observed, resulting in a reduction in the velocity profile. This occurs as the Hartmann number measures the relative implication of drag force that derives from magnetic induction of the velocity of the fluid flow system. However, the Reynolds number accelerates in the velocity profile due to the dominating impact of inertial force.

In this study, numerical treatment with the Lobatto IIIA technique is presented to analyze the dynamics of Darcy–Forchheimer flow for carbon nanotubes (CNTs) in a revolving frame. Stretching the surface causes fluid flow and the model is implemented for the transport of hybrid nanofluids. The governing partial differential system is simplified with the involvement of the boundary layer approximation. Similarity variables are used for the transformation of governing partial differential equations into a system of nonlinear ordinary differential equations. The results for single and multiwalled CNTs are attained by the Lobatto IIIA technique for the analysis of the resulting system. Adequate numerical and graphical illustrations are presented to investigate and understand how different flow parameters affect the velocities and temperature fields. Furthermore, the coefficients of the skin friction and the local Nusselt number are inspected numerically.