Pressure and entropy analysis of Casson tetra hybrid nanofluid flow in a rotating cone disk system with ANN and QNN prediction

Accurate thermo-fluid modeling in rotating systems is essential for the design and optimization of advanced thermal engineering devices. This study develops a machine-learning-assisted framework to predict the pressure distribution, temperature field, and entropy generation of a MoS₂–Ag–SiO₂–GO Casson tetra-hybrid nanofluid with a 50:50 ethylene glycol–water base fluid in a rotating cone–disk system. The modeling contribution integrates Casson tetra-hybrid nanofluid behavior with magnetic-field, porous-medium, thermal-radiation, and heat generation/absorption effects under different rotational configurations of the spinning cone–disk system. Through suitable similarity transformations, the governing equations are reduced to nonlinear ordinary differential equations and solved using the SciPy solve_bvp solver. The results indicate that magnetic, Casson, porous-medium, radiation, and irreversibility parameters strongly influence the thermo-fluid characteristics. The systematic analysis of pressure distribution together with temperature and entropy generation under four rotational configurations, along with a controlled comparison of classical and quantum–classical surrogate models, constitutes the principal distinction of the present study. The generated numerical data are used to train artificial neural network (ANN) and quantum neural network (QNN) models. The dataset comprises 6000 samples, of which 80% are used for training, 10% for validation, and 10% for unseen testing. On the unseen test set, the ANN yields R 2 values of 0.999988, 0.999988, and 0.999990 for pressure, temperature, and entropy generation, respectively, while the corresponding QNN values are 0.998597, 0.998870, and 0.998691. The corresponding RMSE values for ANN are 0.000318, 0.001155, and 0.013248, compared with 0.003400, 0.011234, and 0.154386 for QNN, respectively. Both ANN and QNN predictions agree closely with BVP results, confirming their high predictive capability; however, the ANN produces lower prediction errors and requires substantially less computational time than the QNN under the present implementation. Hence, the ANN provides the more accurate and computationally efficient surrogate for the considered rotating thermo-fluid system.