Hybrid numerical-artificial intelligence framework for modelling of thermo-solutal convection of a ternary nanofluid with diffusive blocks and non-linear radiative effects

Background Efficient thermal management is a critical challenge in advanced technologies such as electronic cooling systems, solar thermal collectors, and biomedical devices. In this study, a novel hybrid numerical-artificial intelligence framework is developed to investigate double-diffusive natural convection of a ternary hybrid nanofluid inside a square cavity containing twin internal blocks modeled as both heat and mass diffusive elements, under the influence of nonlinear thermal radiation. This modeling assumption, rarely addressed in the literature, reflects real-world configurations such as catalytic inserts and reactive membranes where solid components actively participate in both heat and mass exchange. Methods The mathematical model is simulated using the finite element method (FEM) across a wide range of dimensionless parameters: Rayleigh number ( Ra ), buoyancy ratio ( N ), Lewis number ( Le ), thermal conductivity ratio ( k *), mass diffusivity ratio ( D* ), radiation parameter ( Rd ), and surface temperature parameter (λ). Three distinct block configurations are also considered. Significant findings: The results reveal that increasing Ra, N, Rd , and λ enhances both heat and solutal transport, while higher Le suppresses thermal convection but strengthens solutal circulation. Lower values of k* and D * promote stronger gradients, reinforcing double-diffusive effects. Among the tested geometries, diagonal placement of the blocks leads to the most favorable convective performance. To complement the FEM simulations, a supervised artificial neural network (ANN) based on a multi-layer perceptron (MLP) is trained on 7256 high-fidelity data samples, achieving regression coefficients above 0.996 for five key field variables. This hybrid FEM–ANN approach offers a computationally efficient and highly accurate modeling tool for complex thermo-solutal systems.