This study explores the combined effects of exothermic chemical reactions and Cattaneo–Christov heat flux on thermosolutal convection within a nanofluid-filled square cavity containing a rotating Z-shaped fin. The incompressible smoothed particle hydrodynamics (ISPH) approach was employed, utilizing boundary particle renormalization to accurately model boundary conditions. An artificial neural network (ANN) model, trained on ISPH simulation data, predicted the average Nusselt number ( ${\text{Nu}}_{\text{avg}}$) and average Sherwood number ( ${\text{Sh}}_{\text{avg}}$) with high accuracy. A dataset comprising 56 data points was used, from which 40 data points were used for training, 8 for validation, and 8 for testing. The Z-shaped fin, centrally positioned, rotates at a fixed angular velocity, maintaining lower temperature and concentration levels, while the cavity's vertical walls exhibit elevated thermal and solutal conditions. Results indicate that the Z-shaped fin's geometry, exothermic reaction rates, and magnetic field strength significantly influence heat and mass transfer and fluid dynamics. For instance, increasing the Hartmann number ( $\text{Ha}$) from 0 to 50 decreased nanofluid velocity by 61.99%, while ${\text{Nu}}_{\text{avg}}$ and ${\text{Sh}}_{\text{avg}}$ were reduced by 16.87% and 11.81%, respectively. Additionally, increasing the nanoparticle volume fraction from 0 to 0.15 enhanced ${\text{Nu}}_{\text{avg}}$ by 22.43% and ${\text{Sh}}_{\text{avg}}$ by 116.3%. The ANN model, employing the Levenberg–Marquardt algorithm, achieved a coefficient of determination $R=0.99994$ and a mean squared error $\text{MSE}=4.21\times {10}^{-6}$, demonstrating its reliability in predicting thermal performance. These findings underscore the study's relevance to applications such as energy systems, refrigeration, and heat exchangers.

The present study implements the incompressible smoothed particle hydrodynamics (ISPH) method with an artificial neural network (ANN) to simulate the impacts of Cattaneo-Christov heat flux on the double diffusion of a nanofluid inside a square cavity. The cavity contains a rotated wavy circular cylinder and four fins fixed on its borders. The rotational motion of an inner wavy cylinder interacting with a nanofluid flow is handled by the ISPH method. An adiabatic thermal/solutal condition is applied for the embedded wavy cylinder and the plane cavity's walls. The left wall is a source of the temperature and concentration, $T_h\mathrm{\&}{C}_h$, and the right wall with the four fins is maintained at a low temperature/concentration, $T_c\mathrm{\&}{C}_c$. The pertinent parameters are the Cattaneo-Christov heat flux parameter $\left({0\le \delta }_c\le 0.001\right)$, the Dufour number $\left(0\le Du\le 2\right)$, the nanoparticle parameter $\left(0\le \varphi \le 0.1\right)$, the Soret number $\left(0\le Sr\le 2\right)$, the Hartmann number $\left(0\le Ha\le 80\right)$, the Rayleigh number $\left({10}^3\le Ra\le {10}^5\right)$, Fin's length $\left({0.05\le L}_{Fin}\le 0.2\right)$, and the radius of a wavy circular cylinder $\left(0.05\le R_{Cyld}\le 0.3\right)$. The results revealed that the maximum of a velocity field is reduced by $48.65\mathrm{\%}$ as the $L_{Fin}$ boosts from $0.05$ to $0.2$, and by $55.42\mathrm{\%}$ according to an increase in the $R_{Cyld}$ from $0.05$ to $0.3$. Adding a greater concentration of nanoparticles until 10% increases the viscosity of a nanofluid, which declines the velocity field by $36.52\mathrm{\%}.$ The radius of a wavy circular cylinder and the length of four fins have significant roles in changing the strength of the temperature, the concentration, and the velocity field. Based on the available results of the ISPH method for $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$, an ANN model is developed to predict these values. The ideal agreement between the prediction and target values of $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ indicates that the developed ANN model can forecast the $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ values with a remarkable accuracy.

This work simulates thermo-diffusion and diffusion-thermo on heat, mass transfer, and fluid flow of nano-encapsulated phase change materials (NEPCM) within a complex cavity. It is a novel study in handling the heat/mass transfer inside a highly complicated shape saturated by a partial layer porous medium. In addition, an artificial neural network (ANN) model is used in conjunction with the incompressible smoothed particle hydrodynamics (ISPH) simulation to forecast the mean Nusselt and Sherwood numbers ( $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$). Heat and mass transfer, as well as thermo-diffusion effects, are useful in a variety of applications, including chemical engineering, material processing, and multifunctional heat exchangers. The ISPH method is used to solve the system of governing equations for the heat and mass transfer inside a complex cavity. The scales of pertinent parameters are fusion temperature ${\theta }_f=0.05-0.95$, Rayleigh number $Ra={10}^3-{10}^6$, buoyancy ratio parameter $N=-2-1$, Darcy number $Da={10}^{-2}-{10}^{-5}$, Lewis number $Le=1-20$, Dufour number $Du=0-0.25$, and Soret number $Sr=0-0.8$. Alterations of Rayleigh number are effective in enhancing the intensity of heat and mass transfer and velocity field of NEPCM within a complex cavity. The high complexity of a closed domain reduced the influences of Soret-Dufour numbers on heat and mass transfer especially at the steady state. The fusion temperature works well in adjusting the intensity and location of a heat capacity ratio inside a complex cavity. The presence of a porous layer in a cavity's center decreases the velocity field within a complex cavity at a reduction in Darcy number. The goal values of $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ for each data point are compared to those estimated by the ANN model. It is discovered that the ANN model's $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ values correspond completely with the target values. The exact harmony of the ANN model prediction values with the target values demonstrates that the developed ANN model can forecast the $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ values precisely.