Integrated ISPH approach with artificial neural network for magnetic influences on double diffusion of a non-Newtonian NEPCM in a curvilinear cavity

The artificial neural network (ANN) in conjunction with the incompressible smoothed particle hydrodynamics (ISPH) approach, deals with exothermic reaction effects on Cattaneo-Christov (Ca-Ch) heat and mass transport of nano-enhanced phase change material (NEPCM) in a curvilinear cavity. The ANN model, trained on data obtained from ISPH simulations, accurately predicted the mean $\overline{Nu}$ and $\overline{Sh}$ values. Two cases of boundary conditions included $\left(T_h\mathrm{\&}{C}_h\right)$ on top/bottom walls and $\left(T_c\mathrm{\&}{C}_c\right)$ on vertical walls and inner ellipse for C1. The boundary walls of a curvilinear cavity were kept at $\left(T_h\mathrm{\&}{C}_h\right)$ and the inner ellipse was maintained at $\left(T_c\mathrm{\&}{C}_c\right)$ for C2. The pertinent parameters were scaled as Frank-Kamenetskii number $Fk\left(0-1,\right)$ Ca–Ch heat, mass transfer parameters $\left({\delta }_{\theta }\mathrm{\&}{\delta }_{\mathrm{\Phi }}\right)(0-0.2),$ Hartmann number $Ha(0-60),$ buoyancy ratio parameter $N(-2-4)$, power law index parameter $n(1.1-1.4)$, Rayleigh number $Ra({10}^3-{10}^5)$, Soret/Dufour numbers $\left(Sr\mathrm{\&}Du\right)(0-0.5)$, and fusion temperature ${\theta }_f(0.1-0.9)$. The simulation results demonstrated the effectiveness of Ca-Ch heat and mass transport parameters in lowering temperature and concentration within a curvilinear cavity at C1 and C2. Increasing ${\delta }_{\theta }\mathrm{\&}{\delta }_{\mathrm{\Phi }}$ from 0 to 0.2 resulted in a $44.1\mathrm{\%}$ and $48.9\mathrm{\%}$ drop in velocity field at C1 and C2, respectively. Boundary conditions (C1 and C2) significantly affected mass, heat transfer, heat capacity ratio, and velocity field within a curvilinear cavity. An increase in Power law index $n$ from 1.1 to 1.4, reduced a velocity field by $64.68\mathrm{\%}$ and $64.66\mathrm{\%}$ at C1 and C2, respectively. Increasing $Sr$ and $Du$ helped distribute concentration. When $Sr$ and $Du$ were raised from 0 to 0.5, the velocity field increased by $34.17\mathrm{\%}$ and $29.73\mathrm{\%}$, respectively, at C1 and C2.