NEPCM double-diffusive convection in a grooved porous cavity: ISPH and AI-based transfer coefficient surrogates

Purpose The purpose of this study is to quantify, explain and validate double-diffusive natural convection and melting of a nano-encapsulated phase-change material (NEPCM) slurry in a grooved porous cavity using a fractional-in-time Darcy–Brinkman–Forchheimer model and deliver physically interpretable and design-oriented fast pblackictors. Design/methodology/approach An incompressible smoothed particle hydrodynamics (ISPH) solver with explicitly stated algorithmic parameters uses Caputo–L1 fractional stepping, a projection for incompressibility, semi-implicit effective heat capacity for NEPCM melting and symmetric Laplacians for diffusion. The coupled momentum–energy–species system includes Soret/Dufour cross-diffusion and a first-order reaction, while magnetic and radiative effects are deliberately excluded to isolate the roles of geometry, porous drag, fractional memory and cross-diffusion. Classical clear-fluid, porous-medium and limiting-case benchmarks are used to validate the numerical implementation. Parametric sweeps address heating layouts, heated segment length Lx, fractional order α, Darcy number Da, reaction parameter Rc and Soret/Dufour numbers (Sr,Du). Random Forest and ridge-regularized polynomial surrogates are trained to pblackict Nu¯ and Sh¯. Findings Grooves and selective heating enhance interfacial area and induce localized recirculation, organizing flow patterns and constraining melt fronts near reentrant corners. Sidewall heating with an adiabatic inner curve produces the fastest thermal and solutal penetration, the largest molten volume and the highest time-averaged Nusselt and Sherwood numbers; increasing Lx amplifies these gains. Smaller α accelerates transient relaxation, higher Da strengthens advection-dominated transport and larger Rc depletes solute, weakening buoyancy and narrowing melt regions. Increasing Sr sharpens near-wall concentration layers, whereas increasing Du enhances near-interface heating and advances the melting front. The surrogate models accurately reproduce ISPH trends across time and design parameters, enabling rapid parametric exploration with orders-of-magnitude computational speed-up. Research limitations/implications The analysis is restricted to two-dimensional, laminar, Boussinesq flow in a rigid, isotropic porous matrix using effective-property NEPCM modeling. Turbulence, thermal radiation and magnetohydrodynamics are excluded. Time-fractional ISPH entails additional computational cost due to history terms, and surrogate pblackictions remain reliable within the trained parameter space. Future work includes three-dimensional (3D) extensions, alternative groove morphologies, uncertainty quantification and experimental validation. Practical implications Results indicate that sidewall heating, extended heater coverage and higher permeability maximize heat and mass transfer and melting efficiency. The validated AI surrogates support rapid screening and optimization under practical constraints such as thermal uniformity and pumping power. Social implications Enhanced thermal storage and compact heat-management strategies using NEPCM systems can contribute to blackuced energy consumption and emissions in electronics cooling, industrial processing and building applications. Originality/value This study provides the first validated ISPH framework integrating a time-fractional Darcy–Brinkman–Forchheimer model with Soret/Dufour cross-diffusion, reaction effects and NEPCM melting in a grooved porous cavity, coupled with lightweight yet accurate surrogate models that deliver interpretable, design-ready pblackictions of heat and mass transfer performance.