Radial–axial graded porous fins for enhanced melting in latent heat thermal storage

Latent heat thermal energy storage systems (LHTESSs) are limited by the low thermal conductivity of organic phase change materials (PCMs) and the evolving balance between conduction and buoyancy-driven convection during melting. Solid fins enhance early-stage conduction but restrict molten-PCM circulation, whereas uniformly porous fins improve permeability at the expense of heat spreading near the heated tube. This numerical study proposes radial–axial graded porous fins that retain low porosity near the fin root and increase porosity toward the tip, thereby balancing conductive heat spreading and convective transport in a vertical shell-and-tube LHTESS. A transient three-dimensional CFD model coupling the enthalpy–porosity method, Brinkman porous-flow formulation, Boussinesq approximation, and conjugate heat transfer was used to simulate 46 configurations during charging under a constant tube-wall temperature. All results reported in this study were obtained exclusively from numerical simulations; no experimental measurements were performed. The simulations predicted that, at a pore diameter of 3 mm, the fully graded balanced design reduced the complete melting time from 85.0 to 50.0 min, corresponding to a 41.2% reduction relative to the reference configuration. The best-performing configuration, G-A_B_dp5, was predicted to achieve complete melting in 47.9 min, representing a 43.6% reduction. Surrogate models trained exclusively on the CFD-generated data accurately reproduced the transient liquid-fraction response, while SHAP analysis identified the stage-dependent influences of pore diameter, porosity bounds, and axial grading during the transition from conduction-dominated to convection-assisted melting. Because the proposed graded porous fins have not yet been fabricated or directly tested, the predicted 43.6% reduction is a deterministic numerical prediction within the investigated design space and requires experimental verification under realistic manufacturing and operating conditions.