Numerical and experimental investigation with Response Surface Methodology optimization of melting behavior of nanoparticle-dispersed PCM in horizontal shell and spiral coil latent heat thermal energy storage system

• Spiral coil geometry reduces melting time and improves temperature uniformity. • 1 % graphene nanoparticles cut melting time by up to 20.2 % compared to pure PCM. • Charging power increases by 25 % with 1 % graphene NDPCM compared to erythritol. • Optimal HTF: 1–1.5 kg/min flow, 170–180 °C for the better thermal performance. • RSM optimization delivers 97 % predictive accuracy for rapid system design. The intermittent characteristics of renewable energy systems present significant challenges for continuous power supply, necessitating advanced energy storage solutions. Phase change material based thermal energy storage systems have demonstrated effectiveness in addressing these challenges, with shell and coil configurations offering particular advantages for heat transfer enhancement applications across various industries including refrigeration, food processing, and waste heat recovery. This study presents a novel integrated investigation combining experimental characterization, three-dimensional computational fluid dynamics validation, and Response Surface Methodology optimization to examine melting characteristics in a shell and spiral coil latent heat thermal energy storage system; the first study to employ this coupled experimental-CFD-RSM approach for a shell and spiral coil configuration using graphene enhanced erythritol phase change material not previously reported in the literature. 3-D CFD simulations were performed using ANSYS FLUENT and validated against experimental measurements. Statistical optimization employing Response Surface Methodology with Central Composite Design was applied to evaluate the effects of three critical parameters; nanoparticle concentration, mass flowrate, and heat transfer fluid inlet temperature on system performance, yielding predictive mathematical models for design optimization. Experimental results showed that graphene nanoparticle incorporation achieved melting time reductions of 9.9%, 17.7%, and 20.2% for graphene concentrations of 0.1%, 0.5%, and 1.0%, respectively, while enhancing temperature distribution uniformity throughout the phase change material. Optimal operating ranges for heat transfer fluid parameters were established, with diminishing performance benefits for flow rates exceeding 1.5 kg/min. The integrated analysis achieved excellent model reliability ( R 2 = 0.97), enabling formulation of accurate regression equations for melting time prediction across the investigated parameter space.