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A latent heat thermal energy storage (LHTES) unit can store a notable amount of heat in a compact volume. However, the charging time could be tediously long due to weak heat transfer. Thus, an improvement of heat transfer and a reduction in charging time is an essential task. The present research aims to improve the thermal charging of a conical shell-tube LHTES unit by optimizing the shell-shape and fin-inclination angle in the presence of nanoadditives. The governing equations for the natural convection heat transfer and phase change heat transfer are written as partial differential equations. The finite element method is applied to solve the equations numerically. The Taguchi optimization approach is then invoked to optimize the fin-inclination angle, shell aspect ratio, and the type and volume fraction of nanoparticles. The results showed that the shell-aspect ratio and fin inclination angle are the most important design parameters influencing the charging time. The charging time could be changed by 40% by variation of design parameters. Interestingly a conical shell with a small radius at the bottom and a large radius at the top (small aspect ratio) is the best shell design. However, a too-small aspect ratio could entrap the liquid-PCM between fins and increase the charging time. An optimum volume fraction of 4% is found for nanoparticle concentration.

The melting of a coconut oil–CuO phase change material (PCM) embedded in an engineered nonuniform copper foam was theoretically analyzed to reduce the charging time of a thermal energy storage unit. A nonuniform metal foam could improve the effective thermal conductivity of a porous medium at regions with dominant conduction heat transfer by increasing local porosity. Moreover, the increase in porosity contributes to flow circulation in the natural convection-dominant regimes and adds a positive impact to the heat transfer rate, but it reduces the conduction heat transfer and overall heat transfer. The Taguchi optimization method was used to minimize the charging time of a shell-and-tube thermal energy storage (TES) unit by optimizing the porosity gradient, volume fractions of nanoparticles, average porosity, and porous pore sizes. The results showed that porosity is the most significant factor and lower porosity has a faster charging rate. A nonuniform porosity reduces the charging time of TES. The size of porous pores induces a negligible impact on the charging time. Lastly, the increase in volume fractions of nanoparticles reduces the charging time, but it has a minimal impact on the TES unit’s charging power.