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• Critical cell size of a multi-scaled periodic structure has been ascertained. • Lowering porosity or lifting thermal diffusivity lead to a larger critical PPI. • The critical PPI is 5 when SS at 0.75 porosity or Ni at 0.95 porosity. • The occurrence of localised melting has been identified and correlated. The use of metallic periodic structures was considered for melting rate enhancement of a phase change material (PCM) contained in a rectangular enclosure isothermally heated from the side. The critical (optimized) cell size, or pore size, of a periodic structure with fixed porosity, realising the shortest melting time by maximizing the convection and conduction heat transfer rate into the PCM, was studied. Furthermore, the effects of material properties (copper, aluminium, nickel, and stainless steel), enclosure length, wall-melting temperature difference and porosity were numerically investigated. It was observed that increasing porosity and/or reducing thermal conductivity enlarged the critical cell size (i.e. the optimal cell size that minimizes the melting time). The critical PPIs (pores per inch) of copper and aluminium periodic structures for all studied porosities were 10; for nickel, the critical values were 10 PPIs for porosity values of 0.75, 0.8 and 0.85 while it reduces to 5 PPI for the highest porosity considered here being 0.95. Interestingly, showing a different trend, the critical PPI of stainless-steel structures was 5 for the lowest porosity (0.75) and reduced to 3 for higher porosities. The results clearly demonstrated localised melting which was observed in all periodic structures except for the 10 PPI stainless-steel case. Scattered melting islands are observed as opposed to a moving interface when ϕ = (d p / L) α ligament / α PCM > 1. For such cases, localized melting occurs and the PCM is melted at the ligaments away from the heated wall before the melt front reaches those ligaments. [ABSTRACT FROM AUTHOR]

• Critical cell size of a periodic structure with 0.9 porosity has been numerically ascertained for different materials. • Non-brazed scenarios could lead to three times longer melting time, compared to the perfectly brazed case. • The numerically-predicted effective thermal conductivity of the periodic structure agrees well with results available in the literature. To overcome the inherent poor thermal conductivity of most phase change materials (PCM), inserting highly thermally conductive wire nets with periodic structures into them have been proposed. Numerical simulations have been extensively conducted to determine critical cell size and the effect of cell height and interface gap thickness on the heat transfer within the PCM. In addition, predictive correlations of the effective thermal conductivity were put forward. The simulated results indicate that: for structures with the same porosity, the critical cell size gradually decreases as the thermal conductivity of the wire net (ligament material) increases. For the proposed periodic structure embedded in the considered computational domain with 0.90 porosity, the critical pores per inch (PPI) for copper ligaments is approximately 10 PPI, while for stainless steel, it is approximately 3-5 PPI; a shorter cell height with a lower porosity shortens the melting time, therefore, stacking inexpensive metal wire is considered as an interesting alternative to commercially produced metal foams. Moreover, non-brazed scenarios lead to longer melting times, more than three times, compared to a perfectly brazed case. Furthermore, the effective thermal conductivity of the proposed periodic structure has been numerically calculated, which agrees well with some models available in the literature. [ABSTRACT FROM AUTHOR]