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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]