Fig. 1 Logical process of structural design: a-1 pomelo; a-2 microstructure of pomelo peel [26] (the link to the Creative Commons license: http://creativecommons.org/licenses/by/4.0/), b lattice structure of D_L, K_L and their single-cell structures, c gradient arrangement type, lattice structure of D_K_L and single-cell structure

Fig. 2 Temperature loads and boundary conditions for the thermal simulation

Fig. 3 Results of mesh validity tests for three structures with 85% porosity: a K_L, b D _L, c D_K_L

Fig. 4 a SEM image of AlSi10Mg powder, b particle size distribution of the AlSi10Mg powder

Fig. 5 a Schematic of the apparatus used to measure the thermal conductivity of SLM AlSi10Mg lattice structures, b close view of the test stack with the position of the temperature measurements

Fig. 6 a Comparison of theoretical porosity and actual porosity of samples, b unmelted powder on sample connecting rod by SEM, c irregular holes in additively manufactured samples, d samples of three structures with different porosities fabricated by SLM method

Fig. 7 a-c SEM images showing the micrographs of polished as-built samples after etching; d-f micrographs of SLM AlSi10Mg samples after heat treatment. Si-rich areas are projecting parts, and Al-rich areas are base bodies

Fig. 8 XRD pattern: a as-built and heat-treated, b it is a localized plot of 2θ equal to between 60° and 90°, EDX mapping for samples: c as-built, d heat-treated

Fig. 9 a-c Steady-state thermal simulation for three structures with 85% porosity, D_L, K_L and D_K_L, respectively, d the steady-state temperature distribution at different faces of the three structures, e simulated thermal conductivity of the as-built samples, f simulated thermal conductivity of the heat-treated samples

Fig. 10 a Temperature data of six test points on D_K_L samples with 90% porosity, b measured thermal conductivity of the as-built samples, c measured thermal conductivity of the heat-treated samples, d deviation value (W) of measured thermal conductivity from simulated thermal conductivity values for as-built and heat-treated samples (D_L D_K_L and K_L represent the three structures of as-built, and (D_L)' (D_K_L)' and (K_L)' represent the three structures of heat-treated)

Fig. 11 Schematic representation of materials’ internal heat transfer patterns in different treatment states: a As-built, b Heat-treated

Fig. 12 a Heat flow density distribution of single cells: K_L structure, D_K_L structure and D_L structure, b analysis of the degree of tilt of single-cell structural rods, c thermal resistance model of porous materials: (1) vertical direction, (2) horizontal direction

Fig. 13 Relationship between angle and thermal conductivity, heat flow density

Fig. 14 Comparison the thermal conductivity improvement rate of heat-treated AlSi10Mg in the present study with the rate of increase in previously reported studies