The transient 1D dimensionless conduction heat rate approach applied to 3D TPMS structures

• Transient conduction in 3D TPMS structures follows 1D plane wall behavior. • High-porosity structures mimic plane wall behavior better than low-porosity structures. • Simple expressions for dimensionless conduction heat rate can be applied to TPMS structures. Transient conduction within various three-dimensional, triply periodic minimal surface (TPMS) solid structures (Diamond, Primitive, Gyroid, I-WP) of porosities 0.5, 0.7, and 0.9 is predicted numerically. Computational predictions associated with either constant surface temperature or constant surface heat flux boundary conditions are reported in terms of (i) the familiar dimensionless energy transfer, Q / Q o , and (ii) the dimensionless conduction heat rate, q *, with dependence on the Fourier number, Fo . The predicted q * and Q/Q o responses for all twelve 3D TPMS structures considered here are in remarkably good agreement with the q * and Q/Q o histories determined by both (i) the exact solutions for q* and Q/Q o for the 1D plane wall and (ii) previously reported approximate solutions for q * and Q/Q o for the 1D plane wall. The demonstrated successful application of the simple and compact expressions for q *( Fo ) developed for the 1D plane wall to a broad range of complex 3D TPMS structures might be attributed to the zero mean curvature aspects of the TPMS solids.