Dimensionless Conduction Heat Rate Models for 1D Geometries and 3D TPMS Structures with Convection Boundary Conditions

Abstract New dimensionless conduction heat rate-based (DCHR-based) models for transient conduction in one-dimensional geometries (the plane wall, the solid cylinder, and the solid sphere) subject to convection boundary conditions are developed using a semi-analytical methodology. The new models permit quick prediction of instantaneous dimensionless surface temperatures and normalized cumulative energy inputs (both of which range from 0 to 1) that are in good agreement with values found using exact solutions over nine orders of magnitude of dimensionless time. Building on a recently reported similarity in heat conduction behavior exhibited by (i) three-dimensional triply periodic minimal surface (TPMS) structures and (ii) the one-dimensional plane wall for constant temperature or constant heat flux conditions, the new DCHR-based plane wall models are then used to predict the thermal response of four distinct types of TPMS geometries heated by convection. Prediction of the instantaneous values of the surface temperatures and cumulative energy inputs for the TPMS geometries using the new models is demonstrated, and all predictions are compared to benchmark computational solutions of the transient, three-dimensional heat conduction equation for the conditions considered. Excellent agreement between the predictions of the DCHR-based models and computational predictions for the TPMS structures exists over approximately nine orders of magnitude of dimensionless time.