Dimensionless Conduction Heat Rate Models for Cyclic Heating/Cooling of Spheres, Cylinders, Plane Walls, and TPMS Solids

Four approximate models are presented and used to predict the transient response of a solid to heating/cooling (adsorption/desorption) driven by stepwise constant, cyclic surface temperature (species concentration) boundary conditions. The one-dimensional solid sphere, one-dimensional solid cylinder, and one-dimensional plane wall are considered, along with a representative three-dimensional triply periodic minimal surface (TPMS) structure, operating in the quasi-steady regime of the transient response. By comparing the approximate predictions to benchmark numerical solutions, it is shown that a novel, modified dimensionless conduction heat rate (q*) model offers superior performance relative to the other three approximate models which include two variations of the linear driving force (LDF) model that is typically applied to cyclic mass diffusion processes. Building on the recent discovery of a remarkable similarity between the transient conduction responses of three-dimensional TPMS solids and that of the one-dimensional plane wall, application of the modified q* model to a TPMS solid operating in the quasi-steady regime of the cyclic transient response is demonstrated. Utilization of the modified q* model, in lieu of numerically solving the transient, three-dimensional form of the heat conduction (species diffusion) equation applied to TPMS solids undergoing cyclic heating/cooling (adsorption/desorption), can provide reasonably accurate heat (mass) transfer predictions in conjunction with many orders-of-magnitude reduction in computational costs.