CONSTITUTIVE CONVOLUTION AND GRAPH-THEORETICAL REPRESENTATIONS OF THERMODYNAMIC PROCESSES - THERMAL CONDUCTION

It is possible to represent thermodynamic transport processes as eithe r a superposition of constitutive convolution equations in a local reg ion or as a directed graph network between connected regions of the sy stem. Both the local constitutive convolution and directed graph netwo rk representations are based on response functions. These response fun ctions for the local constitutive and the Peusner-directed graph netwo rk representations can be estimated directly from time series data of the physical observables under general stochastic boundary conditions. The response functions can be used to predict the performance of the materials under a range of external conditions. Both of the representa tions accurately characterize the future heat flux behavior. However, the main objective of the present work is to determine if the two repr esentations provide physically meaningful and consistent transport coe fficient values. The findings of the analyses indicate that only the l ocal constitutive equations yielded the correct values for the physica l properties of the materials under test. The nonlinear temporal form of the local constitutive representation is given and then used to est imate the linear and nonlinear thermal conductivity for a range of sam ples.