Unsteady-state exergy analysis for heat conduction of homogeneous solids under periodic boundary conditions

Abstract Thermal exergy analysis is typically performed under a steady-state assumption. This assumption is reasonable when the temperature difference between the environment and the system of interest is very large; however, when the temperature difference is small, the exergetic behavior of the system becomes highly sensitive to the environmental temperature. Additionally, when the system has a large thermal capacity, the storage effect cannot be ignored; as such, the steady-state assumption is not suitable. Under such conditions, unsteady-state exergy analysis should be performed to improve understanding of the system behavior. In this study, we conducted numerical unsteady-state exergy analyses for heat conduction based on the complete forms of energy, entropy, and exergy equations. The system of interest was a one-dimensional homogeneous solid with a thermal diffusivity of 0.5 × 10 −6  J/(m 3 ∙K). We analyzed two cases by assigning two different time-varying temperature boundary conditions using a 24 h periodic sinusoidal function with a constant amplitude of 10 °C but different midlines of 20 °C and 10 °C. This study was focused on the complex exergetic behavior inside the solid based on the concept of exergy balance, how the exergy flows in and out of a subsystem, and how it is stored and consumed. For intuitive interpretation of the unsteady-state results, a zonal classification method was proposed. This method was used to interpret the state of exergy flow (warm/cool) and its direction (inflow/outflow) that varies depending on the temperature relationships. Additionally, the zonal classification method was utilized to interpret the state (warm/cool) and temporal increase/decrease of the exergy storage rate, which uniquely appears in unsteady-state analyses. The application of the developed method to various transient thermal problems will lead to more complete understanding of and greater insight into various thermodynamic phenomena.