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 x 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 degrees C but different midlines of 20 degrees C and 10 degrees 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 vanes 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.(C) 2019 Elsevier Ltd. All rights reserved.