Transient exergy analysis for heat conduction: Quantitative guidelines for selecting pseudo vs. fully unsteady-state methods

Exergy analysis quantifies where and how useful energy is consumed relative to the environment, providing a practical basis for thermodynamic optimization. However, applying exergy analysis presents a challenge for systems with large heat capacity operating near ambient temperatures. In these systems, exergy calculations become highly sensitive to even minor fluctuations in boundary conditions, leading to significant uncertainties. This sensitivity creates a methodological dilemma for engineers: selecting between the computationally inexpensive pseudo unsteady (PU) analysis, which neglects transient thermal storage effects, and the more accurate but resource-intensive fully unsteady (FU) analysis. While both methods account for time-varying boundary conditions, the PU method applies steady-state governing equations at each instant (a quasi-steady snapshot) neglecting thermal storage, whereas the FU method solves the unsteady-state governing equations to track energy/exergy storage explicitly. To establish clear selection criteria, we systematically compare PU and FU methods for transient heat conduction in homogeneous solids across wide ranges of thermal diffusivity α and system length, reporting error ratios relative to FU. Results indicate that the PU method is generally acceptable for materials with high thermal diffusivity, such as metals (α >4.0 × 10−6 m2/s). However, for low-diffusivity materials like polymers (α <1.0 × 10−6 m2/s), neglecting thermal storage yields significant relative error exceeding 10%, necessitating the FU method for accurate evaluation. These findings provide quantitative and actionable guidelines for choosing the appropriate exergy analysis method, balancing computational efficiency against accuracy in transient thermal systems.