Mathematical and thermo-economic analysis of thermal insulation for thermal energy storage applications

Thermal energy storage (TES) is vital for achieving carbon neutrality in the energy sector. To achieve high storage efficiency, insulation with satisfactory performance is required. However, in the field of TES, limited attention has been paid to thermal insulation wherein the exergy loss under periodic operation conditions must be considered. In this study, we derived an analytical solution for the transient heat conduction equation and obtained a concise and explicit expression of the average exergy loss rate under a typical operation mode, where the variation of the internal temperature is a rectangular wave function. The effects of parameters such as the operation temperature, Biot number, Fourier number, insulation thickness, thermal conductivity, and volumetric heat capacity were discussed, and the insulation thickness was optimized by using the life-cycle cost analysis method. The transient effect caused by temperature fluctuations is expected to increase exergy loss. In addition to thermal conductivity, volumetric heat capacity has a considerable influence on insulation performance. In a real-world case, if the transient effect is ignored, the estimated exergy loss is 15.4%–62.5% smaller when the insulation thickness varies from 0.1 to 0.4 m, with the optimal thickness being 27.5% larger, resulting in an additional economic cost of 1.86%.