On the analytical solution of the one-dimensional convection–conduction equation for packed-bed thermal energy storage systems

Temperature distribution modeling within packed-bed thermal energy storage (PBTES) systems is crucial to simulate its integration into heat sources and perform techno-economic analyses to assess the actual benefits associated with its use. This article proposes a one-dimensional convection–conduction equation to model a fluid–solid system by assuming volume-averaged properties for the energy balance and determines the analytic solution through Integral Transforms. The present study analyzes the applicability of this analytic solution considering different operational conditions of PBTES systems. The article revealed that the Péclet number ($\text{Pe}$) and the fluid-to-solid capacity ratio ($\kappa$) must be limited to obtain stable solutions, while the dimensionless time $\tau$ cannot be arbitrary despite computing an analytic solution. A sensitivity study of the solution for parameter $a=\kappa \text{Pe}/2$ defined the minimum dimensionless time required for the solution to be stable. This stability was assessed with existing experimental setups, indicating the solution’s feasibility for air–solid PBTES systems.