Asymptotic analytical solution for the temperature evolution in internally-heated packed-bed tanks for high-temperature solid-air energy storage

Unidirectional flow equations through a porous medium with a localized heat source are used to model the fluid and solid temperatures in a packed-bed, internally-heated thermal energy storage (IH-TES) unit. Numerical results in absence of the heat source term are used to validate the model equations against experimental data from TES units available in the literature. An analytical approximate solution of the equations is obtained via perturbation methods. This solution is used to derive useful relations for the design and operation of IH-TES systems. The presence of the internal heat source substantially modifies the operational scales and the qualitative behavior of the system in relation to previous results on TES units. Practical recommendations to improve the design and operation of the IH-TES system resulting from the analytical solution are provided. For instance, it is found that the heat source must be located at about three-quarters of the packed-bed length for optimal performance, with a very small thickness, proportional to the solid thermal conductivity and inversely proportional to the fluid velocity and the volumetric heat capacity of the gas. Also that a high porosity is recommendable to decrease the heating time.