Thermal dynamics of a block-filled underground hot water store

One of the best methods for seasonal storage of solar heat is the storage of hot water in large unlined rock caverns. A safe method to build self stabilizing very large caverns is to excavate them partially, i.e. to leave a considerable amount of the blasted rock in the cavern.The remaining rock in such a hot water store represents an undesired thermal inertia and it is of great practical interest to estimate how the remaining blocks influence the performance of the store.If the cavity is assumed to be spherical, the remaining blocks spherical as well, the heat diffusitivity of the solid matter constant and the water well stirred, the temperature of the water can rather easily be calculated. In the present paper it is shown that the coupled system of partial differential equations and one ordinary differential equation can be reduced to a Volterra integral equation. The calculations show how the porosity and the size of the remaining blocks influence the water temperature if an arbitrary power is added to or extracted from the cavern.