Solar pond ground heat loss to a moving water table

An analytical solution is presented that calculates the heat loss from the bottom of a solar pond (or any heated object) to a soil that contains a moving water table. The water table is treated as a fluid slab moving as a slug flow in one dimension. Edge effects and horizontal heat conduction are ignored. Both steady-state and time-dependent solutions are presented. Results are presented in terms of an effectiveness ratio—the actual heat flux divided by the steady-state heat flux resulting from a constant temperature heat sink at the depth of the water table. The only water-table parameter that strongly affects the effectiveness is the fluid capacity rate. Thus, for any potential solar pond site, a measurement of the mass flow rate of the water table combined with knowledge of the soil thermal properties will allow a good estimation of the ground heat loss expected over the lifetime of the pond.