Dispersion and recovery of solutes and heat under cyclic radial advection

•Approximate analytical solutions for injection and recovery cycles are derived.•The effects of hydraulic, dispersion, and well parameters on recovery are studied.•In limiting cases, recovery is described by a simple function of plume geometry.•Recovery is a non-monotonic function of cycle period and the retardation factor.•Sensitivity of recovery to parameters depends on the dominant dispersion process.