A packed bed thermal storage tank is modeled using a single phase perturbation model which leads to a single advection–convection differential equation. This equation is derived using the Generalized Integral Transforms Technique (GITT). This approach allows us to obtain an analytical solution for a major case in solar applications where the fluid mass flow rate is time dependent and the inlet temperature is constant. We obtain also a semi-analytical solution for the general case where both fluid mass flow rate and inlet temperature are time-dependent. Analytical solutions for this thermal stock permits any afterwards optimization of solar power plants.