The discharge of a thermal energy storage system, which is modeled as a one-dimensional slab of pure, molten material, is investigated semi-analytically. With the molten material initially at its fusion temperature, double-sided freezing is induced from convective and radiative cooling oil one side, and convective cooling on the other, resulting in two coalescing freeze fronts. The effects of cyclic solar flux, cyclic sk-v temperature, and cyclic,fluid temperature on the freeze front progression of one side of the slab and freeze time for entire slab are examined. Oil applying the quasi-steady approximation for the temperature distribution in each developing solid region, a pseudo-transcendental equation for the temperature of the surface exposed to convection and radiation is derived and solved at discrete time intervals by the Newton-Raphson method. Excellent agreement is obtained with previously published results for freezing caused by convective and radiative cooling only on one side, while the other side remains adiabatic. It is shown that low frequency (high period) cycling of the sky and fluid one temperatures increase the freeze time up to greater than 40% when the solar flux profile is constant or non-cyclic and when surface radiative heat loss is neglected.