A new mathematical approach to heat transfer with freezing and natural convection over a flat geometric domain with two plane parallel cooling faces was discussed. An intuitive solution was developed by introducing a supplementary thermal convective flux at the solid-liquid boundary. On this basis, the freezing front rate was calculated by applying the perturbation method. The calculated data were in satisfactory agreement with the ones obtained experimentally in a parallelepipedic TES unit with a low melting PCM, i.e. maleic anhydride of T-f = 52 degrees C.