Efficient numerical models are derived for problems of natural convection and material solidification in a horizontal differentially heated slender cavity. These 2D 1/2 models are obtained by averaging the equations momentum, heat, and mass conservation along the transverse direction assuming both a constant temperature and a well defined velocity profile in this direction. Based on our former works, the transverse velocity profile is assumed to be either a Poiseuille profile (2D H model and the experimental measurements for this pure tin solidification experiment in the AFRODITE setup .