In this paper. we start from the Chang-Brown model which allows computation of Row, temperature and dopant concentration in a vertical Bridgman-Stockbarger semiconductor growth system, The modifications made by us concern the melt/solid interface, Namely, we assume that the phase transition does not take place on a Rat mathematical surface, but in a thin region (the so-called precrystallization-zone), masking the crystal, where both phases, liquid and solid. co-exist. We deduce for this zone new effective equations which govern flow, heat and dopant transport and make the coupling of these equations with these governing the same phenomena in the pure melt. We compute Row, temperature and dopant concentration for crystal and melt with thermophysical properties similar to gallium-doped germanium using the modified Chang-Brown model and compare the results to those obtained using the Chang-Brown model.