The one-dimensional theoretical model of the traveling liquidus-zone (TLZ) method precisely predicts a sample translation rate for obtaining homogeneous crystals. However, no convection-related terms are included into the model. Here, convection influence on mass transport is numerically investigated. The numerical analysis shows that there are two vortices in the zone. In this case, the flow mainly enhances radial mass transport. In order to correctly understand the convection effect on the mass transport, a new index is introduced instead of the Sherwood number. The new index increases with the sample diameter. In the case of the sample diameter of 2 mm, the mass transport by convection is negligibly small as compared with that by diffusion. This is the main reason that the model prediction agrees well with the ground-based experimental results. In order to reduce the convection influence, microgravity condition is considered in the numerical analysis. (C) 2004 Elsevier B.V. All rights reserved.