The results of a numerical simulation of natural convection due to concentration gradients during dissolution of silicon in an indium solution in a horizontal substrate-solution-substrate system are presented. The Chebyshev-Tau spectral method has been used for the simulations. The results are in very good agreement with the experimental data available in the literature. It is concluded that the discrepancies in the dissolution depths between the previous simulations and experimental data, especially at the earlier stages of the process, are mostly due to combined effects of uncertainties in the predicted properties and insufficient numerical accuracy.