This work aims to assess the adequacy of the often made two dimensional mesh simplification in ash deposition models. Little information is available regarding its validity due to the heavy computational costs that a proper three-dimensional grid model would entail. We have implemented a case study (a deposition probe in a kraft recovery furnace) with 2D and 3D mesh models in order to compare their results regarding the ash deposition and the fluid flow. An additional simulation has been carried out to compare the results between URANS and DES turbulence models. For the particular case studied in this article, the two-dimensional simplification is justified as the results did not vary notably whereas entailing remarkably smaller computational costs. Nonetheless, the usage of DES turbulence model yielded moderately different results, qualitatively closer to deposit observations, justifying perhaps the three-dimensional approach when accuracy is needed for the deposition of fine particles on the lee edges of the tubes.