The numerical modeling of the coupled heat and mass transfer processes prevalent in drying non-hygroscopic and hygroscopic capillary particulate materials is dealt with. A set of volume averaged governing equations is employed for this purpose. An improved unstructured hybrid vertex-centered edge-based finite volume algorithm is used for spatial discretization purposes. Enhancements include reformulation of boundary integral flux-averaging in conjunction with the use of a compact stencil in the computation of diffusive terms. A significant increase in accuracy is demonstrated. For validation purposes the drying of a non-hygroscopic brick and hygroscopic extruded corn meal are modeled. Predicted results for the former case are shown to compare reasonable well with experimental data while for the latter case a very good agreement is obtained.