Abstract Functions and lines have been extensively used to visualize two-dimensional fluid, heat and mass transportation structures. However, some ambiguities related to streamlines, heatlines and masslines still exist, especially for conjugate heat and mass transfer in anisotropic media. Present work aims to clarify these issues from numerical viewpoints, mainly including diffusion coefficient of transportation function at the interface of different media, different numerical approaches for solving visualization functions, non-dimensional forms of heatfunction and massfunction matching the spatial Nusselt and Sherwood numbers. The numerical procedures and code routines for the primitive conserved variables and the functions are illustrated through visualizing fluid, heat and solute transportations of double diffusive natural convection in square enclosures with massive walls or center-inserted body.