The study on the application of unstructured grids in the solution of problems in two-dimensional cylindrical coordinate systems (r-z) is scarce, since one of the challenges facing this application is the accurate calculation of the control volumes. In this article, an unstructured grids-based discretization method, in the framework of a finite volume approach, is presented for the solution of the convection diffusion equations in cylindrical coordinate systems. Numerical simulations are presented for the natural convection and lid-driven cavity flow problems. The numerical results calculated on unstructured grids are found to be in good agreement with those calculated on fine structured meshes. The employment of unstructured grids leads to flexibility of the discretization method for irregular domains of any shape. (C) 2013 Elsevier Ltd. All rights reserved.