In this work, numerical modeling of steady state heat and mass transfer is presented. Both laminar and hydrodynamically fully developed turbulent flow in a pipe are shown. Numerical results are compared with values obtained from analytical solution of such problems. The problems under consideration are often denoted as extended Graetz problems. They occur in heat exchangers using liquid metals as working fluid, in cooling systems for electric components or in chemical process lines. Calculations were carried out gradually decreasing the mesh size in order to examine the convergence of numerical method to analytical solution.