Owing to the lack of the basic theoretical knowledge about numerical simulations, it is difficult for engineering undergraduates to learn how to perform numerical simulation with computer programming for the flow and heat transfer characteristics of fluids in the laminar and turbulent regimes. Based on boundary layer integration approach, the dimensionless governing equations are derived for the fully developed flow and heat transfer of incompressible fluid in the circular tube. The numerical method has been developed for solving the governing equations under laminar and turbulent flow conditions. The calculation method and the computer program are easy to understand, and the numerical results indicate the method and program can simulate the fully developed flow and heat transfer in tubes with high prediction accuracy and fast convergence speed. The present work is expected to provide valuable reference for the undergraduate teaching of computational fluid dynamics, numerical heat transfer, and thermal calculation.