This project is to develop a finite volume code to solve the Navier-Stokes (NS) equations coupled with the energy equation in two dimensional Cartesian coordinates. The codes thus developed are verified and can be directly used to analyze various fluid mechanics and heat transfer phenomena. Before the final code, there has been a process from the introduction to numerical simulation to solving some basic problems, such as diffusion equation, convection-diffusion equation, lid driven cavity problem. The results of the code have been verified by analytical solutions or benchmarks. And finally, the differential heated cavity problem has been solved. For lid driven cavity case and the differential heated cavity case, they are also simulated using a commercial computational fluid dynamics (CFD) software, ANSYS Fluent. The results thus obtained from the code and ANSYS are compared with the benchmark solutions for the two cases available in published journals. A comparative study of these results has been presented in this project.