The report correlates the partial differential equations that govern buoyancy-driven laminar and turbulent flows in differentially heated cavities. It is shown how the equations are discretised on a non-uniform mesh and then solved. The k-epsilon model has been used to represent the effects of turbulence and its low Reynolds number formulation has been used so the equations may be integrated close to the wall. It is intended that the work will provide a bridge between theory and practice, and be useful to researchers relative new to the area of computational fluid dynamics.