The equations that govern fluid flow and heat transfer are extremely complex. In many instances, they are impossible to solve in an analytical (closed-form) manner. In these cases, engineers are forced to rely on numerical techniques and computer simulations to generate a solution. This seminar will give a broad overview of the process of developing numerical solutions to fluid dynamics and heat transfer problems. Starting with the governing equations, we will investigate why they are so difficult to solve and how numerical solutions can provide an alternative. A variety of numerical algorithms will be surveyed; with critical attention paid to how different algorithms are more suited to different types of equations. Select results from a variety of applications will be presented.