Partial differential equations (PDEs) describe a wide range of phenomena, for example fluid flow, heat transfer, and sound propagation, among others. As such, models comprised of sets of PDEs, coupled with suitable boundary and initial conditions, are frequently used to perform computer simulations in an effort to understand the behavior of solutions, as well as being essential components in various types of problems, like those dealing with control and optimal design. Thus, the numerical solution of such models, which is key in performing the computer simulations, is of fundamental importance. In this project, we will begin using a simple PDE model for simulating air ow and heat transfer. We will go through the process of solving this model numerically, using open source software to aid with the tasks of mesh generation, solution of the equations, and post-processing of the numerical results. If time permits, we will expand the model to allow for the simulation of more complicated behavior and study dierences in the solutions obtained for each of the models and by variations in the boundary conditions. Figure 1. Visualization of a sample domain, mesh, and cross-sections from a 3D numerical simulation of air velocity and temperature distribution. References: 1. V. Lopez and H. F. Hamann, "Heat Transfer Modeling in Data Centers", Int. J. Heat Mass Transfer, Vol 54, 2011 2. http://sourceforge.net/projects/netgen-mesher/ 3. http://openfoam.com/ 4. http://code.enthought.com/projects/mayavi/ Prerequisites: Computer programming experience in a language like C or C++; Basic knowledge about PDEs and numerical solution methods for PDEs would be helpful. Keywords: PDE-based simulations, PDEs, numerical methods for PDES, visualization