The PI's will collaborate to develop and validate new stochastic approaches in order to incorporate and propagate uncertainty in direct numerical simulations and reduced-order models of convective heat transfer. The uncertainty may be associated with free stream turbulence, thermal boundary conditions, geometric roughness or even transport coefficients and source terms. On the simulation side, they will employ the generalized polynomial chaos approach -- an extension of Norbert Wiener's pioneering ideas but with enhanced robustness and efficiency. It employs a correspondence between probability distribution functions and polynomial functional representations. On the experimental side, they will use DPIV (Digital Particle Image Velocimetry) and DPIT (Digital Particle Image Thermometry) to measure accurately probability distributions functions. The emphasis of the experiments will be on analyzing uncertainties associated with boundary conditions. The proposed work will have broad impact as it will set the foundations of data assimilation and rigorous sensitivity analysis of convective heat transfer. The proposed approach will affect fundamentally the way new experiments are designed and the type of questions that may be addressed, while the interaction between simulation and experiment will become more meaningful and more dynamic. This, in turn, will find its way in the design of heat transfer equipment and will provide a rigorous reliability framework. On the education front, the new knowledge will contribute towards understanding nonlinear systems subject to noise, fundamentals in stochastic dynamics, data assimilation, and design under uncertainty. The PI's plan to incorporate these new ideas in engineering and applied mathematics courses that they teach at Caltech and Brown University. The award has been funded by the Thermal Transport and Thermal Processing Program of the Chemical and Transport Systems Division, and it is part of a joint program involving Sandia National Laboratory and the NSF in the area of "Engineering Sciences for Modeling, Simulation, Decision-Making and Emerging Technologies.