 The design of naval exhaust funnels must consider the interaction between hot gasses and topside structures, which often include critical electronic devices. Predicting the propagation trajectory, shape, and temperature distribution of an exhaust gas plume is highly strategic in various industrial sectors. Wind flow and gas flow conditions at the funnel exit can affect the plume's propagation, making it difficult to accurately model the problem with numerical simulations. Computational resources have enabled simulations to play a key role in the early design phase, but it remains challenging to fully rely on the quantitative results of these simulations due to input variables uncertainty. Uncertainty quantification, UQ, techniques can be used to evaluate uncertainty propagation in numerical simulations, such as the chimney exit velocity and main flow angle. This paper compares two UQ methods, surrogate-based and polynomial chaos expansion, to determine how each method can best be used to analyze the effect of uncertainty on the plume flow development. This article was authored by Carlo Cravero, Davide de Domenico, and Davide Marzano. We are article.tv, links in the description below.