Impact of Uncertain Parameters on Navier–Stokes Equations With Heat Transfer via Polynomial Chaos Expansion

ABSTRACT Performing sensitivity analysis in computational fluid dynamics is essential for assessing model robustness and reliability, since it determines how parameter variations or boundary conditions affect the simulation results. Specifically, this study focuses on the Navier–Stokes equations coupled with heat transfer, relevant to scenarios where temperature affects fluid flow behavior. Our sensitivity analysis is based on the Intrusive Polynomial Chaos Method (IPCM), which uses Probability Density Functions (PDFs) to describe stochastic variables. We extend previous work on uncertain initial or boundary conditions by focusing on input parameters such as viscosity and thermal diffusivity. We show that the sensitivity equations are well‐posed and solve them numerically using the Finite Element Volume (FEV) method. The Rayleigh–Bénard convection test is used to validate the approach. This test is particularly relevant to applications in solar energy, materials processing, and energy storage, making it an excellent choice for demonstrating the effectiveness of our method.