The main aim of this research is to determine Shannon entropy to quantify uncertainty propagation in coupled heat and fluid flow problems described using full Navier-Stokes (NS) equations. This is completed using a 3D Finite Volume Method solver linked with the Monte-Carlo scheme, where Shannon entropy is computed from its original statistical definition and parametrized versus the initial uncertainty level in some physical parameters inherent in the NS equations. Such entropies are computed for the resulting fluid pressure, velocity, and temperature and they are contrasted with the first two probabilistic moments of these fields following Stochastic Finite Volume Element solution of the same problem. This reference solution is achieved independently with the iterative generalized stochastic perturbation method and also the Monte-Carlo strategy. Polynomial response bases are used for both entropy and moments’ analyses to recover and process the resulting histogram of the PVT discrete solutions in any cell of the grid. This problem is tested on the well-known 3D problem of the lid-driven cavity with Gaussian randomness in heat conductivity and viscosity of the given homogeneous fluid. References [1] R.L. Ossowski, Finite Volume Method in flow problems with random parameters (in Polish). PhD Thesis, Łódź, 2012. [2] M. Kamiński, On Shannon entropy computations in selected plasticity problems. Int. J. Num. Meth. Engrg. 122(18): 5128-5143, 2021. [3] O.C. Zienkiewicz, R.L. Taylor, P. Nithiarasu, The Finite Element Method for Fluid Dynamics. Elsevier Butterworth-Heinemann, 2005.