# Global sensitivity analysis of natural convection in porous enclosure: Effect of thermal dispersion, anisotropic permeability and heterogeneity

## TL;DR

This study applies global sensitivity analysis and uncertainty quantification to natural convection in porous media, revealing key parameters influencing flow and heat transfer, with implications for modeling and design.

## Contribution

It introduces a combined GSA and UQ methodology using polynomial chaos expansion for analyzing natural convection in porous media, accounting for parameter uncertainties.

## Key findings

- Temperature mainly controlled by thermal dispersion coefficient.
- Flow variability influenced by Rayleigh number and permeability anisotropy.
- Heterogeneity affects flow patterns more than heat transfer.

## Abstract

In this paper, global sensitivity analysis (GSA) and uncertainty quantification (UQ) have been applied to the problem of natural convection (NC) in a porous square cavity. This problem is widely used to provide physical insights into the processes of fluid flow and heat transfer in porous media. It introduces however several parameters whose values are usually uncertain. We herein explore the effect of the imperfect knowledge of the system parameters and their variability on the model quantities of interest (QoIs) characterizing the NC mechanisms. To this end, we use GSA in conjunction with the polynomial chaos expansion (PCE) methodology. In particular, GSA is performed using Sobol' sensitivity indices. Moreover, the probability distributions of the QoIs assessing the flow and heat transfer are obtained by performing UQ using PCE as a surrogate of the original computational model. The results demonstrate that the temperature distribution is mainly controlled by the longitudinal thermal dispersion coefficient. The variability of the average Nusselt number is controlled by the Rayleigh number and transverse dispersion coefficient. The velocity field is mainly sensitive to the Rayleigh number and permeability anisotropy ratio. The heterogeneity slightly affects the heat transfer in the cavity and has a major effect on the flow patterns. The methodology presented in this work allows performing in-depth analyses in order to provide relevant information for the interpretation of a NC problem in porous media at low computational costs.