Comparison between two- and one-field models for natural convection in porous media

Abstract

The two-field model (2-F) for natural convection in porous media is studied in relation to the one-field model (1-F), which is the result of the local thermal equilibrium assumption. These models are used to evaluate heat transfer through a porous medium of relatively high permeability contained in a vertical annulus. The conceptual differences between 2- and 1-F models are shown within the context of the theory of mixtures of continuum mechanics. Criteria are generated to determine when the 1-F model can be applied in practical situations as a good approximation, and without introducing errors in the evaluation of the temperature field and wall heat fluxes. This study includes a comparison between the Nusselt numbers obtained from these two models, and also the analysis of local differences between fluid and solid temperatures within the porous cavity. Numerical calculations are carried out for variable porosity, which is modeled either with exponential decaying and damped oscillating functions involving normal distance from the annulus walls. Different correlations for the heat transfer coefficient between solid and fluid phases are analyzed in relation to the 2-F model.