Thermohydraulic Flow Problem in Unsaturated Porous Media: FDM Computational Model

Abstract

The moisture and heat fluxes in undeformable unsaturated porous media involve the movement of water, air, and heat that are induced by thermal and pressure gradients to which the porous medium is subjected under environmental conditions. Herein, the flow of the liquid phase is governed by the advective flow due to the hydraulic gradient and by the convective heat transfer due to the thermal gradient. The flow of the gas phase is governed by the advective flow due to the pressure gradient and the nonadvective flow of dry air and water vapor diffusion. The heat transport can be carried out by conduction, convection, and advection due to the pressure gradient. The mathematical model includes the air mass conservation, water mass conservation, and thermal energy conservation equations. This paper presents a detailed computational model based on the finite difference method (FDM) for one-dimensional analysis of the flow problem of heat and moisture in undeformable unsaturated porous media. Verification examples involving unsaturated flow analysis in isothermal and nonisothermal conditions are presented, highlighting the importance of having a relatively simple computational model to analyze a very complex physical problem.