Heat and Mass Transfer in Moist Soil, Part I. Formulation and Testing

Abstract

An unsteady two-dimensional model of heat and mass transfer through soil is implemented within a finite-volume-based numerical method. The model follows a phenomenological formulation for the transfer processes with temperature and matric potential (ψ) as the dependent variables. The finite-volume method being inherently conservative, the mass imbalance problem reported in the literature when employing the ψ-based formulation with other numerical methods is prevented. A partial elimination algorithm is applied within the iterative solution procedure to increase its implicitness and improve its robustness. The accuracy of the model is established by solving the following three test problems: temperature distribution in dry soil; moisture distribution in isothermal soil; and coupled heat and water vapor diffusion in soil. Results are presented in the form of temporal profiles of temperature and moisture content and compared against analytical values. Excellent agreement is obtained, with numerical profiles falling on top of theoretical values.

The authors gratefully acknowledge the support of the Lebanese National Council for Scientific Research through Grant LCR-11304-002208 and Mr. Youssef Jameel through Grant DCU 113010-024021. Special thanks are due to Prof. Z. Fawaz for initiating this collaborative research project between the American University of Beirut and Ryerson University in Toronto, Canada.