Heat and mass transfer in freezing unsaturated soil
Jame, Yih - Wu
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Progressive freezing of unsaturated soil induces moisture migration from warm to cold regions. The water movement and freezing process are coupled and jointly influence the temperature field and the rate of heat transfer. The overall process with or without significant frost heaving is an important consideration in the fields of hydrology, engineering and agriculture. Efforts to understand the coupled heat and mass transfer processes during freezing of a soil are therefore important. The primary objective of this study was to determine the validity of the Harlan model describing the coupled heat and moisture flow for the soil-water system in which the temperature is below freezing (Harlan, 1973). This involved both the obtaining of suitable experimental data and the development of a computer program for the numerical solution of the model equations. An overview discussion pertaining to this system is presented in order to establish the background understanding necessary to illustrate the development as well as the solution of the governing equations in the model. Temperature and water-content profiles in an unsaturated soil subjected to temperature gradients with the cold-side temperature below freezing were measured in a horizontal column. The column was well insulated to ensure that one-dimensional heat transfer occurred. Measurements of moisture contents within the soil samples as a function of time were carried out by the gamma-ray attenuation method. The results of these laboratory tests were compared with numerical solutions of the coupled heat and mass transfer equations. The model used is essentially that developed by Harlan, in which the major driving force causing moisture movement is assumed to be due to the existence of a total potential gradient created by the temperature gradient. The formulated differential equations were solved numerically by the finite difference method using the Crank-Nicholson scheme. The results are encouraging. The calculated values from the model agree very well with the experimental data for both temperature and moisture content profiles under different conditions imposed on the system. The conclusion is that a modified form of Harlan's model can be successfully applied to solve the problem of the coupled heat and mass transfer in soil during freezing.