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The Cross-Coupling Transport Coefficient for the Steady Flow of Heat in Soil Under a Gradient of Water Content¹

ABSTRACT

A theoretical discussion based on the thermodynamics of irreversible processes (TIP) is given concerning the flux equations for the coupled, steady flows of water and heat in a soil as formulated by Jury and Miller. It is shown that a unique definition of the heat flux vector in a coupled flow process is not possible within the context of TIP alone, although differences between heat flux vectors can be defined uniquely. It is shown also that any set of coupled expressions for simultaneous, steady water and heat flow in soil that is compatible with TIP can be used to derive the Jury-Miller formulation of the flux equations by means of linear transformations. Moreover, the cross-coupling coefficient that links the heat flux to the gradient of water content vanishes identically in this formulation. However, a particular definition of the heat flux is implied by the Jury-Miller equations and its relationship to the measured heat flux cannot be established solely by the methods of TIP. An examination of the data on heat and water flow reported by Jury and Miller indicated that the experimental sensitivity was not sufficient to discriminate among several alternative definitions of the heat flux that can be developed within TIP. This result serves to emphasize the point that the identification of the heat flux actually measured in a coupled flow experiment must be on the basis of either a theoretical model of the coupled flow processes or an application of the general equation of total energy balance.

¹ Contribution from the Dep. of Soil and Environmental Sciences, University of California, Riverside, CA 92521.

² Research Soil Physicist, Professor of Soil Science, and Professor of Soil Physics, respectively.

Received for publication June 6, 1982. Accepted for publication September 16, 1982.

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