TRANSPORT PROCESSES IN THE SOIL-PLANT SYSTEM 715 



proportional to the appropriately denned transmission coefficient and 

 potential gradient. The preceding sections of this paper have con- 

 sidered in some detail the application of the General Transport Law to 

 the flow of water in the soil-plant system. Attention is now given to a 

 more abridged discussion of other important transport phenomena oc- 

 curring in soils and plants— phenomena which are fundamentally simi- 

 lar to the flow of water. 



Heat flow 



Thermal energy is transported primarily by the process of conduc- 

 tion in soils and plant tissues in response to temperature gradients. 

 Transport also occurs, particularly between the plant and soil surfaces 

 and the atmosphere, by radiation and convection. The thermal conduc- 

 tivity of the solid, liquid, and gaseous components of the soil have 

 relative values of 1.0, 1.7, and 0.07. Transport through soil in response 

 to a given temperature gradient is highly dependent ol the volume- 

 fractions of the solid, liquid, and gaseous phases. The specific heat of 

 the soil components also is quite different when expressed on a volume 

 basis. Therefore the temperature responses that occur as the result of 

 heat flux into or from a unit volume of soil also are highly dependent 

 on the volume-fractions of the solids, liquids, and gases that comprise 

 the soil. The thermal properties of plant tissues are dominated by their 

 high moisture content, and the thermal conductivity and heat capacity 

 of living plants may be considered to be equal to those of an equal vol- 

 ume of water held in the same geometric configuration. 



The flow of heat in the soil-plant system is in many respects simi- 

 lar to the flow of water, in that it is a highly dynamic phenomenon 

 which shows characteristic diurnal and seasonal variations and is af- 

 fected, although not as greatly as is water flow, by the bulk density and 

 moisture content of the material through which the flow occurs. Heat- 

 flow problems are simplified by the fact that both the specific heat and 

 the thermal conductivity are largely independent of the temperature 

 and are free of hysteresis effects. In analyzing heat-flow problems in 

 soils and plants, it is necessary to account for the heat sinks and sources 

 found within the system and for the transfer of heat by the movement 

 of water and water vapor in the system. 



Heat-flow problems, because of their greater inherent simplicity, 

 have been analyzed more extensively than problems involving fluid 

 flow in unsaturated porous media, and as a consequence they have 

 been widely used as models for the mathematical analysis of the more 

 complex problems of water flow (Carslaw and Jaeger, 1947; Philip, 

 1957). To analyze fully the highly dynamic behavior of water in the 

 soil-plant atmosphere system, it is necessary to incorporate into the 



