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130    Cha pte r  F o u r

               4.2.3 Effective Thermal Diffusivity
               The effective thermal diffusivity describes the soil thermal inertia
               measured as temperature variation due to heat flow (Porta et al. 1999),
                   2
                     –1
               in m  s :
                                            k
                                       D =   e
                                        T   C                        (4.3)
                                             V
               Because the effective thermal diffusivity is defined as the ratio of
               effective thermal conductivity to volumetric heat capacity, the value
               of effective thermal diffusivity increases with temperature when the
               effective thermal conductivity increases and the heat capacity remains
               almost constant.

               4.2.4  Determination of Soil Thermal Properties
               For many years, the determination of soil thermal properties has gener-
               ated considerable interest among researchers, which evidences the com-
               plexity of the process. Two main approaches have been tried: (1) using
               indirect measurements to experimentally determine soil thermal proper-
               ties, or (2) estimating soil thermal properties from other soil properties.

               Experimental Methods to Determine Thermal Properties
               Apart from the calorimetric methods used by de Vries (1963), many
               indirect methods have been proposed for estimating effective con-
               ductivity, specific heat, and thermal diffusivity of the soil. Thermal
               properties can be determined indirectly by measuring the rise or fall
               of temperature in response to heat input to a line source at the point
               of interest (Jackson and Taylor 1965). On this basis, many methods
               have been developed to determine the soil thermal properties. A clas-
               sification of indirect methods is shown in Fig. 4.1.
                   Various authors have used the solution of the heat-conduction
               equation to indirectly determine the thermal properties of soil, which
               allows for the determination of thermal properties from quantities
               that can be easily measured in situ, for example, temperature, with
               negligible disturbances of the natural state of the soil. The type of
               equation used (implicit or explicit) and the solution of the expres-
               sions used (analytical or numerical) have generated various methods
               with different requirements, both in terms of data and of data acquisi-
               tion and processing resources (Horton et al. 1983).
                   Wierenga et al. (1969) obtained values of soil thermal properties
               based on laboratory and field measurements. Later, Singh and Sinha
               (1977) evaluated thermal diffusivity by using a numerical solution to
               the heat-conduction equation based on Dirichlet-type boundary con-
               ditions and fitting the heat-conduction equation for soil by cubic
               splines. From that moment, exact solutions alternated with approxi-
               mate solutions to the heat-conduction equation, and the accuracy and
               possibilities of use of both types of methods were analyzed.
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