Page 159 - Biosystems Engineering
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138    Cha pte r  F o u r

                   Gori (1983) developed an empirical model for unsaturated frozen
               soils that was extended by Tarnawski et al. (2000) and Tarnawski and
               Gori (2002). Tarnawski et al. (2000) described the development of the
               Kersten function, which is dependent on soil temperature and on the
               degree of saturation. The new Kersten function enabled the predic-
               tion of the soil thermal conductivity at different moisture contents
               and temperatures. The function produced good results for dry soils
               (moisture content below PWP) at temperatures ranging from 30 to
               90°C, and for wet soils at temperatures ranging from 30 to 50°C.
               Tarnawski and Gori (2002) presented a more accurate model to pre-
               dict thermal conductivity at high temperatures. The model was appli-
               cable between 5 and 90°C, with better results for dry soils.
                   In further studies, a model for determining soil thermal conduc-
               tivity that was valid for dry soils at PWP moisture content was
               presented. Such a model improved the estimation of thermal conduc-
               tivity, such that it could be incorporated into heat-transfer models
               that included latent heat as a component (Tarnawski and Leong 2000).
               Later, Tarnawski et al. (2001) developed a software package that
               allowed for determining the soil effective thermal conductivity at
               high temperatures (50 to 90°C). The relationship between conductiv-
               ity and temperature was no longer linear because of the influence of
               mass transport, which showed strong dependence on the soil hydraulic
               properties.
                   Balland and Arp (2005) developed a new method, based on the
               method by Johansen (1975), to seamlessly calculate thermal conduc-
               tivity for various soil conditions, from loose to compact, organic to
               mineral, fine to coarse textured, frozen to unfrozen, and dry to wet.
               This generalization was fine-tuned empirically with data from soil,
               gravel, and peat drawn, for frozen and unfrozen conditions from –30
               to 30°C, and for variable moisture and bulk density conditions from
               dry to saturated. Usowicz et al. (2006) obtained thermal conductivi-
               ties on silt loam in a sloping vineyard from a statistical–physical
               model. It was shown that the performance of the equations relating
               the thermal conductivity with penetration resistance and air-filled
               porosity was greater than it was with penetration resistance and vol-
               umetric water content. Zhang et al. (2007) developed a method for
               estimating the effective thermal conductivity of the soil from thermal
               properties and volume fractions of the components, considering that
               the constituent parts of the multiphase medium were all cubic in
               shape and randomly mixed. In addition, the difference of the thermal
               characteristics between the frozen and unfrozen soils was discussed.
               Lu et al. (2007) developed an improved model that described the rela-
               tionship between thermal conductivity and volumetric water content
               of soils. Soil thermal conductivity could be estimated using soil bulk
               density, sand (or quartz) fraction, and water content. Except for the
               sand, the precision of their model improved considerably the Johan-
               sen (1975) model.
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