Estimating Soil Thermal Conductivity by Weighted Average Models with Soil Solids as a Continuous Medium

In an attempt to further simplify and to refine the modeling of soil thermal conductivity (lambda), two novel weighted average models (WAMs) were developed in which soil solids represent the continuous phase. In the first model, WAM(s)-1, the continuous phase consists of two distinctive minerals groups (quartz and compounded remaining soil minerals), while air and water are treated as dispersed components. In the second model, WAM(s)-2, all soil minerals are compounded and considered the continuous phase, while air and water are dispersed components. In contrast to de Vries' original WAM with two continuous phases (soil air or soil water), the proposed models are very simple due to the following assumptions: using soil solids as a single continuous medium lead to eliminating the discontinuity of thermal conductivity when switching between soil air and soil water as continuous medium, and using the thermal conductivity of dry air simplifies a complex expression for an apparent thermal conductivity of humid soil air. Both models were successfully calibrated and validated using 39 Canadian Field Soil database and 3 Standard Sands and were successfully applied to 10 Chinese soils

Extension of soil thermal conductivity models to frozen meats with low and high fat content

Thermal conductivity models of frozen soils were analyzed and compared with similar models developed for frozen foods. In total, eight thermal conductivity models and 54 model versions were tested against experimental data of 13 meat products in the temperature range from 0 toK40 8C. The model by deVries, with waterCice (wi) as the continuous phase, showed overall the best predictions. The use of wi leads generally to improved predictions in comparison to ice; water as the continuous phase is beneficial only to deVries model, mostly from K1 to K20 8C; fat is advantageous only to meats with high fat content. The results of this work suggest that the more sophisticated way of estimating the thermal conductivity for a disperse phase in the deVries model might be more appropriate than the use of basic multi-phase models (geometric mean, parallel, and series). Overall, relatively small differences in predictions were observed between the best model versions by deVries, Levy, Mascheroni, Maxwell or Gori as applied to frozen meats with low content of fat. These differences could also be generated by uncertainty in meat composition, temperature dependence of thermal conductivity of ice, measurement errors, and limitation of predictive models

Theoretical prediction of the thermal conductivity of frozen foods

Frozen food is theoretically modelled as a porous medium, consisting of an arrangement of cubic fibers surrounded by ice and unfrozen water. The original model, developed for frozen soils, has been improved for the prediction of the thermal conductivity of frozen foods as a function of water content, porosity and temperature. The theoretical prediction of the thermal conductivity is carried out with the solution of the heat conduction equation under the assumption of a prescribed temperature or heat flux distribution. Two thermal conductivityt values are then obtained, based on two thermal assumption, i.e. parallel isotherms or parallel heat flux lines, in order to confine the real solution within the two extremes. The amount of unfrozen water, present in the frozen food, has been taken into from the experimental data, using an empirical relation dependent on the temperature. The final comparison has been carried out between the theoretical solutions and the experimental data available in the literature, in the temperature range from 0 °C to -40 °C. The theoretical results show a fair agreement with the experimental data

Theoretical prediction of the thermal conductivity of frozen foods

Frozen food is theoretically modelled as a porous medium, consisting of an arrangement of cubic fibers surrounded by ice and unfrozen water. The original model, developed for frozen soils, has been improved for the prediction of the thermal conductivity of frozen foods as a function of water content, porosity and temperature. The theoretical prediction of the thermal conductivity is carried out with the solution of the heat conduction equation under the assumption of a prescribed temperature or heat flux distribution. Two thermal conductivityt values are then obtained, based on two thermal assumption, i.e. parallel isotherms or parallel heat flux lines, in order to confine the real solution within the two extremes. The amount of unfrozen water, present in the frozen food, has been taken into from the experimental data, using an empirical relation dependent on the temperature. The final comparison has been carried out between the theoretical solutions and the experimental data available in the literature, in the temperature range from 0 °C to -40 °C. The theoretical results show a fair agreement with the experimental data

Volcanic Soils: Inverse Modeling of Thermal Conductivity Data

Volcanic ash soils are formed from ash and cinder deposits that largely consist of non-crystalline minerals, volcanic glass and organic matter. Their application to engineering ground technology requires a thorough knowledge and good understanding of their historical formation, structure, mineralogy and thermal and hydraulic properties. Consequently, inverse modeling was applied to the thermal conductivity () data of 22 soils from Hokkaido (northern Japan). A large majority of these soils contained volcanic ash that markedly influenced their physical properties. For example, 11 natural soils (volcanic, highland and lowland soils) had average values of 0.14W m(-1)K(-1) and 0.52Wm(-1)K(-1) at dryness ((dry)) and saturation ((sat)), respectively. The inverse modeling of data revealed that the average values of soil solids ((s)) and volcanic glass ((vgl)) were about 0.48Wm(-1)K(-1) and 0.25Wm(-1)K(-1), respectively. The influence of organic matter on (s) was found to have a minor effect. A reverse analysis of saturated frozen soils revealed that, at -5 degrees C, about 87% of water was converted into ice, i.e., unfrozen water content ((un-w))approximate to 0.13

Thermal conductivity of standard sands. Part I. dry-state conditions

A comprehensive thermal conductivity (lambda) database of three dry standard sands (Ottawa C-109, Ottawa C-190, and Toyoura) was developed using a transient line heat source technique. The database contains lambda data representing a variety of soil compactions and temperatures (T) ranging from 25 A degrees C to 70 A degrees C. The tested standard sands, due to their repeatable physical characteristics, can be used as reference materials for validation of thermal probes applied to similar dry granular materials. The measured data show an increasing trend of thermal conductivity at dryness (lambda(dry)) against T in spite of declining quartz lambda with T. The air content (porosity) controls the lambda of dry sands by acting as a very effective thermal insulator around solid soil particles. As a result, a diminutive increase of lambda(dry) with T is driven by increasing lambda of air. The experimental lambda data of dry sands were exceptionally well predicted by de Vries and Woodside-Messmer models, and also by a thermal conductance model, a product of lambda of solids and the thermal conductance factor

Thermal Conductivity of Pyroclastic Soil (Pozzolana) from the Environs of Rome

The paper reveals the experimental procedure and thermo-physical characteristics of a coarse pyroclastic soil (Pozzolana), from the neighborhoods of Rome, Italy. The tested samples are comprised of 70.7% sand, 25.9% silt, and 3.4% clay. Their mineral composition contained 38% pyroxene, 33% analcime, 20% leucite, 6% illite/muscovite, 3% magnetite, and no quartz content was noted. The effective thermal conductivity of minerals was assessed to be about 2.14W·m−1·K−1. A transient thermal probe method was applied to measure the thermal conductivity (λ) over a full range of the degree of saturation (Sr), at two porosities (n) of 0.44 and 0.50, and at room temperature of about 25 ◦C. The λ data obtained were consistent between tests and showed an increasing trend with increasing Sr and decreasing n. At full saturation (Sr = 1), a nearly quintuple λ increase was observed with respect to full dryness (Sr = 0). In general, the measured data closely followed the natural trend of λ versus Sr exhibited by published data at room temperature for other unsaturated soils and sands. The measured λ data had an average root-mean-squared error (RMSE) of 0.007W·m−1·K−1 and 0.008W·m−1·K−1 for n of 0.50 and 0.44, respectively, as well as an average relative standard deviation of the mean at the 95%confidence level (RSDM0.95) of 2.21% and 2.72 % for n of 0.50 and 0.44, respectively. B V. R. Tarnawski vlodek.tarnawski

Canadian Field Soils IV: Modeling Thermal Conductivity at Dryness and Saturation

The thermal conductivity data of 40 Canadian soils at dryness (lambda(dry)) and at full saturation (lambda(sat)) were used to verify 13 predictive models, i.e., four mechanistic, four semi-empirical and five empirical equations. The performance of each model, for lambda(dry) and lambda(sat), was evaluated using a standard deviation (SD) formula. Among the mechanistic models applied to dry soils, the closest lambda(dry) estimates were obtained by MaxRTCM (SD = +/- 0.018 Wm(-1).K-1), followed by de Vries and a series-parallel model (S-||). Among the semi-empirical equations (deVries-ave, Advanced Geometric Mean Model (A-GMM), Chaudhary and Bhandari (C-B) and Chen's equation), the closest lambda(dry) estimates were obtained by the C-B model (+/- 0.022 Wm(-1).K-1). Among the empirical equations, the top lambda(dry) estimates were given by CDry-40 (+/- 0.021 Wm(-1).K-1 and +/- 0.018 Wm(-1).K-1 for18-coarse and 22-fine soils, respectively). In addition, lambda(dry) and lambda(sat) models were applied to the lambda(sat) database of 21 other soils. From all the models tested, only the maxRTCM and the CDry-40 models provided the closest lambda(dry) estimates for the 40 Canadian soils as well as the 21 soils. The best lambda(sat) estimates for the 40-Canadian soils and the 21 soils were given by the A-GMM and the S-|| model

Soil thermal conductivity model by de Vries: Re-examination and validation analysis

The thermal conductivity (lambda) of soils is an important property in a variety of science and engineering applications. One of the most widely used lambda models in soil science was proposed by de Vries (deV-0). This model is complicated and difficult to use as it is based on several controversial assumptions. The deV-0 assumes that a soil system is composed of non-contacting solid particles (rotated uniform ellipsoids) that are dispersed in a continuous homogeneous medium (air or water). Furthermore, deV-0 assumes that soil solids consist of quartz and consolidated bulk minerals. These assumptions do not reflect the true nature of soils that are composed of several compacted minerals, diverse in shape and notably different in size. A critical analysis of this model concluded that its most controversial feature was inherited from an electrical conductivity model for a two-phase dispersion system; specifically, from weighting shape factors of non-contacting rotated oblate ellipsoids. Furthermore, deV-0 has not yet been fully examined and verified with respect to a comprehensive and complete soil lambda database. Also, there is a lack of comparable models to deV-0 that would contain a complete set of clearly described and linked expressions. Consequently, two slightly adjusted versions of deV-0 were developed; namely, deV-1 with soil bulk mineralogy (quartz plus integrated residual minerals) and deV-2 with complete soil mineralogy (i.e., including individual contributions from all soil minerals). Both models underwent successful calibration and verification against lambda data of 39 Canadian field soils and three Standard sands. Markedly improved estimates (lambda(est)) were obtained when, instead of dry air thermal conductivity (lambda(a)), an apparent air thermal conductivity (lambda(a-app) = lambda(a) + lambda(v)) was applied (lambda(v) represents thermal effects caused by migration of water vapour and evaporation/condensation processes). For deV-1, the following reduction of standard deviation (SD) data was obtained: 53.5% for 17 coarse soils, 34% for 22 fine soils, and 44.5% for all 39 soils. Then, the same calibration factors of deV-1 were applied to the deV-2 model and a similar reduction of SD data was obtained (52.7, 24.1 and 40.1%, respectively). Generally, for 39 Canadian field soils, both models (deV-1 and deV-2), with quartz thermal conductivity (lambda(qtz)) of 7.6 W center dot m(-1)center dot K-1, produced very close lambda estimates (SD approximate to 0.099 and 0.094 W center dot m(-1)center dot K-1, respectively). Taking into account the simplicity of mineral composition and fewer calibration coefficients, deV-1 was a preferable choice. For that reason, soil bulk mineralogy appears to be a good equivalent to complete soil mineralogy. Also, for Standard sands (100% sand: C-109, C-190, NS-04), improved lambda(est) were obtained by replacing lambda(a) with lambda(a-app). Finally, the deV-1 model was successfully applied to 10 Chinese soils and the following average SD values were obtained: for four coarse soils 0.135 W center dot m(-1)center dot K-1, whereas for six fine soils 0.127 W center dot m(-1)center dot K-1.HighlightsThe original lambda model by de Vries (deV-0) underestimates experimental lambda data.Two modified deV-0 versions were developed: deV-1, quartz + bulk minerals; deV-2, all soil minerals.Improved estimates were obtained when, instead of dry air lambda, an apparent air lambda was applied.The deV-1 model was successfully applied to 10 Chinese soils