Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model (original) (raw)
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Journal of Water Resource and Protection, 2014
Penetration of chemicals in the soil ground through irrigation water or rainfall induces important risks for the environment. These risks are badly known and may lead to direct contamination of the environment (atmosphere or ground water) or harmful effects on organisms living at ground level, indirectly affecting men. It is thus necessary to estimate these potential chemical risks on the environment. For that reason, the gradual change of these products (fertilizers, solutions, pollutants, ...) in the ground has been the subject of a lot of recent research works, based in particular on the study of non-saturated porous media in a theoretical, numerical or experimental way. Most of these works are incomplete and, in order to simplify the problem, they don't take into accounts some process, which may be of prime importance under particular natural conditions. Complexity of such studies results from their multidisciplinary nature. In this communication, we study simultaneous transport of pollutant, the water that provides transport and the heat transfer in a 200 cm long cylindrical column full of sand taken as a non-saturated porous medium. We consider two kinds of conditions on the temperature at the column surface: the case of constant temperature and the case of sinusoidal temperature. We evaluate the influence of this temperature on the transfers. This study is purely numerical. We use the control volume method to determine hydrous, thermal and pollutant concentration profiles.
1997
Soil surface dynamics involve coupled transfer of heat, water, and solute. An experimental and theoretical study of heat, water, and solute transfer in closed compacted soil columns under surface temperature wave amplitudes is presented. The temperature wave amplitudes ranged from 17.9 to 21.0 C. Potassium chloride solution was used to moisten Clarinda clay and Fayette silty clay loam soils. Initial water contents of 0.403 and 0.279 and initial solute concentrations of 0.062 and 0.052 mol kg 1 were used in Clarinda and Fayette soils, respectively. The moistened soils were packed and compacted in PVC columns (0.075 m diameter and 0.30 m high). Bulk densities of the compacted Clarinda and Fayette soils were 1403 and 1585 kg m 3 , respectively. The columns were buried in soil such that column surfaces were exposed to natural as well as artificial radiation and thermal conditions. The coupled nonsteady-state balance equations of mass and energy were solved numerically to predict soil temperature, water content, and solute concentration distributions. The theoretical model described soil temperature, water content, and solute concentration well as compared with the measured values. The Fickian diffusive solute flux was one or two orders of magnitude greater than salt-sieving and thermal-diffusion solute fluxes.
Heat and contaminant transport in unsaturated soil
Solute transport in unsaturated porous media can be viewed as a coupled phenomenon with water and heat transport, together with mechanical behaviour of media. In this paper, solute transport is formulated mathematically considering heat and water flow in deformable porous media. Advection, dispersion and diffusion of chemical species in the liquid phase are considered. Convection and conduction for heat flow is taken into account. Water flow is considered in both vapour and liquid phases. Equilibrium equation, energy conservation, mass conservation and linear momentum for water, gas and solute are written and solved simultaneously using finite element method. The developed model is validated by solving some examples and comparing results with the results of experimental observation.
Numerical study of water and heat transfer in unsaturated clay-loam soil
International Journal for Simulation and Multidisciplinary Design Optimization, 2014
This present study is the numerical estimation of the temperature distribution and the water content distribution underground soil under the Mediterranean climate type. We use as input data of ambient temperature, air humidity and solar radiation, average values during 10 years estimated from data supplied by the local meteorological station (Tizi-Ouzou, Northern Algeria, 36°47′59″, North latitude and 4°1′59″, East longitude). A theoretical model, based on heat and water transfer equations, was established for an unsaturated soil submitted to the climatic conditions of this site. The mathematical model established in mono dimensional type, for a semi infinite transfer model, is based on Whitaker theory of heat and mass transfers in unsaturated porous medium (Withaker 1977, 1980) with the hypothesis that air pressure into soil porosity is equal to atmospheric pressure. The equations were discretized according to the finite volume method, which is more adapted for this type of problem...
On the Influence of Boundary Conditions in Modeling Heat Transfer in Soil
Journal of engineering physics and thermophysics, 2017
A procedure to determine the thermal diffusivity of soils, which is based on the heat-transfer equation, has been developed. Experimental investigations were carried out to establish the infl uence of boundary conditions on the soil surface on the solution of inverse problems of modeling of heat transfer in soil. On the basis of these data, the author has calculated thermal diffusivity in soils with the proposed methods developed for the case with one and two harmonics and a comparison of these methods has been made; the calculated characteristics and experimental results have also been compared.
Thermal properties of soils as affected by density and water content
Biosystems engineering, 2003
Thermal properties dictate the storage and movement of heat in soils and as such influence the temperature and heat flux in soils as a function of time and depth. The ability to monitor soil heat capacity is an important tool in managing the soil temperature regime to affect seed germination and crop growth. The effect of water content and bulk density on the specific heat, volumetric heat capacity, and thermal diffusivity of some sieved and repacked soils was investigated through laboratory studies. These laboratory experiments used the calorimetric method to determine specific heat of soils. The soils used were classified as sand and clay. For the type of soils studied, specific heat increased with increased moisture content. Also, volumetric heat capacity increased with increased moisture content and soil density. Volumetric heat capacity ranged from 1Á48 to 3Á54 MJ m À3 8C À1 for clay and from 1Á09 to 3Á04 MJ m À3 8C À1 for sand at moisture contents from 0 to 0Á25 (kg kg À1 ) and densities from 1200 to 1400 kg m À3 . Specific heat ranged from 1Á17 to 2Á25 kJ kg À1 8C À1 for clay and from 0Á83 to 1Á67 kJ kg À1 8C À1 for sand at moisture contents from 0Á02 to 0Á25 (kg kg À1 ) and soil density of 1300 kg m À3 . The volumetric heat capacity and specific heat of soils observed in this study under varying moisture content and soil density were compared with independent estimates made using derived theoretical relations. The differences between the observed and predicted results were very small. Clay soil generally had higher specific heat and volumetric heat capacity than sandy soil for the same moisture content and soil density. The results also show that thermal diffusivity vary with moisture content and soil texture. Sandy soil exhibited a thermal diffusivity peak at a definite moisture content range. Clay soil, however, did not exhibit a sharp thermal diffusivity peak.
A Theoretical Model of the Thermal Conductivity of Idealized Soil
HVAC&R Research, 1995
Accurate prediction of soil thermal conductivity is of prime importance in the numerical simulation of heat transmission through soils. This paper focuses upon empirical and semi-empirical prediction methods for soil thermal conductivity. A family of empirical correlations are presented which relate soil thermal conductivity to saturation for five soil types: gravel, sand, silt, clay, and peat. These correlations are developed from a database of measured data available in the literature. Also, a theoretical model of soil thermal conductivity is developed for granular materials composed of rotund particles in an almost dry state. This theoretical model includes the effects of the micro-structure and the conductivity of the solid phase. It explicitly relates soil thermal conductivity to dry density and agrees well with experimental data. This paper also presents a review and discussion of those factors which affect soil thermal conductivity, previously reported prediction methods, and conductivity measurement techniques.
Thermal conductivity and diffusivity of soil
International Communications in Heat and Mass Transfer, 1990
The thermal conductivity and diffusivity of soil has been experimentally measured using the line heat source transient method. Representative samples of different textures were collected and analyzed from different localities and depths. The effect of temperatures, in the range of -10°C â 35°C and moisture content up to 40% on the conductivity and diffusivity were investigated. The results of this
J. Agric. Sci, 2001
A pressure-based coupled heat and mass transfer model was used to simulate temperature and soil suction in a drying process within a clay soil column. Closed form functions were used for all parameters needed in the governing equations. Model predictions were compared with experimental data using the mean relative percentage deviation method. Thermocouples and mini-gypsum blocks were used to monitor the data collected hourly at different depths of the soil column. The model showed very high sensitivity to the proposed hydraulic conductivity function, while lower sensitivity was found for the proposed thermal conductivity function. This result highlights the importance of a proper hydraulic conductivity estimate while a rough estimate for thermal conductivity would have no significant adverse effect on the predicted values.