Abstract
After a spacious research and consideration on various approaches of thermal coupled formulations in porous media, a new mathematical form of coupled heat, moisture, and air transfer in unsaturated soil is proposed upon taking the effect of combined volumetric moisture content and temperature gradients and air pressure changes. In this matter, in the convective flows through the unsaturated heated soil, the effects of sensible and latent heat of vapor are also composed with the water and dry air fluxes. Thus in this aspect, some new material parameters are defined for the derived equations, which are related to thermodynamic specifications of soil and the soil-water characteristic curve. After that, the application of the model is presented with a numerical example of a ground heat exchanger which is buried in the earth vertically. It could be considered as an interior heating source which operates in extracting saved energy from the earth or emitting heat to the ground. Then, by using some thermal graphs, the influence of the different operating ratio is investigated which are compared with the full operating mode at all times. Meanwhile, the mode1 is verified by comparing its results against those established by other researchers. By the results, it was found that the volumetric water content and specific heat capacity are the main factors could be effective to generate directly the thermal and isothermal diffusivities and conductivities in terms of the thermodynamic properties.
Similar content being viewed by others
References
L. Fengzhi, L. Yi, L. Yingxi and L. Zhongxuan, Numerical simulation of coupled heat and mass transfer in hygroscopic porous materials considering the influence of atmospheric pressure, Numerical Heat Transfer, B 45(3) (2004) 249–262.
J. Irudayaraj, Y. Wu, A. Ghazanfari and W. Yang, Application of simultaneous heat, mass and pressure transfer equations to timber drying, Numerical Heat Transfer, A 30(3) (1996) 233–247.
J. Wang, N. Christakis, M. K. Patel, M. Cross and M. C. Leaper, A computational model of coupled heat and moisture transfer with phase change in granular sugar during varying environmental conditions, Numerical Heat Transfer, A 45(8) (2004) 751–776.
K. Boomsma and D. Poulikakos, On the effective thermal conductivity of a threedimensionally structured fluidsaturated metal foam, Int. J. Heat Mass Transfer, 44 (2001) 827–836.
L. Z. Zhang, Numerical study of heat and mass transfer in an enthalpy exchanger with a hydrophobic-hydrophylic composite membrane core, Numerical Heat Transfer, A 51(7) (2007) 697–714.
Stephen O. Olutimayin and Carey J. Simonson, Measuring and modeling vapor boundary layer growth during transient diffusion heat and moisture transfer in cellulose insulation, Int. J. of Heat and Mass Transfer, 48 (2005) 3319–3330.
Q. Jiang and R. K. N. D. Rajapakse, A boundary integral equation formulation for coupled heat-moisture transfer in porous media, Inr. J. Engng Sci., 29(8) (1991) 889–900.
W. K. Lewis, The rate of drying of solid materials, The journal of industrial and engineering chemistry, Symp. Drying (1921) 427–432.
L. A. Richards, Capillary conduction of liquids through porous mediums, Physics, 1 (1931) 318–333.
W. O. Smith, Thermal transfer of moisture in soils, Trans. Am. Geophys, Union 24 (1943) 511–523.
J. R. Philip and D. A. deVries, Moisture movement in porous media under temperature gradients, Trans. Am. Geophys, Union 38 (1957) 222–232.
W. Woodside and J. M. Kuzmak, Effect of temperature distribution on moisture flow in porous materials, Trans. Am. Geophys, Union 39 (1958) 676–680.
A. V. Luikov, On thermal diffusion of moisture, (in Russian), Zh. Prikl. Khim, 8 (1935).
A. V. Luikov, Moisture gradients in the drying clay, Trans. Cernm. Sot, 35 (1936) 123–129.
M. A. Sophocleous, Analysis of water and heat flow in unsaturated-saturated porous media, Water Resources Research, 15(5) (1979) 1195–1206.
P. C. D. Milly, Moisture and Heat Transport in Hysteretic, Inhomogenious Porous Media: A Matric Head-Based Formulation and a Numerical Model, Water Resources Research, 18(3) (1982) 489–498.
P. C. D. Milly, A simulation analysis of thermal effects on evaporation from soil, Water Resources Research, 20(8) (1984) 1087–1098.
M. A. Celia, E. T. Boulotas and R. Zarba, A general mass conservative numerical solution for the unsaturated flow equation, Water Resources Research, 26(7) (1990) 1483–1496.
A. Chanzy and L. Bruckler, Signification of soil surface moisture with respect to daily bare soil evaporation, Water Resources Research, 29(4) (1993) 1113–1125.
G. W. Wilson, D. G. Fredlund and S. L. Barbour, Coupled soil-atmosphere modeling for soil evaporation, Can. Geotech. J., Ottawa, Canada, 31(2) (1994) 151–161.
A. V. Luikov, Heat and Mass Transfer in Capillary porous Bodies, Pergamon Press, Oxford, U.K. (1996).
G. D. Fulford, A survey of recent Soviet research on the drying of solids, Can. J. Chem. Engng 47 (1969) 378–391.
A. V. Luikov, Systems of differential equations of heat and mass transfer in capillary-porous bodies (review), Int. J. Heat Mass Transfer, 18 (1975) l–14.
O. Krischer, Die Wissenschaftlichen Grundlagen der Trocknungstechnik, Springer, Berlin (1963).
S. A. Taylor, and J. W. Cary, Analysis of the simultaneous flow of water and heat or electricity with the thermodynamics of irreversible processes, in 7th International Congress of Soil Science Transactions, 1 (1960) 80–90.
D. R. Nielsen D. R., R. D. Jackson, J. W. Cary and D. D. Evans, Soil Water. American Society of Agronomy and Soil Science Society of America, Madison, Wisconsin (1972).
R. Ash and R. M. Barrer, Three phase flow in a temperature gradient, Trans. Faraday Sot, 59, 2260–2261, 1963.
H. Vink, Diffusion in porous media, Ark. Kemi 17 (1962) 311–317.
R. G. Mokadam, Application of the thermodynamics of irreversible process to the flow of a multicomponent liquid through porous media, Znt. Chem. Engng 3 (1963) 571–576.
J. Y. Baladi, Transient heat and mass transfer in soils, Ph.D. Thesis, Purdue University, West Lafayette, Indiana (1975).
D. L. Slegel and L. R. Davis, Transient heat and mass transfer in soils in the vicinity of heated porous pipes, J. Heat Transfer, 99C(4) (1977) 541–546.
A. R. Sepaskhah, L. L. Boersma, L. R. Davis and D. L. Slegel, Experimental analysis of a subsurface soil warming and irrigation system utilizing waste heat, American Society of Mechanical Engineers Paper, No. 73-WA/HT-11, Winter Annual Meeting, Detroit, Michigan (1973).
J. G. Knudsen and L. L. Boersma, Future developments in waste heat utilization, Summary Report of a National Workshop held at Portland, Oregon, 16–17 December 1964, Circular No. 49. Engineering Experiment Station, Oregon State University (1975).
M. Geraminegad and S. K. Saxena, A coupled thermoelastic model for saturated-unsaturated porous media, Geotechnique, London, 36(4) (1986) 539–550.
D. W. Pollock, Simulation of fluid flow and energy transport processes associated with high-level radioactive waste disposal in unsaturated alluvium, Water Resources Research, 22(5) (1986) 765–775.
J. Ewen and H. R. Thomas, Heating unsaturated medium sand, Geotechnique, 39(3) (1989) 455–470.
H. R. Thomas and S. D. King, Coupled Temperature/Capillary Potential Variations in Unsaturated Soil, Journal of Engineering Mechanics, ASCE, 117(11) (1991) 2475–2491.
H. R. Thomas, E. E. Alonso and A. Gens, Modelling thermo/hydraulic/mechanical processes in the containment of nuclear waste, Proc., 1st Int. Conf. on Unsaturated Soils, 2 (1995) 1135–114195.
H. R. Thomas and Y. He, Analysis of coupled heat, moisture and air transfer in a deformable unsaturated soil, Geotechnique, London, 45(4) (1995) 677–789.
S. Olivella, Nonisothermal multiphase flow of brine and gas through saline media, Doctoral thesis, Dept. of Geotech, Engrg., Universitat Politenica Catalunya, Barcelona, Spain (1995).
H. R. Thomas, S. W. Rees and N. J. Sloper, Three dimensional heat, moisture and air transfer in unsaturated soils, International Journal for Numerical and Analytical Methods in Geomechanics, 22(2) (1998) 75–95.
H. R. Thomas and Sansom M. R., Fully coupled analysis of heat, moisture, and air transfer in unsaturated soil, Journal of Engineering Mechanics, 121 (1995) 392–406.
D. G. Fredlund and V. Dakshanamurthy, Prediction of moisture flow and related swelling or shrinking in unsaturated soils, Geotech. Engrg., Bangkok, Thailand, 13 (1982) 15–49.
Lu Ning and William J. Likos, Unsaturated Soil Mechanics, Published by John Wiley & Sons, Inc., Hoboken, New Jersey (2004).
M. Nakano and T. Miyazaki, The Diffusion and nonequilibrium thermodynamic equations of water vapor in soils under temperature gradients, Soil Sci., 128(3) (1979) 184–188.
R. C. Weast, Handbook of chemistry and physics, 57th Ed., CRC Press, Cleveland, Ohio (1976).
D. Q. Yang, H. Rahardjo, E. C. Leong, V. Choa and S. K. Kong, A coupled heat, moisture and air flow model for unsaturated soils, 3rd Asian Young Geotechnical Engineers Conference, Singapor (1997) 337–346.
L. Barden, Consolidation of compacted and unsaturated clays, Geotechnique, London, 15(3) (1965) 267–286.
Li Xinguo, Jun Zhao and Qian Zhou, Inner heat source model with heat and moisture transfer in soil around the underground heat exchanger, Applied Thermal Engineering, 25 (2005) 1565–1577.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Jun Sang Park
Mohammad Hossein Jahangir is a Ph.D student of civil engineering at Khaje Nasirodine Toosi University of Technology in Tehran. His scientific interests are in heat and mass transfer, thermal science, thermodynamics in unsaturated soils, numerical methods and earthquake engineering. He Published more than 20 papers in international scientific journals and conferences since 2008 up to now. Mr. Jahangir is a chartered senior engineer, a fellow of the Iranian Inventors Association, a member in good standing of Iranian Society of Civil Engineers and a Fellow of the Institution of Structural Engineers.
Seyed Amirodin Sadrnejad graduated at Cardiff College, University of Wales, in civil and geo-environmental engineering (1986), and got his Ph.D in 1989 on Finite Elements Methods and Geomechanics. Professor Sadrnejad is currently one of the members for the geotechnical engineering of Khaje Nasirodine Toosi University of Technology in Tehran. His research interests are in the areas of numerical methods, nanotechnology in civil engineering, geomechanics and hydraulic structures. He is the author or coauthor of over 200 scientific publications and 10 books, reviewer of many international journals in civil engineering, editor of several conference proceeding and editor-in-chief of the International Journal of Civil Engineering published by ISCE.
Rights and permissions
About this article
Cite this article
Jahangir, M.H., Sadrnejad, S.A. A new coupled heat, moisture and air transfer model in unsaturated soil. J Mech Sci Technol 26, 3661–3672 (2012). https://doi.org/10.1007/s12206-012-0839-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-012-0839-z