Skip to main content
Log in

Transient Heat and Moisture Flow Around Heat Source Buried in an Unsaturated Half Space

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

This article presents solutions for the transient heat and moisture transport due to both disk heat source and cylindrical heat source buried in an unsaturated half space. The solutions are presented in Hankel–Laplace transform domain and in dimensionless style. Coupled effect of thermally driven moisture transport is especially investigated because of its importance to alter the flow field in low-permeability medium. Parametric study has been performed to assess the effects of five independent dimensionless parameters on flow field. The stability and accuracy of the present solutions are demonstrated from the comparison between the results obtained from these solutions and those by using a well-established finite element code CODE_BRIGHT. Despite the simplified assumptions required in order to obtain analytical solutions in Hankel–Laplace transform domain, the results incorporate the main mechanisms involved in the coupled thermo-hydraulic (T-H) problem, and they may be eventually used for validation purposes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anders G.J., Radhakrishna H.: Power cable thermal analysis with consideration of heat and moisture transfer in the soil. IEEE Trans. Power Deliv. 3(4), 1280–1288 (1988). doi:10.1109/61.193921

    Article  Google Scholar 

  • Basha, H.A., Selvadurai, A.P.S.: Heat-induced moisture transport in the vicinity of a spherical heat source. Int. J. Numer. Anal. Methods Geomech. 22, 969–981 (1998). doi:10.1002/(SICI)1096-9853(199812)22:12<969::AID-NAG952>3.0.CO;2-R

    Google Scholar 

  • Benjamin J.G., Gaffarzadeh M.R.: Cruise, R.M.: Coupled water and heat transport in ridged soils. Soil Sci. Soc. Am. J 54(4), 963–969 (1990)

    Article  Google Scholar 

  • Booker J., Savvidou C.: Consolidation around a point heat source. Int. J. Numer. Anal. Methods Geomech. 9, 173–184 (1985). doi:10.1002/nag.1610090206

    Article  Google Scholar 

  • Crump K.S.: Numerical inversion of Laplace transform using a Fourier series approximation. J. ACM 23, 89–96 (1976). doi:10.1145/321921.321931

    Article  Google Scholar 

  • Chen G.J.: Consolidation of multilayered half space with anisotropic permeability and compressible constituents. Int. J. Solids Struct. 41, 4567–4586 (2004). doi:10.1016/j.ijsolstr.2004.03.019

    Article  Google Scholar 

  • Chen G.J., Ledesma A.: Coupled solution of heat and moisture flow in unsaturated clay barriers in a repository geometry. Int. J. Numer. Anal. Methods Geomech. 31, 1045–1065 (2007). doi:10.1002/nag.565

    Article  Google Scholar 

  • Durbin F.: Numerical inversion of the Laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J. 17, 371–376 (1974)

    Google Scholar 

  • ENRESA: FEBEX project final report: full-scale engineered barriers experiment for a deep geological repository for high level radioactive waste in crystalline host rock. Technical Publication 1/2000, Madrid, 2000.

  • Fityus S.G., Smith D.W.: Solution of the unsaturated soil moisture equation using repeated transforms. Int. J. Numer. Anal. Methods Geomech. 25, 1501–1524 (2001). doi:10.1002/nag.181

    Article  Google Scholar 

  • Hartley, J.G.: An analysis of the thermal stability of the soil environment of underground electrical cables. PhD thesis, Georgia Institute of Technology, Atlanta (1977)

  • Hartley J.G., Black W.Z.: Transient simultaneous heat and mass transfer in moist, unsaturated soils. J. Heat Transfer 101, 376–382 (1981)

    Article  Google Scholar 

  • Korn G.A., Korn T.M.: Mathematical handbook for scientists and engineerings. McGraw-Hill Inc., NY (1968)

    Google Scholar 

  • Lalouin L., Nuth M., Vulliet L.: Experimental and numerical investigations of the behaviour of a heat exchanger pile. Int. J. Numer. Anal. Methods Geomech. 30, 763–781 (2006). doi:10.1002/nag.499

    Article  Google Scholar 

  • Olivilla S., Gens A., Carrera J., Alonso E.E.: Numerical formulation for a similar (CODE_BRIGHT) for the coupled analysis of saline media. Eng. Comput. 13, 87–112 (1996). doi:10.1108/02644409610151575

    Article  Google Scholar 

  • Pan, E.: Green’s functions in layered poroelastic half-spaces. Int. J. Numer. Anal. Methods Geomech. 23, 1631–1653 (1999). doi:10.1002/(SICI)1096-9853(199911)23:13<1631::AID-NAG60>3.0.CO;2-Q

    Google Scholar 

  • Philip J.R., De Vries D.A.: Moisture movement in porous materials under temperature gradients. Eos Trans. AGU 38, 222–232 (1957)

    Google Scholar 

  • Pullan A.J.: The quasilinear approximation for unsaturated porous media flow. Water Resour. Res. 26(6), 1219–1234 (1990)

    Article  Google Scholar 

  • Savvidou C., Booker J.: Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties. Int. J. Numer. Anal. Methods Geomech. 13, 75–90 (1989). doi:10.1002/nag.1610130107

    Article  Google Scholar 

  • Selvadurai A.P.S.: The analytical method in geomechanics. Appl. Mech. Rev. 60, 87–106 (2007). doi:10.1115/1.2730845

    Article  Google Scholar 

  • Small J.C., Booker J.: The behavior of layered soil or rock containing a decaying heat source. Int. J. Numer. Anal. Methods Geomech. 10, 501–519 (1986). doi:10.1002/nag.1610100504

    Article  Google Scholar 

  • Svemar, C., Pusch, R.: Prototype repository—project description. Aspo Hard Rock Laboratory. International Progress Report IPR-00-30, SKB: Sweden, 2000.

  • Taguchi I., Kurashige M.: Fundamental solutions for a fluid-saturated, transversely isotropic, poroelastic solid. Int. J. Numer. Anal. Methods Geomech. 26, 299–321 (2002). doi:10.1002/nag.202

    Article  Google Scholar 

  • Thomas H.R.: Modelling two-dimensional heat and moisture transfer in unsaturated soils, including gravity effects. Int. J. Numer. Anal. Methods Geomech. 9, 573–588 (1985). doi:10.1002/nag.1610090606

    Article  Google Scholar 

  • Vardoulakis I., Harnpattanapanich T.: Numerical Laplace-Fourier transform inversion technique for layered soil consolidation problems: I. Fundamental solutions and validation. Int. J. Numer. Anal. Methods Geomech. 10, 347–365 (1986). doi:10.1002/nag.1610100402

    Article  Google Scholar 

  • Wynn P.: On a device for computing the e m (S n ) transformation. Math. Tables Aids Comput. 10, 91–96 (1956). doi:10.2307/2002183

    Article  Google Scholar 

  • Yu L.: Axisymmetric solutions for layered and porous viscoelastic media. Chin. J. Rock Soil Mech. 22(3), 276–280 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Li Yu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yu, L., Chen, G. Transient Heat and Moisture Flow Around Heat Source Buried in an Unsaturated Half Space. Transp Porous Med 78, 233–257 (2009). https://doi.org/10.1007/s11242-008-9298-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-008-9298-5

Keywords

Navigation