Skip to main content
SpringerLink
Log in

Modeling of heat and moisture transfers with stress–strain formation during convective air drying of deformable media

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

A mathematical formulation of heat, mass and momentum transfers’ phenomena during drying of saturated deformable porous media was developed. The effect of the fluid pressure gradient on the fluid transfer is described by using the Darcy law. An elastic comportment has been used to close the mechanical problem. The model is solved numerically by using finite elements method based on Arbitrary Lagrangian–Eulerian description. The evolutions of moisture content, liquid pressure and stresses within a clay sample were discussed. A large tensional stress, which could induce a crack, was observed at the product surface exposed to the drying air.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

ρi :

Averaged density (kg m−3)

ρi :

Intrinsic averaged density (kg m−3)

Cp:

Heat capacity (J kg−1 K−1)

g:

Gravity acceleration (m s−2)

k:

Permeability (m2)

Km:

Mass transfer coefficient (m s−1)

Mv :

Molar weight of water vapor (kg mol−1)

p:

Water pressure (Pa)

Pv,sat :

Water vapor pressure (Pa)

R:

Universal gas constant (Pa m3 K−1)

RH:

Relative humidity of air (kg kg−1)

T:

Temperature (K)

u:

Displacement vector of the solid (m)

v:

Averaged velocity (m s−1)

vls :

Liquid velocity relative to the solid

w:

Moisture (kg kg−1 dry basis)

βT :

Coefficient of thermal expansion (−)

βw :

Coefficient of humid expansion (−)

Φ:

Porosity (−)

ε:

Strain tensor (−)

η:

Dynamic viscosity (kg m−1 s−1)

κ:

Thermal conductivity (W m−1 K−1)

μ and λ:

Coefficients of Lamé (Pa)

ν:

Volume (m3)

σ :

Stress tensor (Pa)

t:

Time (s)

KT:

Convective heat transfer coefficient (W m2 K−1)

q:

Heat flux (W)

\( \dot{m} \) :

Rate of moisture vaporization (kg m−2 s−1)

aw:

Water activity (−)

\( \Uplambda_{v} \) :

Heat of vaporization (J kg−1)

s:

Solid

l:

Liquid

References

  1. Banaszak J, Kowalski SJ (2002) Drying induced stresses estimated on the base of elastic and viscoelastic models. Chem Eng J 86:139–143

    Article  Google Scholar 

  2. Banaszak J, Kowalski SJ (2005) Theoretical and experimental analysis of stresses and fractures in clay like materials during drying. Chem Eng Process 44:497–503

    Google Scholar 

  3. Caceres G, Bruneau D, Jomaa W (2007) Two-phase shrinking porous media drying: a modeling approach including liquid pressure gradients effects. Dry Technol 25:1927–1934

    Article  Google Scholar 

  4. Chemkhi S, Jomaa W, Zagrouba F (2009) Application of a coupled thermo-hydro-mechanical model to simulate the drying of nonsaturated porous media. Dry Technol 27:842–850

    Article  Google Scholar 

  5. Chemkhi S, Zagrouba F, Bellagi A (2004) Mathematical model for drying of highly shrinkable media. Dry Technol 22:1023–1039

    Article  Google Scholar 

  6. Couture F, Laurent S, Roques MA (2007) Drying of two-phase media: simulation with liquid pressure as driven force. AIChE J 53:1703–1717

    Article  Google Scholar 

  7. Gawin D, Pesavento F, Schrefler BA (2003) Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation. Comput Methods Appl Mech Eng 192:1731–1771

    Article  MATH  Google Scholar 

  8. Hasatani M, Itaya Y (1992) Fundamental study on shrinkage of formed clay during drying. Viscoelastic strain-stress and heat/moisture transfer. Dry Technol 10:1013–1036

    Article  Google Scholar 

  9. Hasatani M, Itaya Y (1996) Drying induced strain and stress: a review. Dry Technol 14:1011–1040

    Article  Google Scholar 

  10. Itaya Y, Taniguchi S, Hasatani M (1997) A numerical study of transient deformation and stress behavior of a clay slab during drying. Dry Technol 15:1–21

    Article  Google Scholar 

  11. Itaya Y, Uchiyama S, Hatano S, Mori S (2005) Drying enhancement of clay slab by microwave heating. Dry Technol 23:1243–1255

    Article  Google Scholar 

  12. Kechaou N (1989) Séchage des gels fortement déformables: études de la diffusion interne de l’eau et modélisation. Institut National Polytechnique de Loraine, Loraine

    Google Scholar 

  13. Ketelaars AAJ (1993) Drying deformable media, kinetics, shrinkage and stress. University of Eindhoven, Eindhoven

    Google Scholar 

  14. Ketelaars AAJ, Jomaa W, Puiggali JR, Coumans WJ (1992) Drying shrinkage and stress. Drying’92, international drying symposium, pp 293–303

  15. Ketelaars T, Pel L, Coumans WJ, Kerkhof PJAM (1995) Drying kinetics: a comparison of diffusion coefficients from moisture concentration profiles and drying curves. Chem Eng Sci 50:1187–1191

    Article  Google Scholar 

  16. Kiennemann J, Chartier T, Pagnoux C, Baumard JF, Huger M, Lamerant JM (2005) Drying mechanisms and stress development in aqueous alumina tape-casting. J Eur Ceram Soc 25:1551–1564

    Article  Google Scholar 

  17. Kowalski SJ (2008) Guest editorial: R&D in thermo-hydro-mechanical aspect of drying. Dry Technol 26:258–259

    Article  Google Scholar 

  18. Kowalski SJ (2010) Control of mechanical processes in drying. Theory Exp Chem Eng Sci 65:890–899

    Google Scholar 

  19. Kowalski SJ, Mielniczuk B (2008) Analysis of effectiveness and stress development during convective and microwave drying. Dry Technol 26:64–77

    Article  Google Scholar 

  20. Kowalski SJ, Rajewska K (2002) Drying induced stresses in elastic and viscoelastic saturated materials. Chem Eng Sci 57:3883–3892

    Article  Google Scholar 

  21. Kowalski SJ, Rajewska K, Rybicki A (2004) Mechanical effects in saturated capillary-porous materials during convective and microwave drying. Dry Technol 22:2291–2308

    Article  Google Scholar 

  22. Kowalski SJ, Rajewska K, Rybicki A (2005) Stresses generated during convective and microwave drying. Dry Technol 23:1875–1893

    Article  Google Scholar 

  23. Kowalski SJ, Rybicki A (2004) Qualitative aspects of convective and microwave drying of saturated porous materials. Dry Technol 22:1173–1189

    Article  Google Scholar 

  24. Kowalski SJ, Rybicki A (2007) The vapour-liquid interface and stresses in dried bodies. Trans Porous Media 66:43–58

    Article  MathSciNet  Google Scholar 

  25. Kowalski SJ, Rybicki A (2009) Cohesive strength of materials during drying processes. Dry Technol 27:863–869

    Article  Google Scholar 

  26. Mihoubi D (2004) deshydratation d’argiles par compression et séchage. Aspects de modélisation et de simulation. Université de Pau et des Pays de l’Adour

  27. Mihoubi D, Bellagi A (2008) Two-dimensional heat and mass transfer during drying of deformable media. Appl Math Model 32:303–314

    Article  MATH  Google Scholar 

  28. Mihoubi D, Bellagi A (2009) Stress generated during drying of saturated porous media. Trans Porous Media 80:519–536

    Article  Google Scholar 

  29. Mihoubi D, Zagrouba F, Vaxelaire J, Bellagi A, Roques M (2004) Transfer phenomena during the drying of a shrinkable product: modelling and simulations. Dry Technol 22:91–109

    Article  Google Scholar 

  30. Musielak G (2004) Modelling of the heat and mass transport phenomena in kaolin during the first and the second periods of drying. Chem Process Eng 25:393–409

    Google Scholar 

  31. Perre P, Turner W (1997) Microwave drying of softwood in an oversized waveguide. AIChE J 43:2579–2595

    Article  Google Scholar 

  32. Scherer GW (1992) Crack-tip stress in gels. J Non Cryst Solids 144:210–216

    Article  Google Scholar 

  33. Whitaker S (1972) Fundamental principles of heat transfer. Pergamon Press Inc, New York

    Google Scholar 

  34. Whitaker S (1986) Flow in porous media I: a theoretical derivation of Darcy’s law. Trans Porous Media 1:3–25

    Article  Google Scholar 

  35. Zagrouba F (1993) Séchage mixte par convection et un apport rayonnant micro-ondes des milieux déformables. Modélisation des phénomènes de transferts de chaleur et de matière. Institut Nationale Polytechnique de Lorraine

  36. Zagrouba F, Mihoubi D, Bellagi A (2002) Drying of clay. II: Rheological modelisation and simulation of physical phenomena. Dry Technol 20:1895–1917

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Thermal Processing Laboratory, CRTEn, B.P. 95, 2050, Hammam-Lif, Tunisia

    D. Mihoubi

  2. National Engineers School of Monastir, 5000, Monastir, Tunisia

    A. Bellagi

Authors
  1. D. Mihoubi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Bellagi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Mihoubi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mihoubi, D., Bellagi, A. Modeling of heat and moisture transfers with stress–strain formation during convective air drying of deformable media. Heat Mass Transfer 48, 1697–1705 (2012). https://doi.org/10.1007/s00231-012-1014-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-012-1014-x

Keywords

Search

Navigation