Skip to main content
SpringerLink
Log in

Porous Materials Drying Model Based on the Thermodynamics of Irreversible Processes: Background and Application

  • Chapter
  • First Online:
Transport Phenomena and Drying of Solids and Particulate Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 48))

Abstract

This chapter focuses on the heat and mass transfer (drying) in capillary-porous bodies using both the mechanistic and non-equilibrium thermodynamic approaches. A new coupled mathematical modeling to predict heat and moisture (liquid and vapor) transfer in wet capillary-porous bodies with particular reference to prolate spheroidal solids is presented and discussed. The mathematical model is based on the thermodynamics of irreversible processes by considering variable transport coefficients and equilibrium or convective boundary conditions at the surface of the solid. All the partial differential equations presented in the model have been written in prolate spheroidal coordinates. The finite-volume method has been used to obtain the numerical solution of the governing equations. Application has been done to wheat kernel drying and comparison between predicted and experimental data has showed good agreement.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Fortes, M.: A non-equilibrium thermodynamics approach to transport phenomena in capillary-porous media with special reference to drying of grains and foods. Doctorate thesis, Faculty of Purdue University, United States of America (1978)

    Google Scholar 

  2. Middleman, S.: An Introduction to Mass and Heat Transfer: Principles of Analysis and Design. John Wiley & Sons Inc., New York (1998)

    Google Scholar 

  3. Crank, J.: The Mathematics of Diffusion. Oxford Science Publications, New York (1992)

    Google Scholar 

  4. Gebhart, B.: Heat Conduction and Mass Diffusion. McGraw-Hill, New York (1993)

    Google Scholar 

  5. Skelland, A.H.P.: Diffusional Mass Transfer. Wiley, New York (1974)

    Google Scholar 

  6. Lima, A.G.B., Nebra, S.A.: Theoretical analysis of the diffusion process inside prolate spheroidal solids. Drying Technol. 18(1–2), 21–48 (2000)

    Article  Google Scholar 

  7. Carmo, J.E.F.: Non steady-state diffusion phenomenon in oblate spheroidal solids. Case studies: drying of lentil. Doctorate thesis, Process Engineering, Federal University of Campina Grande, Campina Grande, Brazil (2004). (In Portuguese)

    Google Scholar 

  8. Lima, A.G.B., Queiroz, M.R., Nebra, S.A.: Simultaneous moisture transport and shrinkage during drying of solids with ellipsoidal configuration. Chem. Eng. J. 86, 85–93 (2002)

    Article  Google Scholar 

  9. Lima, A.G.B., Queiroz, M.R., Nebra, S.A.: Heat and mass transfer model including shrinkage applied to ellipsoidal products: case study for drying of bananas. Develop. Chem. Eng. Miner. Process. 10, 281–304 (2002)

    Google Scholar 

  10. Oliveira, V.A.B., Lima, A.G.B.: Mass diffusion inside prolate spherical solids: An analytical solution. Braz. J. Agro-Ind. Prod. 4(1), 41–50 (2002)

    Google Scholar 

  11. Lima, D.R., Farias, S.N., Lima, A.B.G.: Mass transport in spheroids using the Galerkin method. Braz. J. Chem. Eng. 21(4), 667–680 (2004)

    Article  Google Scholar 

  12. Carmo, J.E.F., Lima, A.G.B.: Drying of lentil including shrinkage: a numerical study. Drying Technol. 23, 1977–1992 (2005)

    Article  Google Scholar 

  13. Cihan, A., Kahveci, K., Hacihafizoğlu, O., Lima, A.G.B.: A diffusion based model for intermittent drying of rough rice. Heat Mass Transf. 44, 905–911 (2008)

    Article  Google Scholar 

  14. Hacihafizoğlu, O., Cihan, A., Kahveci, K., Lima, A.G.B.: A liquid diffusion model for thin-layer drying of rough rice. Eur. Food Res. Tech. 226, 787–793 (2008)

    Article  Google Scholar 

  15. Oliveira, V.A.B., Lima, A.G.B.: Drying of wheat based on the non-equilibrium thermodynamics: a numerical study. Drying Technol. 27, 306–313 (2009)

    Article  Google Scholar 

  16. Oliveira, V.A.B., Lima, W.C.P.B., Farias Neto, S.R., Lima, A.G.B.: Heat and mass diffusion and shrinkage in prolate spheroidal bodies based on non-equilibrium thermodynamics: a numerical investigation. J. Porous Media 14(7), 593–605 (2011)

    Article  Google Scholar 

  17. Oliveira, V.A.B., de Lima, A.G.B., Silva, C. J.: Drying of wheat: a numerical study based on the non-equilibrium thermodynamics. Int. J. Food Eng. 8(3), Article 19 (2012)

    Google Scholar 

  18. Luikov, A.V., Mikhailov, Y.A.: Theory of Energy and Mass Transfer. Pergamon Press Ltd, Oxford (1965)

    MATH  Google Scholar 

  19. Luikov, A.V.: Heat and Mass Transfer in Capillary Porous Bodies. Pergamon Press, New York (1965)

    Google Scholar 

  20. Mikhailov, M.D., Shishedjiev, B.K.: Temperature and moisture distributions during contact drying of a moist porous sheet. Int. J. Heat Mass Transf. 18, 15–24 (1975)

    Article  Google Scholar 

  21. Luikov, A.V.: Systems of differential equations of heat and mass transfer in capillary porous bodies: review. Int. J. Heat Mass Transf. 18, 1–14 (1975)

    MATH  Google Scholar 

  22. Fortes, M., Okos, M.R.: Drying theories: their bases and limitations as applied to foods and grains. In: Mujumdar, A. (ed.) Advances in Drying, vol. 1, pp. 119–154. Hemisphere Publishing Corporation, New York (1980)

    Google Scholar 

  23. Whitaker, S.: Heat and mass transfer in granular porous media. In: Mujumdar, A. (ed.) Advances in Drying, vol. 1, pp. 23-61. Hemisphere Publishing Corporation, New York (1980)

    Google Scholar 

  24. Fortes, M., Okos, M.R.: Non-equilibrium thermodynamics approach to heat and mass transfer in corn kernels. Trans. ASAE 24, 761–769 (1981)

    Article  Google Scholar 

  25. Ribeiro, J.W., Cotta, R.M., Mikhailov, M.D.: Integral transform solution of Luikov’s equations for heat and mass transfer in capillary porous media. Int. J. Heat Mass Trans. 36(18), 4467–4475 (1993)

    Article  MATH  Google Scholar 

  26. Irudayara, J., Wu, Y.: Analysis and application of Luikov’s heat, mass and pressure transfer model to a capillary porous media. Drying Technol. 14(3–4), 803–824 (1996)

    Google Scholar 

  27. Santos, G.T., Fortes, M., Martins, J.H., Monteiro, P.M.B.: Convective drying analysis of a single wheat kernel based on an irreversible thermodynamic model. Drying Technol. 31(16), 1979–1993 (2013)

    Article  Google Scholar 

  28. Fortes, M., Okos, M.R., Barret Jr, J.R.: Heat and mass transfer analysis of intra-kernel wheat drying and rewetting. J. Agric. Eng. Res. 26, 109–125 (1981)

    Article  Google Scholar 

  29. Lima, A.G.B., Farias Neto, S.R., Silva, W.P.: Heat and mass transfer in porous materials with complex geometry: fundamentals and applications. In: Delgado, J.M.P.Q. (ed.) Heat and Mass Transfer in Porous Media. Springer, Berlin (2012)

    Google Scholar 

  30. Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics. Springer, Berlin (1966)

    Book  MATH  Google Scholar 

  31. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications Inc., New York (1972)

    MATH  Google Scholar 

  32. Philip, J.R., De Vries, D.A.: Moisture movement in porous materials under temperature gradients. Trans. Am. Geophys. Union 38(2), 222–232 (1957)

    Article  Google Scholar 

  33. De Vries, D.A.: Simultaneous transfer of heat and moisture in porous media. Trans. Am. Geophys. Union 39(5), 909–916 (1958)

    Article  Google Scholar 

  34. Krischer, O.: Die Wissenschaftlichen Grundlagen der Trocknungstechnik, vol. Kap. IX. Springer, Berlin (1963)

    Book  Google Scholar 

  35. Berger, D., Pei, D.C.T.: Drying of hygroscopic capillary porous solids: a theoretical approach. Int. J. Heat Mass Transf. 16, 293–302 (1973)

    Article  Google Scholar 

  36. De Groot, S.R.: Thermodynamics of Irreversible Processes. North Holland Publishing Company, Amsterdan (1951)

    MATH  Google Scholar 

  37. Prigogine, I.: Thermodynamic of Irreversible Processes, 2nd edn. Wiley, New York (1961)

    Google Scholar 

  38. Oliveira, V.B.: Heat and mass transfer inside prolate spheroidal solids via thermodynamics of irreversible processes. Doctorate thesis, Process Engineering, Federal University of Campina Grande, Campina Grande, PB, Brazil (2004). (In Portuguese)

    Google Scholar 

  39. Brebbia, C.A., Dominguez, J.: Boundary Elements: an Introductory Course. McGraw-Hill Company, New York (1989)

    MATH  Google Scholar 

  40. Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, New York (1980)

    MATH  Google Scholar 

  41. Maliska, C.R.: Computational Heat Transfer and Fluid Mechanics, 2nd edn. LTC, Rio de Janeiro (2004). (In Portuguese)

    Google Scholar 

  42. Kwon, Y.W., Bang, H.: The finite Element Method Using Matlab. CRC Press, Bora Raton (1997)

    Google Scholar 

  43. Mohapatra, D., Rao, P.S.: A Thin layer drying model of parboiled wheat. J. Food Eng. 66, 513–518 (2005)

    Article  Google Scholar 

  44. Singh, H., Singh, A.K., Kushwaha, H.L., Singh, A.: Energy consumption pattern of wheat production in India. Energy 32, 1848–1854 (2007)

    Article  Google Scholar 

  45. FAO Statistical Yearbook 2013. World food and agriculture. Food and Agriculture Organization of the United Nations, Rome (2013)

    Google Scholar 

  46. Brooker, D.B., Bakker-Arkema, F.W., Hall, C.W.: Drying and Storage of Grains and Oilseeds. AVI Book, New York (1992)

    Google Scholar 

  47. Kazarian, E.A., Hall, C.W.: Thermal properties of grains. Trans. ASAE. 8, 33–37 (1965)

    Article  Google Scholar 

  48. Figliola, R.S., Beasley, D.E.: Theory and Design for Mechanical Measurement. Wiley, New York (1995)

    Google Scholar 

  49. Hartley, J.G.: Coupled heat and moisture transfer in soils: a review. In: Mujumdar, A.S. (ed.) Advances in Drying, vol. 4, pp. 199–247. Hemisphere Publishing Corporation, Washington (1987)

    Google Scholar 

  50. Shukla, K.N.: Diffusion Process During Drying of Solids. World Scientific, Singapore (1990)

    Book  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to express their thanks to CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil), and FINEP (Financiadora de Estudos e Projetos, Brazil) for supporting this work; to the authors of the references in this chapter that helped in our understanding of this complex subject, and to the Editors by the opportunity given to present our research in this book.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Federal University of Campina Grande, Av. Aprígio Veloso, 882 Bodocongó, Campina Grande, PB, Zip Code: 58429-900, Brazil

    A. G. Barbosa de Lima, J. C. S. de Melo & C. Joaquina e Silva

  2. LFC – Building Physics Laboratory, Civil Engineering Department Faculty of Engineering, University of Porto, Porto, Portugal

    J. M. P. Q. Delgado

  3. Department of Civil Engineering, State University of Paraíba, Araruna, PB, Brazil

    V. A. B. de Oliveira

Authors
  1. A. G. Barbosa de Lima
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. P. Q. Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. A. B. de Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. C. S. de Melo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. Joaquina e Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. G. Barbosa de Lima .

Editor information

Editors and Affiliations

  1. Faculty of Engineering of University of Porto, Laboratory of Building Physics, Department of Civil Engineering, Porto, Portugal

    J.M.P.Q. Delgado

  2. Department of Mechanical Engineering, Federal University of Campina Grande, Brazil, Brazil

    A.G. Barbosa de Lima

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

de Lima, A.G.B., Delgado, J.M.P.Q., de Oliveira, V.A.B., de Melo, J.C.S., Joaquina e Silva, C. (2014). Porous Materials Drying Model Based on the Thermodynamics of Irreversible Processes: Background and Application. In: Delgado, J., Barbosa de Lima, A. (eds) Transport Phenomena and Drying of Solids and Particulate Materials. Advanced Structured Materials, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-04054-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04054-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04053-0

  • Online ISBN: 978-3-319-04054-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation