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Some Considerations on Modeling Heat and Mass Transfer in Porous Media

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Abstract

In this paper some considerations are presented about the equations needed to set up a model of the process of heat and mass transfer in porous media. A clear classification is made of the various types of equations used and of their physical meaning. Special attention is paid to the thermodynamic equilibrium equations and to their derivation since they are too often taken for granted. The importance of the various transport mechanisms (of mass and energy) is analyzed and the consequences that can arise when some term is neglected are indicated.

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References

  1. De Groot, S. R. and Mazur, P.: Non-Equilibrium Thermodynamics, Dover, New York, 1984.

  2. Eu, B. C.: Kinetic Theory and Irreversible Thermodynamics, Wiley, New York, 1992.

    Google Scholar 

  3. Kuiken, G. D. C.: Thermodynamics of Irreversible Processes, Wiley, Chichester (UK), 1994.

    Google Scholar 

  4. Burshtein, A. I.: Introduction to Thermodynamics and Kinetic Theory of Matter, Wiley, New York, 1996.

    Google Scholar 

  5. Hassanizadeh, M. and Gray W. G.: General conservation equations for multiphase systems: 1 Averaging technique, Adv. Water Res. 2(1979), 131–144.

    Google Scholar 

  6. Hassanizadeh, M. and Gray W. G.: General conservation equations for multiphase systems: 2 Mass, momenta, energy and entropy equations, Adv. Water Res. 2(1979), 191–203.

    Google Scholar 

  7. Hassanizadeh, M. and Gray W. G.: General conservation equations for multiphase systems: 3 Constitutive theory for porous media flow, Adv. Water Res. 3(1980), 25–40.

    Google Scholar 

  8. Bear, J.: Dynamics of Fluids in Porous Media, Dover, New York, (reprinted 1988).

  9. Bachmat Y. and Bear, J.: Macroscopic modeling of transport phenomena in porous media. 1: The continuum approach, Transport in Porous Media 1(1986), 213–240.

    Google Scholar 

  10. Bear, J. and Bachmat Y.: Macroscopic modeling of transport phenomena in porous media. 2: Applications to mass, momentum and energy transport, Transport in Porous Media 1(1986), 241–269.

    Google Scholar 

  11. Bear, J. and Bachmat Y.: Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Acad. Publ., Dordrecht, 1990.

    Google Scholar 

  12. Nozad, I., Carbonell, R. G. and Whitaker, S.: Heat conduction in multiphase systems - I: Theory and experiment for two-phase systems, Chem. Eng. Sci. 40(5) (1985), 843–855.

    Google Scholar 

  13. Auriault, J. L.: Effective macroscopic description for heat conduction in periodic composites, Int. J. Heat Mass Transfer 26(6) (1983), 861–869.

    Google Scholar 

  14. Auriault, J. L. and Royer, P.: Double conductivity media: a comparison between phenomenological and homogenization approaches, Int. J. Heat Mass Transfer 36(10) (1993), 2613–2621.

    Google Scholar 

  15. Auriault, J. L. and Ene, H. I.: Macroscopic modeling of heat transfer in composites with interfacial thermal barrier, Int. J. Heat Mass Transfer 37(18) (1993), 2885–2892.

    Google Scholar 

  16. Stauffer, D. and Aharony, A.: Introduction to the Percolation Theory, 2nd edn, Taylor & Francis, London, 1992.

    Google Scholar 

  17. Bertasi, M., Bigolaro, G. and De Ponte, F.: Fibrous insulating materials as standard reference materials at low temperatures, in R. P. Tye (ed.), ASTM STP 660, ASTM, Philadelphia, 1978.

    Google Scholar 

  18. Arduini, M. C. and De Ponte, F.: Combined radiation and conduction heat transfer in insulating materials, in Proceedings, 10th ETPC, High Temperatures - High Pressures 19(1986), 237.

    Google Scholar 

  19. Whitaker, S.: Simultaneous heat mass and momentum transfer in porous media: A theory of drying, Advances in Heat Transfer 13(1977), Academic Press, New York.

    Google Scholar 

  20. Whitaker, S.: Heat and mass transfer in granular porous media, Advances in Drying 1(1980), Hemisphere, New York.

    Google Scholar 

  21. Defay, R. and Prigogine, I.: Tension superficielle et adsorption, Éditions Desoer, Liège, 1951.- A revised English edition also exists: R. Defay, I. Prigogine, A. Bellemans and D. H. Everett, Surface Tension and Adsorption, Longman, London, 1966.

    Google Scholar 

  22. Zemansky, M.W. and Dittman R. H.: Heat and Thermodynamics, 6th edn, McGraw-Hill, New York, 1981.

    Google Scholar 

  23. Glasstone, S.: Physical Chemistry, 2nd edn, Mcmillan, London, 1948.

    Google Scholar 

  24. Denbigh, K.: The Principles of Chemical Equilibrium, 4th edn, Cambridge Univ. Press, Cambridge, 1981.

    Google Scholar 

  25. ASHRAE: Handbook of Fundamentals, ASHRAE, Atlanta, 1993.

    Google Scholar 

  26. Krischer, O. and Kröll, K.: Die wissenschaftlichen Grundlagen der Trocknungstechnik, Springer-Verlag, Berlin, 1963.

    Google Scholar 

  27. Whitaker, S.: Flow in porous media I: A theoretical derivation of Darcy's law, Transport in Porous Media 1(1986), 3–25.

    Google Scholar 

  28. Whitaker, S.: Flow in porous media II: The governing equations for immiscible two-phase flow, Transport in Porous Media 1(1986), 105–125.

    Google Scholar 

  29. Baggio, P., Bonacina C. and Strada, M.: Trasporto di calore e di massa nel calcestruzzo cellulare, La Termotecnica 45(12) (1993), 53–60. [in Italian].

    Google Scholar 

  30. Conner, W. C., Lane, M. A. and Hoffman, A. J.: Measurement of the morphology of high surface area solids: Hysteresis in mercury porosimetry, J. Colloid Interf. Sci. 100(1) (1984), 185–193.

    Google Scholar 

  31. Park, C. Y. and Ihm, S. K.: New hypoteses for mercury porosimetry with percolation approach., AIChe J. 36(11) (1990), 1641–1648.

    Google Scholar 

  32. Lane, A., Shah, N. and Conner, W. C.: Measurement of high-surface-area solids: Porosimetry as a percolation process, J. Colloid Interf. Sci. 109(1) (1986), 235–242.

    Google Scholar 

  33. Wall, G. C. and Brown, R. J. C.: The determination of pore-size distributions from sorption isotherms and mercury penetration in interconnected pores: The application of percolation theory, J. Colloid Interf. Sci. 82(1) (1981), 235–242.

    Google Scholar 

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

    Google Scholar 

  35. Daian J. F.: Condensation and isothermal water transfer in cement mortar Part I: - Pore size distribution, equilibrium, water condensation and imbibition, Transport in Porous Media, 3(1988), 563–589.

    Google Scholar 

  36. Daian J. F.: Condensation and isothermal water transfer in cement mortar Part II: - Transient condensation of water vapor, Transport in Porous Media 4(1989), 1–16.

    Google Scholar 

  37. Bazant, Z. P. and Najjar, L. J.: Nonlinear water diffusion in nonsaturated concrete, Matériaux et constructions (Paris), 5(25) (1972), 3–20.

    Google Scholar 

  38. Bird, R. B., Stewart, E. W. and Lightfoot, E. N.: Transport Phenomena, Wiley, New York, 1960.

    Google Scholar 

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

    Google Scholar 

  40. Nasrallah, S. B. and Perre, P.: Detailed study of a model of heat and mass transfer during convective drying of porous media, Int. J. Heat Mass Transfer 31(5) (1988), 957–967.

    Google Scholar 

  41. Perre, P. and Degiovanni, A.: Simulation par volumes finis des transferts couplés en milieux poreux a nisotropes: séchage du bois à basse et à haute température, Int. J. Heat Mass Transfer 33(11) (1990), 2463–2478.

    Google Scholar 

  42. Ilic, M. and Turner, I.W.: Convective drying of a consolidated slab of wet porous material, Int. J. Heat Mass Transfer 32(12) (1989), 957–967.

    Google Scholar 

  43. Ilic, M. and Turner, I. W.: Convective drying of a consolidated slab of wet porous material including the sorption region, Int. Comm. Heat Mass Transfer 17(1990), 39–48.

    Google Scholar 

  44. Gregg, S. J. and Sing, K. S. W.: Adsorption, Surface Area and Porosity, 2nd edn, Academic Press, London, 1982.

    Google Scholar 

  45. Fuentes, C., Haverkamp, R., Parlange, J. Y., Brutsaert, W., Zayany, K. and Vachaud G.: Constraints on parameters in three soil-water capillary retention equations, Transport in Porous Media 6(1991), 445–449.

    Google Scholar 

  46. Scheidegger, A. E.: The Physics of Flow Through Porous Media, 2nd edn, Univ. of Toronto Press, 1960.

  47. Baggio, P., Maiorana, C. and Schrefler B. A.: Thermo-hygro-mechanical analysis of concrete, Int. J. Num. Meth. Fluids 20(1995), 573–595.

    Google Scholar 

  48. Gawin, D, Baggio, P. and Schrefler B. A.: Coupled heat, water and gas flow in deformable porous media, Int. J. Num. Meth. Fluids 20(1995), 969–987.

    Google Scholar 

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Baggio, P., Bonacina, C. & Schrefler, B. Some Considerations on Modeling Heat and Mass Transfer in Porous Media. Transport in Porous Media 28, 233–251 (1997). https://doi.org/10.1023/A:1006525729566

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