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TECHNICAL NOTES

Analytical Solution of Coupled Diffusion Equations in Semi-Infinite Media

[+] Author and Article Information
O. Fudym

Laboratoire de Génie des Procédés des Solides Divisés, UMR 2392 CNRS, Ecole des Mines d’Albi, 81013 Albi, France

J.-C. Batsale

Laboratoire inter-établissements TREFLE-Site ENSAM, 33405 Talence, France

R. Santander, V. Bubnovich

Departamento de Ing. Mecánica, Universidad de Santiago de Chile, Santiago, Chile

J. Heat Transfer 126(3), 471-475 (Jun 16, 2004) (5 pages) doi:10.1115/1.1731317 History: Received September 11, 2003; Revised January 23, 2004; Online June 16, 2004
Copyright © 2004 by ASME
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References

Luikov, A. V., 1966, Heat and Mass Transfer in Capillary—Porous Bodies, Pergamon Press, Oxford.
De Vries,  D. A., 1958, “Simultaneous Transfer of Heat and Moisture in Porous Media,” Trans., Am. Geophys. Union, 39(5), pp. 909–916.
Smirnov,  M. S., 1962, “On a System of Differential Equations for Highly Intensive Heat and Mass Transfer,” Int. J. Heat Mass Transfer, 5, pp. 521–524.
Mikhailov,  M. D., 1973, “General Solutions of the Diffusion Equations Coupled at Boundary Conditions,” Int. J. Heat Mass Transfer, 16, pp. 2155–2164.
Mikhailov,  M. D., and Shishedjiev,  B. K., 1975, “Temperature and Moisture Distributions During Contact Drying of a Moist Porous Sheet,” Int. J. Heat Mass Transfer, 18, pp. 15–24.
Mikhailov, M. D., and Ozisik, M. N., 1984, Unified Analysis and Solutions of Heat and Mass Diffusion, John Wiley, New York.
Cotta, R. M., 1994, “The Integral Transform Method in Computational Heat and Fluid Flow,” Proceedings of the Tenth Int. Heat Transfer Conf., T. and F. Ichem Brighton, ed., UK, 1 , pp. 43–60.
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Thum, R. L., Barichello, L. B., Vilhena, M. T., and Cotta, R. M., 2001, “An Analytical Approach to the Solution of Multidimensional Drying Problems,” Proceedings of the 2nd Int. Conf. On Comp. Heat and Mass Transfer, COPPE/EE/UFRJ, Rio de Janeiro, Brazil.
Prata, A. T., and Damanesco-Ferreira, L. S., 1990, “Evaluation of a Parametric Model for Heat and Mass Transfert in Unsaturated Porous Media,” in Multiphase Transport and Particulate Phenomena, Neyat Veziroglu Hemisphere Publishing Corp., 1 , pp. 201–220.
Maillet, D., André, S., Batsale, J. C., Degiovanni, A., and Moyne, C., 2000, Thermal Quadrupoles: Solving the Heat Equation Through Integral Transforms, John Wiley.
Fudym,  O., Ladevie,  B., and Batsale,  J. C., 2002, “A Semi-Numerical Approach for Heat Conduction in Heterogeneous Media: One Extension of the Analytical Quadrupole Method,” Numer. Heat Transfer, Part B, 42(4), pp. 325–348.
Stehfest,  H., 1970, “Algorithm 368. Numerical Inversion of Laplace Transform,” Commun. A.C.M.,53, pp. 47–49.
De Vries,  D. A., and Peck,  A. J., 1958, “On Cylindrical Probe Method of Measuring Thermal Conductivity With Special Reference to Soils,” Aust. J. Phys., 11, pp. 225–271.

Figures

Grahic Jump Location
Moisture content/temperature ratio at the impermeable wall of a semi-infinite slab as a function of time for various locations: Lu=0.0122;δ=5.64 10−4;a*=6.49 10−7 m2⋅s−1

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