Science Journal of Applied Mathematics and Statistics

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Mathematical Problem Appearing in Industrial Lumber Drying: A Review

Received: 21 February 2014    Accepted:     Published: 20 March 2014
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Abstract

This article is a review of our work on the modeling of lumber drying that we have started in 2003. We consider a lumber drying process in a kiln chamber where from mathematical point of views, this is an initial and boundary value problem. The Moisture Content (MC) is measured at the center of the lumber by applying a nail that thousands times of the pore size of the wood. This leads to apply macro modeling for the diffusion process of the water inside the lumber. MC acts as the state variable u of the thickness x and time t. The state variable satisfies a diffusion equation. The Equilibrium Moisture Content (EMC) of the air acts as the boundary condition. We report the progress on mathematical modeling and compared the results with data from industry.

DOI 10.11648/j.sjams.20140201.14
Published in Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 1, February 2014)
Page(s) 26-30
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Boundary Value Problem, Initial Value Problem, Diffusion Equation, Lumber Drying

References
[1] E. Cahyono & La Gubu, "Wood drying process: modeling for linear diffusivity with respect to the water content", Proceeding SEMINAR MIPA IV ITB, Bandung Indonesia, 2004, pp. 112-114.
[2] E. Cahyono, D. C. Tjang & La Gubu, "Modeling of wood drying", Proceedings of International Conference on Mathematics And Its Applications, Yogyakarta Indonesia, 2003, pp. 227-232.
[3] E. Cahyono, "Modeling of Wood Drying: A Step Function Approach to the Diffusivity," Proceedings of the 2nd International Conference on Research and Education in Mathematics, Kuala Lumpur, Malaysia, 2005, pp. 358–364.
[4] E. Cahyono, Y Soeharyadi & Mukhsar, "A smooth diffusion rate model of wood drying: a simulation toward more efficient process in industry," Jurnal Teknik Industri, vol. 10, no. 1, 2008, pp. 1-10.
[5] La Gubu & E. Cahyono, "A quasi-linear diffusivity approach for diffusion process of lumber drying," Proceedings of the International Conference on Applied Mathematics, Bandung, Indonesia, 2005, pp. 1002-1006.
[6] N. S. Hoang and A. G. Ramm, "An inverse problem for a heat equation with piece wise constant thermal conductivity," Journal of Mathematical Physics, vol. 50, 2009, no. 063512.
[7] U. Hornung, Homogenization and Porous Media, Springer-Verlag, Berlin, 1997.
[8] E. Kreyszig, Advanced Engineering Mathematics, 7th ed., John Wiley & Son, Singapore, 1999.
[9] K. W. Morton & D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
[10] S. Omarsson, Numerical analysis of moisture related distortion in sawn timber, PhD thesis, Dept. of Structural Mechanics, Chalmers University of Technology, Goteborg, Sweden, 1999.
[11] S. Ormarsson, D. Cown and O. Dahlblom, "Finite element simulations of moisture related distortion in laminated timber products of Norway spruce and radiata pine," in 8th International IUFRO Wood Drying Conference, 2003, pp. 27-33.
[12] S. Omarsson, O. Dahlblom, and H. Peterson, "A numerical study of shape stability of sawn timber subjected to moisture variation. Part 2: Simulation of drying board," Wood Science and Technology, vol. 33, 1999, pp. 407-423.
[13] S. Omarsson, O. Dahlblom, and H. Peterson, "A numerical study of shape stability of sawn timber subjected to moisture variation. Part 3: Influence of annual ring orientation," Wood Science and Technology, vol. 34, 2000, pp. 207-219.
[14] J. Passard and P. Perre, "Creep test under water-saturated conditions: do the anisotropy ratios of wood change with the temperature and time dependency?", 7th International IUFRO Conference on Wood Drying, 2001.
[15] A. G. Ramm. An inverse problem for heat equation. Journal of Mathematical Analysis and Applications, 2001, vol. 264, pp. 691–697.
[16] A. G. Ramm, "An inverse problem for the heat equation II," Applied Analysis, 2002, vol. 81, no. 4, pp. 929-937.
Author Information
  • Dept. Mathematics FMIPA Univ. Halu Oleo, Kendari, Indonesia

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    Edi Cahyono. (2014). Mathematical Problem Appearing in Industrial Lumber Drying: A Review. Science Journal of Applied Mathematics and Statistics, 2(1), 26-30. https://doi.org/10.11648/j.sjams.20140201.14

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    ACS Style

    Edi Cahyono. Mathematical Problem Appearing in Industrial Lumber Drying: A Review. Sci. J. Appl. Math. Stat. 2014, 2(1), 26-30. doi: 10.11648/j.sjams.20140201.14

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    AMA Style

    Edi Cahyono. Mathematical Problem Appearing in Industrial Lumber Drying: A Review. Sci J Appl Math Stat. 2014;2(1):26-30. doi: 10.11648/j.sjams.20140201.14

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  • @article{10.11648/j.sjams.20140201.14,
      author = {Edi Cahyono},
      title = {Mathematical Problem Appearing in Industrial Lumber Drying: A Review},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {2},
      number = {1},
      pages = {26-30},
      doi = {10.11648/j.sjams.20140201.14},
      url = {https://doi.org/10.11648/j.sjams.20140201.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sjams.20140201.14},
      abstract = {This article is a review of our work on the modeling of lumber drying that we have started in 2003. We consider a lumber drying process in a kiln chamber where from mathematical point of views, this is an initial and boundary value problem. The Moisture Content (MC) is measured at the center of the lumber by applying a nail that thousands times of the pore size of the wood. This leads to apply macro modeling for the diffusion process of the water inside the lumber. MC acts as the state variable u of the thickness x and time t. The state variable satisfies a diffusion equation. The Equilibrium Moisture Content (EMC) of the air acts as the boundary condition. We report the progress on mathematical modeling and compared the results with data from industry.},
     year = {2014}
    }
    

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    AB  - This article is a review of our work on the modeling of lumber drying that we have started in 2003. We consider a lumber drying process in a kiln chamber where from mathematical point of views, this is an initial and boundary value problem. The Moisture Content (MC) is measured at the center of the lumber by applying a nail that thousands times of the pore size of the wood. This leads to apply macro modeling for the diffusion process of the water inside the lumber. MC acts as the state variable u of the thickness x and time t. The state variable satisfies a diffusion equation. The Equilibrium Moisture Content (EMC) of the air acts as the boundary condition. We report the progress on mathematical modeling and compared the results with data from industry.
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