Volume 2, Issue 1, February 2014, Page: 26-30
Mathematical Problem Appearing in Industrial Lumber Drying: A Review
Edi Cahyono, Dept. Mathematics FMIPA Univ. Halu Oleo, Kendari, Indonesia
Received: Feb. 21, 2014;       Published: Mar. 20, 2014
DOI: 10.11648/j.sjams.20140201.14      View  3082      Downloads  132
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.
Boundary Value Problem, Initial Value Problem, Diffusion Equation, Lumber Drying
To cite this article
Edi Cahyono, Mathematical Problem Appearing in Industrial Lumber Drying: A Review, Science Journal of Applied Mathematics and Statistics. Vol. 2, No. 1, 2014, pp. 26-30. doi: 10.11648/j.sjams.20140201.14
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.
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.
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.
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.
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.
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.
U. Hornung, Homogenization and Porous Media, Springer-Verlag, Berlin, 1997.
E. Kreyszig, Advanced Engineering Mathematics, 7th ed., John Wiley & Son, Singapore, 1999.
K. W. Morton & D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
S. Omarsson, Numerical analysis of moisture related distortion in sawn timber, PhD thesis, Dept. of Structural Mechanics, Chalmers University of Technology, Goteborg, Sweden, 1999.
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.
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.
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.
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.
A. G. Ramm. An inverse problem for heat equation. Journal of Mathematical Analysis and Applications, 2001, vol. 264, pp. 691–697.
A. G. Ramm, "An inverse problem for the heat equation II," Applied Analysis, 2002, vol. 81, no. 4, pp. 929-937.
Browse journals by subject