Theoretical Thermal Conductivity Equation for Uniform Density Wood Cells
Keywords:Resistive-circuit modeling, wood cell, thermal conductivity, moisture content, heat transfer, cellular structure, finite element modeling, anisotropy
AbstractThe anisotropy of wood creates a complex problem requiring that analyses be based on fundamental material properties and characteristics of the wood structure to solve heat transfer problems. A two-dimensional finite element model that evaluates the effective thermal conductivity of a wood cell over the full range of moisture contents and porosities was previously developed, but its dependence on software limits its use. A statistical curve-fit to finite-element results would provide a simplified expression of the model's results without the need for software to interpolate values. This paper develops an explicit equation for the values from the finite-element thermal conductivity analysis. The equation is derived from a fundamental equivalent resistive-circuit model for general thermal conductivity problems. Constants were added to the equation to improve the regression-fit for the resistive model. The equation determines thermal conductivity values for the full range of densities and moisture contents. This new equation provides thermal conductivity values for uniform-density wood material using inputs of only oven-dry density and moisture content. An explicit method for determining thermal conductivity of uniform density wood cells has potential uses for many wood applications.
Gu H, Hunt JF (2006) Two-dimensional finite element heat transfer model of softwood. Part III. Moisture content effect on thermal conductivity. Wood Fiber Sci 39(1): 159-166.nHart CA (1964) Theoretical effect of gross anatomy upon conductivity of wood. Forest Prod J 14(1):25-32.nHunt JF, Gu Hm (2006) Two dimensional finite element heat transfer model of wood—Part I. Effective thermal conductivity. Wood Fiber Sci 38(4):592-598.nIerardi JA (1999) A computer model of fire spread from engine to passenger compartments in post-collision vehicles. M.S. thesis., Worcester Polytechnic Institute, Worcester, MA, Fire Protection Engineering: 205 pp.nIncropera FP, DeWitt DP (1981) Fundamentals of heat and mass transfer. 4th Ed. John Wiley & Sons, New York.nInsightful Corporation (2001) S-PLUS 6 for Windows Programmer's Guide. Insightful Corporation, Seattle, WA.nMacLean JD (1941) Thermal conductivity of wood. Heat Piping Air Cond 13:380-391.nSiau JF (1995) Wood: Influence of moisture on physical properties. Department of Wood Science and Forest Products, Virginia Polytechnic Institute and State University, Blacksburg, VA. 227 pp.nStamm AJ, Smith WE (1969) Laminar sorption and swelling theory for wood and cellulose. Wood Sci Technol 3(1): 301-323.n
The copyright of an article published in Wood and Fiber Science is transferred to the Society of Wood Science and Technology (for U. S. Government employees: to the extent transferable), effective if and when the article is accepted for publication. This transfer grants the Society of Wood Science and Technology permission to republish all or any part of the article in any form, e.g., reprints for sale, microfiche, proceedings, etc. However, the authors reserve the following as set forth in the Copyright Law:
1. All proprietary rights other than copyright, such as patent rights.
2. The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In the case of whole articles, such third parties must obtain Society of Wood Science and Technology written permission as well. However, the Society may grant rights with respect to Journal issues as a whole.
3. The right to use all or part of this article in future works of their own, such as lectures, press releases, reviews, text books, or reprint books.