• 论文与研究报告 •

### 有限差分法逆求木材导热系数

1. 东北林业大学材料科学与工程学院 哈尔滨 150040
• 收稿日期:2014-05-21 修回日期:2014-06-23 出版日期:2015-04-25 发布日期:2015-05-20
• 通讯作者: 蔡英春
• 基金资助:

国家自然科学基金项目(31270595)。

### Inverse Determination of Thermal Conductivity of Wood Using Finite Difference Method

Zhao Jingyao, Fu Zongying, Huan Siqi, Cai Yingchun

1. School of Material Science and Engineering, Northeast Forestry University Harbin 150040
• Received:2014-05-21 Revised:2014-06-23 Online:2015-04-25 Published:2015-05-20

【目的】 提出一种基于有限差分法逆求木材导热系数的方法,以期弥补传统测量法设备复杂、价格高昂的不足,为后续建立导热系数的回归方程提供可靠数据。【方法】 运用一维热传导控制方程描述木材升温过程中内部温度变化。以兴安落叶松弦切锯材为对象,通过试验获得锯材沿厚度方向的温度数据(温度检测: 使用NEC Remote Scanner Jr. DC3100多点信号巡检仪通过埋入锯材的T形热电偶获得),采用有限差分逆求法,合理化边界条件后编程求解其在不同含水率、不同温度下的径向导热系数(其中,控制方程离散后的导热系数差分矩阵采用追赶法求解,所有差分方程均在Matlab2010b软件编程并运行),探讨并分析其随含水率、温度的变化规律。【结果】 1) 兴安落叶松锯材径向导热系数计算值沿厚度方向存在一定波动性,但其平均值0.106 1 W ·m-1K-1(标准差0.010 8)符合实际要求,且与理论计算值(0.110 9,0.125 2W ·m-1K-1)较为接近; 2) 含水率、温度对导热系数影响显著,且前者影响高于后者(含水率与温度的F-检验分别为126.942 1,99.008 3); 含水率、温度共同作用对导热系数亦存在显著影响(交互作用的F-检验为164.297 5); 导热系数随含水率的升高而增大,随温度的升高亦增大; 3) 木材材性与内部含水率分布对导热系数的影响较大。【结论】 通过试验获得木材内部可靠的温度分布与变化数据后,运用有限差分逆求法可快速、准确获得内部与测温点相对应位置的导热系数, 尽管计算值存在一定波动性,但其平均值与理论计算值相吻合,说明运用该方法测算木材导热系数是可行的。相比传统导热系数测量方法,该方法最大优势在于经济且不受试样尺寸限制; 同时,可以测算试样内部任意层位置导热系数。今后为提高测算精度,木材内部由于水分迁移产生的热量变化与材性差异应考虑使用该方法; 同时,为推广此方法,将程序可视化亦是今后研究的方向。

Abstract:

【Objective】To develop a precise, quick and economic method for determination the thermal conductivity of wood, this paper proposed a new numeral method based on the inverse finite difference method, which can overcome the drawback of traditional methods such as depending on relatively complex and expensive instrumentations. This will provide reliable data for the development of thermal conductivity's regression equation. 【Method】A one-dimensional governing equation of the heat conduction was used to describe the temperature variation inside the lumber during the heating process. The timbers obtained through tangential cut in larch (Larix gmelinii) plantation, with dimensions of 600 mm in length, 220 mm in width, and 40 mm in thickness, and moisture contents of 28.3%, 41.2%, 62.3%, were used in the experiments. Temperature along the thickness direction was obtained via experiments. The detection of temperature was obtained using NEC Remote Scanner Jr. DC3100 with T-type in wood. With inverse finite difference method and rationalization of boundary condition, the determination of thermal conductivity in radial direction with different moisture content and temperature was achieved. Difference matrix of thermal conductivity from the discrete control equations could be solved by tridiagonal matrix algorithm (TDMA). All difference equation were programmed and run in Matlab 2010b. At the end, the variation law of thermal conductivity with the changing of moisture content and temperature was discussed and analyzed. 【Result】The results showed that: 1) although some fluctuation along the thickness direction of thermal conductivity in larch plantation was observed, the average value (0.106 1 W ·m-1K-1, standard deviation(SD) was 0.010 8) agreed with theoretical calculating value (0.110 9, 0.125 2W ·m-1K-1); 2) MC and T had apparent effect on the thermal conductivity and the former influences slightly higher than the latter (FMC-test is 126.942 1, FT-test is 99.008 3). The interaction of MC and T also had apparent effect on the thermal conductivity (FMC×T-test is 164.297 5). The thermal conductivity increased with increasing MC and T; 3) Wood properties and the distribution of MC had apparent effect on the thermal conductivity. 【Conclusion】Reliable temperature data in wood was obtained via experiments. The thermal conductivity in the position corresponding to temperature measuring points was obtained quickly and accurately with IFDM. Although some fluctuation of thermal conductivity was observed, the average value agreed with theoretical calculating value. It indicted that the determination of thermal conductivity with finite difference method is feasible. Compared with traditional method, the main advantage of our method is economic and unconstrained in size of specimen. The thermal conductivity of any layer of wood can be obtained. To improve precision, heat changes with moisture migration and the difference of wood properties should be considered. To expand the method, program visualization should also be researched in the future.