高速压制粉末散体空间分形维数及热传导

journal6 ›› 2008, Vol. 29 ›› Issue (5): 53-56.

高速压制粉末散体空间分形维数及热传导

(中南大学数学科学与计算技术学院，湖南长沙 410083）

出版日期:2008-09-25 发布日期:2012-05-20
作者简介:谷成玲(1983-)，女,山东莱芜人,中南大学硕士生,主要从事粉末散体空间的分形特征研究；秦宣云(1965-)，男,湖南长沙人,中南大学数学科学与计算技术学院副教授,博士,主要从事分形几何及应用、图形及图像处理等研究.
基金资助:
国家重点基础研究发展规划973项目(2006CB605207); 湖南省科技计划项目（2007RS4028）；中南大学博士后基金项目

Fractal Dimension and Thermal Conductivity Model of Granular Powder Space in High Velocity Compaction

(School of Mathematical Science and Computing Technology，Central South University,Changsha 410083,China)

Online:2008-09-25 Published:2012-05-20

摘要/Abstract

摘要：基于分形理论,利用粉末散体空间的堆积密度、粉末颗粒的密度和孔隙介质的密度，推导出了计算粉末散体空间分形维数的公式；利用等效热阻法建立了粉末散体空间有效热导率的串联分形模型，并给出了考虑热辐射条件的有效热导率的计算公式.通过分形维数和有效热导率计算公式的函数曲线，分析了堆积密度对分形维数以及分形维数、温度对有效热导率的影响，结果表明：粉末散体空间分形维数随堆积密度增大而增大，有效热导率随分形维数增大而减小，随温度升高而增大.

关键词： 粉末散体空间, 分形维数, 有效热导率, 热辐射

Abstract: Based on the fractal theory,a formula of computing the fractal dimension of the granular powder space is deduced using the accumulated density,powder particles’density and density of the pore media.At the same time,with the method of equivalent resistance,a series fractal model referring to effective themal conductivity of powder dispersion’s space is established.In addition,a formula is given considering the heat radiation.Through the curves of the fractal dimension and effective thermal conductivity's formula,it is analysed that the packing density has the impact to fractal dimension and the fractal dimension and temperature have influence on the effective thermal conductivity.The results indicate that fractal dimension of granular powder space goes higher with packing density increasing and effective thermal conductivity decreases with fractal dimension and increases with temperature.

Key words: granular powder space, fractal dimension, effective themal conductivity, heat radiation

谷成玲, 秦宣云, 郑洲顺, 崔彩虹. 高速压制粉末散体空间分形维数及热传导[J]. journal6, 2008, 29(5): 53-56.

GU Cheng-Ling, QIN Xuan-Yun, ZHENG Zhou-Shun, CUI Cai-Hong. Fractal Dimension and Thermal Conductivity Model of Granular Powder Space in High Velocity Compaction[J]. journal6, 2008, 29(5): 53-56.