高温作业专用服装温度变化的数学原理及其应用  

Mathematical Principle and Application of Temperature Change in Clothing for High Temperature Operation

作　　者：卢鹏[1] 徐昌贵 LU Peng;XU Changgui(College of Mathematics,Southwest Jiaotong University,Chengdu,Sichuan 610031,China)

机构地区：[1]西南交通大学数学学院,四川成都610031

出　　处：《宜宾学院学报》2020年第6期81-86,共6页Journal of Yibin University

基　　金：西南交通大学教改项目“基于导师制的数学建模强化训练、提升工科学生科研能力”(1804096)。

摘　　要：利用传热学、微积分等基础理论建立在稳定环境中专用服装热传导的偏微分方程组模型.根据实验要求和导热特性确定初值条件、边值条件和分界面条件,给出显式差分法和隐式差分法两种有限差分求解算法.采用更为方便与稳定的隐式差分法对模型进行求解,得出温度随时间变化的规律.对所得结果进行了稳定状态下的验证,可为服装的生产与研制提供理论指导依据.Based on the knowledge of heat transfer and calculus,a set of partial differential equations(PDEs)model for clothing heat conduction in stable environment was established.According to the experimental requirements and thermal conductivity,the initial conditions,boundary conditions and interface conditions were determined.At the same time,two finite difference algorithms,explicit difference method and implicit difference method,were given.A more convenient and stable implicit difference method was used to solve the model,and the law of temperature changing with time was obtained.Finally,the results are verified in a stable state,which can be used to guide the production and development of garments.

关 键 词：偏微分方程 数学模型 有限差分 温度变化 

分 类 号：O29[理学—应用数学]