基于分层差分方程的热防护服热量分布规律的模拟

Simulation of Heat Distribution Law of Thermal Protective Clothing Based on Lay-ered Difference Equation

摘要: 为研究耐热服装在高温环境中的热量分布情况，降低在高温环境工作下耐热服装的制作成本，且缩短其研发周期，本文首先建立对于不同材质层的“高温作业防护服–空气–皮肤”热传导方程来研究不同层的热量分布情况，其中热传导方程中热扩散率依据介质材料的参数值而定。我们利用两种方法来解决偏微分方程的边界条件问题。在方法一中引入热阻的概念，根据数值分析中求解偏微分方程的Crank-Nicolson隐式格式，即可求出不同材质层中温度–空间–时间的相关结果。在模型二中，考虑将四种不同材质层视为一个整体，分别对四种不同材质层中热传导方程运用古典显式差分法迭代进行求解偏微分方程数值解。结果表明我们的方法是可行的。

Abstract: In order to study the heat distribution of heat-resistant garments in high-temperature environ-ments and further to reduce the production cost of heat-resistant garments under high-temperature environment, and shorten the development cycle, in this paper, we first establish a model of high-temperature protective clothing-air-skin for different material layers. The heat conduction equation is used to study the heat distribution of different layers, where the thermal diffusivity in the heat transfer equation depends on the parameter values of the dielectric material. We propose two models to solve the boundary condition problem in partial differential equations. The concept of thermal resistance is introduced in Model I. According to the Crank-Nicolson implicit scheme for solving partial differential equations in numerical analysis, the temperature-space-time correlation results in different material layers can be obtained. In Model II, four different material layers are considered as a whole. Thus, the classical heat differential equations are used to solve the partial differentials of the heat conduction equations for the four layers. Numerical solution of the equation shows that the methods are workable.