利用热传导方程研究高温作业专用服设计的数学模型

Study on Mathematical Model of High Temperature Apparel Design by Using Heat Conduction Equation

本文利用热力学知识建立数学模型,研究在实验室环境下,三层隔热材料组成的专用作业服装的隔热效果,计算假人皮肤外侧的温度随时间变化情况。首先根据Fourier试验定律,建立关于温度函数u(x,t)的一维分段热传导方程,使用有限差分法化简该热传导方程,得到有限差分方程组,近似计算原热传导方程的数值解。其次,当第II层厚度不确定时,结合建立的热传导方程,使用二分法计算出的最优厚度。最后进行灵敏度分析对模型的稳定性进行验证,同时确定出当第II和第IV层厚度都不确定时两层的最优厚度。

In this paper, we use the thermodynamics knowledge to establish the mathematical model in order to study the thermal insulation effect of the special operation clothing composed of three layers’ insulation materials in the laboratory environment, and calculate the temperature change outside the mannequins’ skin with time. Firstly, according to the Fourier test law, a one-dimensional segmental heat conduction equation for the temperature function u(x,t) is established. Simpli-fied the heat conduction equation by the finite difference method, the finite difference equations are obtained to approximate the numerical solution of the original heat conduction equation. Secondly, when the thickness of the second layer is uncertain, combined with the established heat conduction equation, the optimal thickness is calculated by the dichotomy method. Finally, the sensitivity analysis is performed to verify the stability of the model, and the optimal thickness of the two layers is determined when the thicknesses of the second and fourth layers are both uncertain.