ABSTRACT

This paper describes a methodology for mathematical modeling, computing, and research of two mutually connected problems: 2D non-stationary temperature distribution in logs stored for a long time in an open warehouse at periodically changing ambient air temperature in winter and change in the icing degrees of the logs during this time. Mathematical descriptions of the periodically changing ambient air temperature and of three types of relative icing degree of the logs that result under the influence of that temperature have been presented. These descriptions are introduced in coupled 2D non-linear mathematical models of the heat distribution in logs during their freezing and defrosting. The paper presents solutions of the models with explicit form of the finite-difference method. Results from a simulative investigation of the 2D non-stationary temperature distribution, average mass temperature, and three types of icing degree of beech logs with industrial dimensions (diameter of 0.4 m and length of 0.8 m), moisture content of 0.6 kg·kg⁻¹, and initial temperature of 0°C during their 5 days and nights alternating freezing and defrosting in an open warehouse at sinusoidal change of the ambient air temperature with various initial values below −5°C and different amplitudes are graphically presented and analyzed.

摘要

本文描述了一种数学建模、计算和研究两个相互关联的问题的方法：在冬季周期性变化的环境气温和结冰度的变化下，长期存放在露天仓库中的原木的二维非平稳温度分布在此期间的日志。给出了周期性变化的环境空气温度和在该温度影响下产生的三种类型的测井相对结冰程度的数学描述。这些描述是在原木冷冻和解冻过程中热分布的耦合二维非线性数学模型中引入的。论文给出了具有显式形式的有限差分方法的模型的解。^-1，初始温度为 0°C，在开放式仓库中 5 天和黑夜交替冷冻和除霜，环境空气温度呈正弦变化，各种初始值低于 -5°C 和不同的幅度被图形化地呈现和分析。