简化瞬态导热物体温度场解析解研究

SIMPLIFICATION OF THE ANALYTICAL SOLUTION FOR TEMPERATURE DISTRIBUTION OF A BODY IN TRANSIENT HEAT CONDUCTION

将瞬态导热过程中物体内温度分布简化为仅随时间而变的所谓“薄壁”温度场问题进行了进一步的研究。对3种已有的简化判断指标:体内无因次温差Θ_a、体内无因次极限温差Θ_b、物体外壁无因次温度梯度Θ_c的分析表明,采用Θ_a或Θ_c是不合适的,采用Θ_b亦有一定误差,提出以max(|Θ_1|,|Θ_2|)<C做为判断标准,导出了其精确表达式和简便判别式,并且绘出图线。研究结果还表明,各判断指标可表述成Bi准则和Fo准则的函数,但此函数是非单调的。

The problem whether the temperature field solution of a body in transient heat conduction can be obtained by using lumped capacity method or not is further investigeted in this paper. All the criteria such as (?)_a, (?)_b. (?)_cproposed in previous works are analysed. The results show that (?)_aand (?)_care unsuitable to be used as the judgement stardands and the use of (?)_bleads to a big deviation in some regions, A new critirion max (|(?)|_1, |(?)|_2)<C is presented. The exact equ. and concise expression are deduced, and some calculated data are plotted. The data also prove that the relation between the criteria, Bi and Fo are not monotic.