无限大区域内四管冻结的稳态温度场解析解

Analytical Solution of Steady State Temperature Field of Four Freezing Pipes in an Infinite Region

采用势函数叠加理论推导了4根冻结管以任意形式排列冻结时的稳态温度场解析解,得出了4根冻结管以等间距直线、矩形和菱形等排列时的稳态温度场特定解,并用热学数值模拟方法对解析解进行验证.结果表明,解析解的计算结果与数值模拟结果较吻合.

Based on the potential superposition theory, this paper gives analytical solutions to steady state frozen temperature of four freezing pipes arranged at random. Particular solutions are derived for some par- ticular arrangements, such as four freezing pipes with rectangle arrangement and rhombus arrangement. Comparison of the analytical solutions with the numerical thermal analysis shows that the analytical solu- tions are precise enough.