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利用保形变换、分离变量及区域衔接方法分析了地下直埋管道的温度场,得到了级数形式的解。由于问题具有非正交性质,本文提出了一种确定级数项系数的边界离散方法。该方法也适用于其它类型的可分离变量的非正交问题。文中还对工程实例进行了计算,结果表明,目前仍在使用的简化算法具有较大相对误差。
The temperature field of the underground buried pipeline was analyzed using conformal transformation, separated variables, and regional convergence methods, and the solutions in the form of series were obtained. Due to the non-orthogonal nature of the problem, this paper proposes a boundary discretization method for determining the coefficient of the series term. This method is also applicable to non-orthogonal problems of other types of separable variables. The paper also calculates the engineering examples. The results show that the simplified algorithm still in use has a relatively large relative error.