引用本文: 李翔宇, 袁江宏, 沈火明, 李映辉. 均质圆盘热传导问题的新解法1)[J]. 力学与实践, 2021, 43(6): 973-975.
LI Xiangyu, YUAN Jianghong, SHEN Huoming, LI Yinghui. A NEW METHOD FOR SOLVING THE HEAT CONDUCTIONS IN A HOMOGENOUS CIRCULAR DISK$^{1)}$[J]. MECHANICS IN ENGINEERING, 2021, 43(6): 973-975.
 Citation: LI Xiangyu, YUAN Jianghong, SHEN Huoming, LI Yinghui. A NEW METHOD FOR SOLVING THE HEAT CONDUCTIONS IN A HOMOGENOUS CIRCULAR DISK$^{1)}$[J]. MECHANICS IN ENGINEERING, 2021, 43(6): 973-975.

## A NEW METHOD FOR SOLVING THE HEAT CONDUCTIONS IN A HOMOGENOUS CIRCULAR DISK^1)

• 摘要: 本文旨在利用泊松公式发展均质圆盘稳态热传导问题的一种新解法。这种简单而优雅的解法可由复变函数中解析函数所满足的柯西-黎曼方程结合圆域中泊松公式直接获得。所得的积分形式解与经典的傅里叶级数解完全一致。这项工作搭建了级数解和积分解之间的桥梁,丰富了数学物理方法的教学素材,并为相关数学等式赋予了物理解释。

Abstract: This paper aims to develop a new method for solving the steady heat conduction in a homogenous circular disk by using the Poisson's formula. This simple and elegant method originates directly from the Cauchy-Riemann equations in combination with the Poisson's formula for a circular region. The solution obtained by the new method is expressed in an integral form, which is further proved to be completely consistent with the classic solution in Fourier series. By establishing the connection between the known Fourier series' solution and the new integral one, this work not only enriches the teaching materials for the course "Methods of Mathematical Physics", but also provides a clear physical interpretation for the corresponding mathematical equation.

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