各向异性介质二维稳态热传导问题的分析解

The Analytical Solution of the Two-Dimensional Steady-State Heat Conduction in an Anisotropic Medium

本文利用双变量函数及其偏导数在闭区间上完整的双重付里叶级数表达式求得矩形区域中各向异性介质稳态热传导问题的分析解。文中例子给出各向异性介质内的温度场和热流密度的数字结果,并讨论介质的各向异性效应。

The analytical solution of the steady—state heat conduction in the anisotropic medi- um with a rectangular shape is proposed by the complete Fourier double—series expression of a dou- ble-variable function and its partial derivatives in a closed region.Some numerical examples regard- ing to the temperature field and the heat flux distribution are presented.The anisotropy effect of the medium is also discussed.