四边给定温度的各向异性矩形板稳态热传导解析研究

采用复级数方法给出了四边给定温度的各向异性矩形极稳态热传导解析解。将解析解代入温度边界条件及角点条件，用正弦级数的方法确定待求系数。数值计算结果表明本文解收敛稳定，讨论了各向异性板温度场的对称性并提出温度分布的中心对称性。针对四边给定温度分布的各向异性板温度场进行数值求解，讨论了材料热各向异性程度、各向异性角、跨宽比对温度场分布的影响。

Analytic Investigation of Steady-Syate Heat Conduction Problem of Rectangular Plate with Specified Boundary Temperature

This article deals with the development of a general analytic solution to the steady-statetemperature in a anisotropic rectangular plate with boundary temperature by complex series method. Theanalytic solution is substituted into boundary conditions and code conditions. The underdetermined coeffi-cients are solved by sine series method. Some examples show the good validity of the solutions. The sym-metry of temperature distributions in the plate is discussed and the centered-symmetry in the temperaturefield is suggested. Using the analytic method presented, numerical values of the temperature distributionin an anistropic plate under prescribed boundary temperature conditions are provided. The discussions arepresented regarding the effect of anisotropy of the conductive material, anisotropic angle and the ratio oflength to width on the temperature distribution.