基于格林函数法的常功率热源有限厚平板表面温度计算

摘要

For computation of thermal conductivity for sheet -like material in constant power plane heating test , based on Green's Function Method , the analytical expression functions of surface temperature for limited thick plate with one side constant power heating were derived .A numerical calculation method was employed to calculate the functions , and the approximate calculation value of the functions of surface temperature showed convergence characteristic in an example of aerated concrete .Additionally , the errors of nu-merical calculation of the function brought by different plus terms and heating time were analyzed .As the number of plus terms was greater than or equal to 40, the calculation error might be less than 1%in a short time heating.%为解决薄板状材料常功率平面热源法的导热系数计算问题，基于格林函数法，推导得到有限厚板状材料单面常功率加热时的表面温度函数解析表达式。以加气混凝土为例，应用数值计算方法，计算得到有限厚度平板材料的表面温度响应函数近似值，计算结果表现出较强的收敛特征。比较了表面温度响应函数中求和项数及加热时间对计算误差的影响，发现当求和项数m≥40时，在较短加热时间内计算误差才可能小于1％。