计算外壁热响应的非线性瞬态导热反问题方法

研究组合结构外壁热响应特性，采用Beck’s序列函数法，优化算法各个环节，建立应用多个温度测点、多个未来时间步的计算模型。文章通过假设热流变化呈三角波形，计算结构内部温度场，并取其中数点温度信息作为反问题输入条件迭代反演得到外壁热流响应，得到热流误差不超过0.5%、温度误差不超过0.01%的理想结果，并得到测点数量、位置等因素对计算误差的影响。该计算方法可应用于包装结构在模拟火灾等特殊环境中的外壁热响应研究。

Calculation of the boundary heat response based on nonlinear transient heat conduction

Beck’s series function algorithm is applied to obtain the boundary heat response characteristics of combined bodies. Each step of the algorithm is optimized. A mathematical model containing multi-temperature measuring points and multi-future time steps is established. A triangular waveform heat flux is assumed as the boundary condition to solve the direct heat conduction problem to obtain the temperature field in the object. Then temperatures at some points are chosen as the input condition to calculate the boundary heat response. The errors of the results of iteration for the heat fluxes are lower than 0.5% and the errors of temperatures are lower than 0.01%. The effects of the number of measuring points, the positions of the measuring points and future time steps on the calculating errors are analyzed. The calculating method can be used to study the boundary heat response characteristics of the package structure in the fire simulation.