热损耗条件下导热系数反演模型及实验研究

Inversion Model and Experimental Study of Thermal Conductivity Under Heat Loss Conditions

通过导热反问题反演求解导热系数通常误差较大,本文构建考虑热损耗条件下的虚拟薄板模型精确求解导热系数。首先通过数值算例验证模型的准确性和稳定性,正向问题使用有限差分法进行求解,反问题求解采用人工蜂群算法进行目标函数最优化。然后搭建第二类边界条件下导热正向装置,进行导热系数实例反演和实验研究,并将新模型与理论模型反演结果对比分析。结果表明理论模型反演结果的相对误差约为-14.76%,而新模型下导热系数反演相对误差达到-4.67%。新模型较理论模型反演结果更精确,有效降低了热损耗对反演的影响,提高了反演精度,更符合实际工况。

The relative error of the thermal conductivity estimated by the inverse heat transfer problem is usually high.In this paper,a virtual thin plate inversion model is constructed,and the thermal conductivity inversion is solved under heat loss conditions.Firstly the accuracy and stability of the model is validated by numerical examples.The forward problem is solved by finite difference method and the objective function is optimized by artificial bee colony algorithm.Then a device for generating positive heat conduction problems under the second boundary condition is built,and used for the experiments study of thermal conductivity inversion,and also compared and analyzed the inversion results of the new model and theoretical model.The relative error of the theoretical model inversion is about-14.76%,while the relative error of the new model is-4.67%.The results show that the virtual thin plate model effectively reduces the influence of heat loss on the inversion results,and improves the inversion accuracy,which is better than the inversion results of the theoretical model,is more in line with the actual conditions.