用于求解背表面恒温导热反问题的标定方法和实验验证

doi:10.11949/0438-1157.20250632

摘要/Abstract

摘要：

针对一维线性有限区域下的背表面恒温的导热反问题，建立了数学模型，通过拉氏变换和标定消参，推导了对应的标定积分方程，用于预测表面热流。为验证其准确性与可行性，搭建了电加热实验平台，采用内置了热电偶的不锈钢304物块作为实验样品，通过氮化铝加热片施加可控热流，利用冰水冷却系统维持背表面恒温。利用标定实验和重建实验所得数据求解了预测的表面热流，同时通过对实验中各部分吸收热流的分析，得出了实际的样品表面热流。将预测的与实际的表面热流进行对比，两者的相对均方根误差为7.3552%。结果表明，在背表面恒温条件下，采用标定积分方程方法预测表面热流的拟合度很高，具有较好的准确性。此外，实验的不确定性分析表明，加热片热容为主要误差来源，计算得出的实际热流的不确定度百分比控制在8%以内；仿真模拟结果显示背表面恒温误差较小，能满足实验要求。

关键词: 导热反问题, 标定积分方程方法, 热流预测, 背表面恒温, 热传导, 传热, 实验验证

Abstract:

Calibration integral equation method (CIEM) is a new theoretical system for solving inverse heat conduction problems (IHCPs). It features fast solution speed, parameter-independence and high accuracy. For the inverse heat conduction problems with constant temperature on the back surface, the corresponding calibration integral equation was derived by establishing a mathematical model in a one-dimensional finite region. After regularized and discretized, it can be used to predict the surface heat flux. To validate its accuracy and feasibility, an electric heating experimental platform was built. A stainless steel 304 block with embedded thermocouples was used as the experimental sample. A controllable heat flux was applied through an aluminum nitride heater, and the constant temperature of the back surface was maintained by an ice water cooling system. The predicted surface heat flux was solved using the data from the calibration and the reconstruction experiments. Meanwhile, through the analysis of the heat flux absorbed by each part in experiments, the actual heat flux on the sample surface was calculated. Comparing the prediction result with the actual one, the relative root mean square error is 7.3552%. The result indicates that, under the constant temperature boundary condition of the back surface, CIEM has a high fitting degree and good effectivity in surface heat flux prediction. In addition, the experimental uncertainty analysis shows that the heat capacity of the heater is the main error, and the uncertainty percentage of the actual heat flux calculated is controlled within 8%. The simulation results show that the constant temperature error of the back surface is relatively small, meeting the experimental requirements.

Key words: inverse heat conduction problems, calibration integral equation method, heat flux prediction, constant temperature on back surface, heat conduction, heat transfer, experimental validation

中图分类号:

TK124

曾福葆, 程锐钦, 陈鸿初. 用于求解背表面恒温导热反问题的标定方法和实验验证[J]. 化工学报, DOI: 10.11949/0438-1157.20250632.

Fubao ZENG, Reiqin CHENG, Hongchu CHEN. Calibration method and experimental validation for resolving inverse heat conduction problem with constant temperature on back surface[J]. CIESC Journal, DOI: 10.11949/0438-1157.20250632.

图/表 12

图1 有限区域一维线性热传导示意图

Fig.1 Schematic diagram of one-dimensional linear heat conduction in finite region

图2 实验仪器与材料

Fig.2 Experimental instruments and materials

图3 实验平台整体布置图

Fig.3 The overall layout of the experimental platform

表1 莫来石HM 1800组分的物性参数

Table 1 Physical parameters of mullite HM 1800 components

材料	密度ρ/(kg·m^-3)	比热容c/(J·kg^-1·K^-1)
Al₂O₃	3900	785
SiO₂	2650	700
空气	1.29	1005

图4 加热片热容测定实验的数据

Fig.4 Data in thermal capacity measurement experiment of heater

图5 热物性参数验证加热实验结果

Fig. 5 Results of Heating experiments for thermophysical parameters verification

图6 各测量点温度变化曲线

Fig.6 Temperature change curves of different measurement points

图7 各部分功率变化曲线

Fig.7 Power change curves of four parts

图8 表面热流预测结果对比图

Fig.8 Comparison chart of surface heat flux prediction result

图9 各参数引起的不确定度

Fig.9 Uncertainties caused by different parameters

图10 实际表面热通量的不确定度

Fig.10 Uncertainty of the actual surface heat flux

图11 背表面恒温仿真验证结果

Fig.11 Simulation validation results of constant temperature on back surface

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