Abstract This paper reports the results of an investigation to solve the inverse problem of estimating the strengths of different strip heat sources embedded in a flat plate under laminar steady-state forced convection and by way of this propose a novel method to detect hot spots from remote measurements. A Bayesian framework is adopted to infer the strength of the heat sources from thermochromic liquid crystal (TLC) temperature measurements. This framework consists of the forward model, the measured data, and the inverse model. The forward model simulates the conjugate three-dimensional heat transfer problem with the specified thermophysical properties, and the boundary conditions. The input data for the forward model is a combination of different heat source strengths, and the output is temperature data obtained at the bottom surface of the cork. The input-output data of the numerical simulations are used to build a proxy or surrogate (artificial neural network, ANN) that acts as a replacement for the actual forward model to increase the computational speed and decrease the computational time while solving the inverse problem. Calibrated thermochromic liquid crystal sheets are attached at the bottom surface of the cork for mapping the temperature data, so that the top surface where the convection takes place is undisturbed. In the inverse model, Bayesian statistics, along with the Gibbs sampling algorithm is adopted for analyzing the posterior distribution to estimate the mean, the maximum a posteriori and the standard deviation of the heat source strengths. Validation and robustness of the inverse methodology have been examined. The estimated heat source values are input to the forward model to determine the hot spot temperatures on the flat plate. This is a key spin-off from the present study, wherein based on temperature measurements at a convenient place, the hot spot in a geometry can be remotely ‘estimated.’ A comparison of the simulated and the measured values of the hot spot temperatures is reported for different flow Reynolds numbers.

中文翻译：

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一种利用液晶热成像检测热点和估计离散热源强度的新方法

摘要 本文报告了解决在层流稳态强制对流下估计嵌入平板中的不同带状热源强度的逆问题的研究结果，并由此提出了一种从远程检测热点的新方法。测量。采用贝叶斯框架从热致变色液晶 (TLC) 温度测量中推断热源的强度。该框架由正向模型、测量数据和逆向模型组成。正向模型模拟具有指定热物理特性和边界条件的共轭三维传热问题。正向模型的输入数据是不同热源强度的组合，输出是在软木塞底面获得的温度数据。数值模拟的输入输出数据用于构建代理或代理（人工神经网络，ANN），作为实际正向模型的替代品，以在解决逆问题的同时提高计算速度并减少计算时间。校准后的热致变色液晶片贴在软木塞的底面，用于绘制温度数据，从而使发生对流的顶面不受干扰。在逆模型中，采用贝叶斯统计和吉布斯采样算法分析后验分布，估计热源强度的均值、后验最大值和标准差。已经检查了逆方法的验证和稳健性。估计的热源值被输入到正向模型以确定平板上的热点温度。这是本研究的一个关键衍生产品，其中基于方便位置的温度测量，可以远程“估计”几何中的热点。针对不同的流动雷诺数报告了热点温度的模拟值和测量值的比较。