ABSTRACT

This paper presents an inverse methodology to estimate the parameters of the non-uniform heat generation (function estimation) within a flat plate assembly using steady-state conjugate heat transfer experiments on the flat plate assembly. Steady-state laminar conjugate forced convection experiments on a flat plate assembly are conducted on a horizontal wind tunnel to estimate the parameters of the non-uniform heat generation within flat plate assembly using the inverse methodology. Bayesian inference based Metropolis Hastings–Markov Chain Monte Carlo (MH–MCMC) algorithm and experimental temperatures are employed in the inverse methodology. The experimental temperatures are measured at convenient locations of the flat plate assembly using liquid crystal thermography. In order to accomplish the retrieval, first, steady-state experiments on only the cork material are conducted to estimate the thermal conductivity of the cork material accurately for use in the estimation of the heat generation rate so that the additional error due to uncertainty in the thermal conductivity of the cork material does not affect our final goal of estimating heat generation rate. Following this, steady-state experiments on the cork setup (consisting of a non-uniform heat generation heater and two symmetric cork plates) are conducted to ascertain the nature of heat generation of the heater using measured temperatures and fundamental rate laws. The priors are generated using coupled artificial neural network (ANN) and Levenberg–Marquardt (LM) algorithm for Bayesian inference. Using the Bayesian inference with priors, the parameters of non-uniform heat generation are then estimated in terms of the mean, maximum a posteriori with standard deviation. Finally, the simulated heat powers and temperatures are estimated with retrieved parameters of the non-uniform heat generation. These compared very well with the measured heat powers and temperatures. Finally, a recipe for solving a practical problem, in which only measured temperatures are available, is provided.

摘要

本文提出了一种逆向方法，使用平板组件上的稳态共轭传热实验来估计平板组件内非均匀发热（函数估计）的参数。平板组件的稳态层流共轭强制对流实验在水平风洞中进行，以使用逆向方法估计平板组件内非均匀发热的参数。基于贝叶斯推理的 Metropolis Hastings–Markov Chain Monte Carlo (MH–MCMC) 算法和实验温度用于逆向方法。使用液晶热成像法在平板组件的方便位置测量实验温度。为了完成检索，首先，仅对软木材料进行稳态实验，以准确估计软木材料的热导率，用于估计热产生率，这样由于软木材料热导率的不确定性引起的额外误差不会影响我们的最终目标是估算发热率。在此之后，对软木装置（由不均匀发热的加热器和两个对称的软木板组成）进行稳态实验，以使用测量的温度和基本速率定律来确定加热器的发热性质。先验是使用耦合人工神经网络 (ANN) 和用于贝叶斯推理的 Levenberg–Marquardt (LM) 算法生成的。使用先验贝叶斯推理，然后根据平均值、最大后验概率和标准差来估计非均匀发热的参数。最后，使用非均匀发热的检索参数估算模拟的热功率和温度。这些与测得的热功率和温度相比非常好。最后，提供了解决实际问题的方法，其中只有测量的温度可用。