Real-time reconstruction of the time-dependent heat flux and temperature distribution in participating media by using the Kalman filtering technique

Abstract

The Kalman filtering (KF) algorithm is introduced to solve the inverse coupled radiation-conduction heat transfer problem in the participating medium for the first time. The time-dependent surface heat flux and internal temperature distribution of the participating medium is reconstructed simultaneously from the (non-intrusive transient temperature) measurements made on the other surface. The governing energy equation and radiative transfer equation are calculated by using the finite volume method (FVM). Different forms of transient heat flux are employed to test the performance of the KF method. The influence of initial state, initial state error covariance, measurement noise, process noise, measurement noise covariance, process noise covariance, sampling step, refractive index, medium thickness, and absorption coefficient on the accuracy and stability are discussed thoroughly. All the retrieval results show that the surface heat flux and internal temperature distribution can be reconstructed simultaneously in real time. Compared with the hybrid algorithm of KF and recursive least-square estimator (RLSE), the KF algorithm can obtain better reconstruction results and a noticeable decrease of the sensitivity to measurement noise, initial temperature distribution, and absorption coefficient is observed from the retrieval results.