Simultaneous estimation of internal temperature field and boundary time-dependent heat flux in absorbing and scattering media using the unscented Kalman smoothing technique

Based on the future measured temperature, the Rauch-Tung-Striebel smoothing technique coupled with unscented Kalman filter is introduced to resolve the nonlinear inverse radiation-conduction heat transfer problem, which is nonlinear because of specific heat and thermal conductivity with temperature and existence of the radiative heat transfer. For the direct process, the finite volume method is applied to calculate the energy equation and radiative transfer equation is computed by the discrete ordinate method. Based on the measurement temperature signals of the right surface, the left surface time-dependent heat flux and interior temperature in absorbing and scattering medium are retrieved in near real time by using the proposed method. The different number of the future measured temperature, measurement noise, and process noise covariance are applied to examine the feasibility and reliability of the present algorithm. All retrieval results show that the Rauch-Tung-Striebel smoothing technique coupled with unscented Kalman filter is accurate and stable. Compared to the unscented Kalman filter, the accuracy of the retrieval temperature distribution is improved significantly, the deviation and oscillation of the retrieval time-dependent heat flux are also decreased substantially.