Temperature response spatiotemporal correlation model of heat transfer system

Abstract

For a linear heat transfer system, the unit step response of the temperature field to any system inputs, such as internal and external heat sources, is specific. This means that there is a definite temperature response correlation between any spatial points in the system spatiotemporally, which is independent of the system inputs. It is significant to achieve a quantitative description of the temperature response spatiotemporal correlation between the spatial points for solving the temperature field reconstruction problem of the heat transfer system with unknown inputs. In this paper, a temperature response spatiotemporal correlation model (RSTCM) of the heat transfer system is established originally to reveal the inherent quantitative relationship between the responses of any system spatial points theoretically. Firstly, an external description of the spatiotemporal mapping relationship of the heat transfer process is established according to the heat transfer equations. Furthermore, a basic RSTCM form is proposed and a response spatiotemporal correlation matrix is determined with the help of the external description. Finally, considering the ill-posed characteristic of the response spatiotemporal correlation problem, the regularization technology is employed to transform the original problem into a well-pose problem and to provide a response spatiotemporal correlation matrix with regularization. Effectiveness of the RSTCM is verified by the existing heat transfer experimental data. Besides, adaptability of the proposed model is demonstrated by the achieved numerical experiment results on a two-dimensional heat transfer system.