Abstract
The boundary element method (BEM) and sequential function specification method (SFSM) are used to research the inverse problem of boundary heat flux identification in the two-dimensional heat conduction system. The future time step in the SFSM is optimized by introducing the residual error principles to get the more accurate inversion results. For the forward problems, the BEM is used to calculate the required temperature value of discrete point; for the inverse problems, the impacts of different future time steps, measuring point position, and measuring error on the inversion results are discussed. Furthermore, the comparison is made for the optimal future time step obtained by introducing the residual error principle and the inherent future time step. The example analysis shows that the method proposed still has higher accuracy when the measuring error exists or the measuring point position is far away from the boundary heat flux.
Highlights
The inverse heat conduction problems (IHCP) are to measure the temperature at the heat conduction system boundary or internal point or points by using the experimental method to obtain partial temperature information and inverse some unknown parameters: the boundary condition, material thermophysical parameter, internal heat source and boundary geometry, and so on [1,2,3,4]
Qian et al solved the unsteady IHCP by using the sequential function specification method (SFSM) and conjugate gradient method, which sufficiently demonstrated the effectiveness of these two methods, analyzed, and compared the advantages and disadvantages of these two methods [14,15,16]
Lesnic et al identified the thermophysical parameters in one-dimensional transient heat conduction problems by using the boundary element method (BEM) [21]
Summary
The inverse heat conduction problems (IHCP) are to measure the temperature at the heat conduction system boundary or internal point or points by using the experimental method to obtain partial temperature information and inverse some unknown parameters: the boundary condition, material thermophysical parameter, internal heat source and boundary geometry, and so on [1,2,3,4]. Lin et al proposed an improved SFSM and researched the IHCP with time-varying internal heat source [17]. Lesnic et al identified the thermophysical parameters in one-dimensional transient heat conduction problems by using the BEM [21]. Weizhen proposed a subsection identification method, by which the IHCP identified by variable thermophysical parameters was solved. Zhou et al solved the heat conductivity coefficient in the two-dimensional transient inverse problems by using the BEM and gradient regularization method and obtained the relatively accurate inversion results [26]. For the boundary heat flux identification problem in the heat conduction system, the BEM is used to solve the two-dimensional unsteady forward problem without internal heat source; the SFSM is used to solve the inverse problem. In the process of solving the inverse problem, the future time step in the inversion process is optimized by introducing the residual error principle to improve the inversion accuracy
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