A novel formulation and sequential solution strategy with time-space adaptive mesh refinement for efficient reconstruction of local boundary heat flux

Abstract Inverse heat conduction problems appear in a variety of applications in industry and academia. Due to their mathematical challenges, they have been studied extensively over the last decades. Nevertheless, the solution of three dimensional transient inverse heat conduction problems are still computationally expensive. Commonly used solution approaches include the regularization-based approaches such as Tikhonov regularization or iterative regularization that result in formulating and solving optimization problems. A radically different solution approach is presented in this paper to provide efficient solutions of three dimensional transient inverse heat conduction problems on thin-plates that are used very often in industrial applications. Instead of solving optimization problems subject to constraints given in terms of three dimensional partial differential equations, the suggested approach transforms the inverse problem into an easy-to-solve direct problem that only needs the reconstruction of a Dirichlet boundary condition. This yields an approximated solution. Furthermore, a new time-space adaptive mesh refinement strategy is proposed to further reduce computational effort at an acceptable level of estimation precision. The accuracy and efficiency of the proposed sequential approach as well as the time-space adaptive mesh refinement strategy are validated by four representative case studies arising from practice. Estimation results with experimental data are also presented. The current work is considered as an important step forward towards the efficient solution of transient three dimensional inverse heat conduction problems, which is particularly useful for developing heat-flux soft sensors in practical problems arising from different fields such as pool boiling, falling films and steelmaking.