Multidimensional inverse transient heat conduction problems by direct sensitivity coefficient method using a finite-element scheme

A recently developed algorithm called the direct sensitivity coefficient method has been extended to deal with the transient effect of inverse heat conduction problems. The method was successfully applied to multidimensional steady-state problems. Different sensitivity coefficients have been used to assess the physical responses of the domain considered under unit loading conditions for steady-state inverse problems. The concept of the finite-element discretization has been applied to evaluate the global responses under the total loading condition. The method developed is capable of dealing with unknown surface heat flux; surface temperature, heat transfer coefficient, or any combination of the above. In this article, the formulation as well as the theory adopted is discussed. The finite-element procedures for solving two-dimensional transient problems are specifically illustrated. Analysis of a selected benchmark problem is conducted. Results based on information with and without future temperatures are presented with emphasis on accuracy estimations. Recommendations for further work are also included.