The estimation of space and time dependent strength of a volumetric heat source in a one-dimensional plate

Abstract

An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used to estimate the space and time dependent strength of a volumetric heat source with no prior information for the functional forms of timewise and spatial variations of the source strength. Simulated experimental data, needed for the inverse analysis, are generated by adding random errors to the calculated exact temperatures for the boundaries and interior of the plate. In order to examine the accuracy of estimations under the most strict conditions, test cases such as sawtooth shaped spatial variation of the source strengths are considered. The effects of the number and location of temperature sensors on the accuracy of the estimations are systematically examined. The estimates are significantly improved when the thermocouples are positioned close to the locations where the source strength exhibits peaks and valleys.