Estimation of temperature distributions and thermal stresses in a functionally graded hollow cylinder simultaneously subjected to inner-and-outer boundary heat fluxes

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to simultaneously estimate the unknown time-dependent inner and outer boundary heat fluxes in a functionally graded hollow circular cylinder from the knowledge of temperature measurements taken within the cylinder. Subsequently, the distributions of temperature and thermal stresses in the cylinder can be determined as well. It is assumed that no prior information is available on the functional forms of the unknown heat fluxes; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors and locations in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat fluxes, temperature distributions, and thermal stresses can be obtained for the test case considered in this study.