Inverse Determined Boundary Condition Without Prior Knowledge on the Function Form in One-Dimensional Heat Conduction Problems

摘要

A direct procedure is presented for the inverse determination of the temperature and heat flux boundary without prior knowledge on the function form of the estimated boundary in the one-dimensional heat conduction problem. A linear inverse model for the determination of the boundary condition is proposed and is constructed from the finite-difference model of the differential heat conduction equation based on the assumption that the temperature measurements are available over the problem domain. In contrast to the traditional approach, Ihe iteration in the proposed inverse model can be done only once and the inverse problem can be solved in a linear domain. In the example, comparisons between the exact boundary condition and the estimated ones (without measurement errors) are made to confirm the validity of the proposed model. The close agreement between the exact solutions and the estimated results shows the potential of the proposed model in finding the accurate value of the boundary in one-dimensional heat conduction problem.