Determination of thermal conductivities by inverse analysis for one-dimensional heat conduction problems

摘要

Two finite difference procedures are presented for the inverse determination of the thermal conductivity in a one-dimensional heat conduction domain. The thermal conductivity is reconstructed from the inverse analysis based on the assumption that the temperature distribution is either available over the entire domain or at discrete grid points. The convergence and stability of the inverse algorithms are investigated. It is concluded that both procedures are first-order accurate methods. To confirm the validity of the numerical procedures, the calculated thermal conductivity are verified by comparing with the available analytical solutions. The close agreement between the two results confirms that the proposed finite difference techniques are effective procedures for the inverse determination of thermal conductivity in a one-dimensional heat conduction domain. The methods are applicable for linear and non-linear spatially as well as temperature dependent thermal conductivities. Additionally, the uniquesess of the present techniques is that a priori knowledge of the functional form for the thermal conductivity is not mandatory.