Estimating the boundary condition in a 3D inverse hyperbolic heat conduction problem

Abstract

This study is intended to provide an inverse method for estimating the unknown boundary condition T( x, 0, z, t) in a 3D non-Fourier heat conduction problem. In this study, finite-difference methods are employed to discretize the problem domain, and then a linear inverse model is constructed to identify the unknown boundary condition. The matrix forms of the original differential governing equations are rearranged in order that the unknown conditions can be represented explicitly, and the linear least-squares method is then adopted to determine their solution. The results show that the proposed method is capable of generating precise solutions using just a small number of measuring points. Furthermore, it is indicated that the method is capable of providing good numerical approximations even where measurement errors are present. The phenomenon of complicated reflection and interaction of thermal waves reflects the fact that the inverse non-Fourier heat conduction problem is different from the inverse Fourier heat conduction problem. In contrast to traditional approaches, the proposed inverse analysis method: requires no prior information regarding the functional form of the unknown quantities. In addition, only one iteration is necessary for calculation, and no initial guess is required. Furthermore, the existence and uniqueness of the solutions can be easily identified.