An inverse non-Fourier heat conduction problem approach for estimating the boundary condition in electronic device

Abstract

This study is intended to provide an inverse method for estimating the unknown boundary condition T(0, y, t) in a non-Fourier heat conduction electronic device. 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 present approach is to rearrange the matrix forms of the differential governing equations and to estimate the unknown conditions. Then, the linear least-squares method is adopted to obtain the solution. The results show that one measuring point is sufficient to estimate the unknown boundary condition T(0, y, t) without measurement errors. When considering the measurement errors, the magnitudes of the discrepancies in the boundary condition T(0, y, t) are directly proportional to the size of measurement errors. Due to the complicated reflection and interaction of the thermal waves, this phenomenon reflects the fact that the inverse non-Fourier heat conduction problem is different from the inverse Fourier heat conduction problem. In contrast to the traditional approach, the advantage of applying this method in inverse analysis is that no prior information is needed on the functional form of the unknown quantities. In addition, no initial guess is required and the calculation can be done in only one iteration.