A two-dimensional inverse problem in estimating the heat generation rate in an electronic device

摘要

This study is intended to provide an inverse method for estimating the heat generation rate in an electronic device. Finite-difference methods are first employed to discretize the problem domain and then a linear inverse model is constructed to identify the heat generation rate condition. The present approach is to rearrange the matrix form of differential governing equation and estimated coefficients of unknown condition. Then, the linear least-squares error method is adopted to find the solution. The results show that only one measuring point is sufficient to estimate the heat generation rate when the measurement errors are neglected. When the measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. The advantage of applying this method in inverse analysis is that no prior information is needed on the functional form of the unknown quantities, and initial guess and iteration are not required.