A three-dimensional inverse heat conduction problem approach for estimating the heat flux and surface temperature of a hollow cylinder

This study is intended to provide a different perspective for solving the three-dimensional, inverse, steady heat conduction problem for a hollow cylinder. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations and estimate unknown conditions. Then, the linear least-squares method is adopted to find the solution. The results show that one needs only a few measuring points in order to estimate the boundary temperature and heat flux when the measurement errors are negligible. When the measurement errors are considerable, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions.