The inverse estimation of the thermal boundary behavior of a heated cylinder normal to a laminar air stream

This study provides an inverse analysis to determine the thermal boundary behavior of a heated cylinder normal to a laminar air stream. A finite-difference method is used to discretize the governing equations and then a linear inverse model is constructed. The present approach is to rearrange the matrix forms of the governing differential equations and to estimate the unknown conditions of the cylinder from the linear inverse model. The linear least-squares error method is then adopted to find the solutions of the unknown thermal boundary conditions such as surface temperatures, local heat flux, local Nusselt numbers, and even the unknown temperature of the hot wire imbedded in the center of the cylinder. The results show that only few measuring points inside the cylinder are needed to estimate the unknown quantities of the thermal boundary behavior even when measurement errors are considered. From this study it is confirmed that the proposed method is effective and applicable for the two-dimensional inverse heat conduction problems.