The heat transfer coefficient spatial distribution reconstruction by an inverse technique

This article presents a technique for obtaining the spatial distribution of the heat transfer coefficient (HTC) for an impingement heat exchange directly from transient temperature measurements. The HTC retrieval problem is formulated through the boundary temperature and the heat flux. That formulation makes it possible to utilize the superposition principle as the temperature field depends linearly on both the mentioned boundary conditions (BC). The unknown boundary temperature and heat flux are approximated by the set of trial functions chosen by the user. The key point is to utilize the definition of the convective BC in the objective function formulation. This fact allows us to take advantage of the fact that for the impingement heat exchange the HTC is constant in time. Such definition of the minimized function improves the stability of the solution in the presence of the measurement errors.