An Inverse Analysis Method for Estimation of Heat Flux and Temperature-Dependence of Heat Transfer Coefficient

Abstract

Transient thermal stresses develop in pipes during start-up and shut-down. In previous papers the present authors [1–4] proposed an inverse method for determining the optimum thermal inlet liquid temperature history which reduced the maximum transient thermal stress in pipes. The papers considered multiphysics including heat conduction, heat transfer, and elastic deformation. The inverse method used the relationship between inner surface temperature history, transient temperature distribution and transient thermal stresses. The coefficient of heat transfer plays an important role in the evaluation of thermal stress. In this study an inverse method was developed for estimating heat flux and temperature-dependence of the coefficient of heat transfer from the history of the outer surface temperature and the liquid temperature. The method used the relationship between the outer surface temperature and the inner surface temperature. For the regularization of solution the function expansion method was applied in expressing the history of flux on the inner surface. Numerical simulations demonstrated the usefulness of the proposed inverse analysis method. By examining the effect of measurement errors of temperature on the estimation, the robustness of the method was shown.