Numerical Analysis of the Estimation of Three Boundary Conditions in Two Dimensional Inverse Heat Conduction Problem

Abstract

A simultaneous estimation of three boundary conditions of heat conduction problem is proposed by numerical approach. A finite-difference method is used to discretize the governing equations. The aim is to estimate the evolution of the distributions of the unknown heat fluxes from the transient temperature histories taken with several sensors sensors inside a two-dimensional sheet. The temperatures are known at three lines in the finite body. The estimation algorithm of this inverse heat conduction problem is based on the iterative regularization method and on the conjugate gradient method. The alternative direction implicit method is used to solve the direct, the adjoin and the variation problems. For each boundary condition, a descent parameter is computed. An optimal choice of the vector of the descent parameters is used in this study and shows an increase in the convergence rate. All numerical simulations are performed for two-dimensional linear heat conduction problem. The temperatures are given with measurement errors and the iterative process is stopped in accordance with the residua criterion. Numerical results are presented in this study. The temperature and heat fluxes graphs are smoothed. The accuracy and efficiency of the inverse analysis for simultaneously estimating the heat fluxes and the temperature is examined by several cases. Finally, the effects of sensor position and the magnitude of measurement error on the inverse solutions are discussed. Numerical results for some representative cases prove that heat fluxes and temperature can be predicted well by this method. In this paper, simulation results are presented and numerical performance of the method will be discussed.